Layout Aware Monte Carlo with GDSFactory

Towards layout-aware optimization and monte-carlo simulations

import os

os.environ["LOGURU_LEVEL"] = "CRITICAL"
import json
from functools import partial
from pathlib import Path

import gdsfactory as gf  # conda install gdsfactory
import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
import meow as mw
import numpy as np
import optax
import sax
from gdsfactory.gpdk import PDK
from numpy.fft import fft2, fftfreq, fftshift, ifft2
from tqdm.notebook import tqdm, trange

PDK.activate()

Simple MZI Layout

@gf.cell
def simple_mzi():
    c = gf.Component()

    # components
    mmi_in = gf.components.mmi1x2()
    mmi_out = gf.components.mmi2x2()
    bend = gf.components.bend_euler()
    half_delay_straight = gf.components.straight(length=10.0)

    # references
    mmi_in = c.add_ref(mmi_in, name="mmi_in")
    mmi_out = c.add_ref(mmi_out, name="mmi_out")
    straight_top1 = c.add_ref(half_delay_straight, name="straight_top1")
    straight_top2 = c.add_ref(half_delay_straight, name="straight_top2")
    bend_top1 = c.add_ref(bend, name="bend_top1")
    bend_top2 = c.add_ref(bend, name="bend_top2").dmirror()
    bend_top3 = c.add_ref(bend, name="bend_top3").dmirror()
    bend_top4 = c.add_ref(bend, name="bend_top4")
    bend_btm1 = c.add_ref(bend, name="bend_btm1").dmirror()
    bend_btm2 = c.add_ref(bend, name="bend_btm2")
    bend_btm3 = c.add_ref(bend, name="bend_btm3")
    bend_btm4 = c.add_ref(bend, name="bend_btm4").dmirror()

    # connections
    bend_top1.connect("o1", mmi_in.ports["o2"])
    straight_top1.connect("o1", bend_top1.ports["o2"])
    bend_top2.connect("o1", straight_top1.ports["o2"])
    bend_top3.connect("o1", bend_top2.ports["o2"])
    straight_top2.connect("o1", bend_top3.ports["o2"])
    bend_top4.connect("o1", straight_top2.ports["o2"])

    bend_btm1.connect("o1", mmi_in.ports["o3"])
    bend_btm2.connect("o1", bend_btm1.ports["o2"])
    bend_btm3.connect("o1", bend_btm2.ports["o2"])
    bend_btm4.connect("o1", bend_btm3.ports["o2"])

    mmi_out.connect("o1", bend_btm4.ports["o2"])

    # ports
    c.add_port(
        "o1",
        port=mmi_in.ports["o1"],
    )
    c.add_port("o2", port=mmi_out.ports["o3"])
    c.add_port("o3", port=mmi_out.ports["o4"])
    return c

mzi = simple_mzi()
mzi

Simulate MZI

We used the following components to construct the MZI circuit:

• mmi1x2
• mmi2x2
• straight
• bend_euler

We need a model for each of those components to be able to simulate the circuit with SAX. Let's create some dummy models for now.

def mmi1x2():
    S = {
        ("o1", "o2"): 0.5**0.5,
        ("o1", "o3"): 0.5**0.5,
    }
    return sax.reciprocal(S)

def mmi2x2():
    S = {
        ("o1", "o3"): 0.5**0.5,
        ("o1", "o4"): 1j * 0.5**0.5,
        ("o2", "o3"): 1j * 0.5**0.5,
        ("o2", "o4"): 0.5**0.5,
    }
    return sax.reciprocal(S)

def straight(length=10.0, width=0.5):
    S = {("o1", "o2"): 1.0}  # we'll improve this model later!
    return sax.reciprocal(S)

def bend_euler(length=10.0, width=0.5, dy=10.0, radius_min=7, radius=10):
    return straight(length=length, width=width)  # stub with straight for now

Let's create a SAX circuit with our very simple placeholder models:

models = {
    "mmi1x2": mmi1x2,
    "mmi2x2": mmi2x2,
    "straight": straight,
    "bend_euler": bend_euler,
}
mzi1, _ = sax.circuit(mzi.get_netlist(recursive=True), models=models)
?mzi1

inst_name: bend_btm1
inst_name: bend_btm2
inst_name: bend_btm3
inst_name: bend_btm4
inst_name: bend_top1
inst_name: bend_top2
inst_name: bend_top3
inst_name: bend_top4
inst_name: mmi_in
inst_name: mmi_out
inst_name: straight
inst_name: straight2

the resulting circuit is just a model function on its own! Hence, calling it will give the result:

mzi1()

{('o1', 'o1'): Array(0.+0.j, dtype=complex128),
 ('o1', 'o2'): Array(0.5+0.5j, dtype=complex128),
 ('o1', 'o3'): Array(0.5+0.5j, dtype=complex128),
 ('o2', 'o1'): Array(0.5+0.5j, dtype=complex128),
 ('o2', 'o2'): Array(0.+0.j, dtype=complex128),
 ('o2', 'o3'): Array(0.+0.j, dtype=complex128),
 ('o3', 'o1'): Array(0.5+0.5j, dtype=complex128),
 ('o3', 'o2'): Array(0.+0.j, dtype=complex128),
 ('o3', 'o3'): Array(0.+0.j, dtype=complex128)}

Waveguide Model

Our waveguide model is not very good (it just has 100% transmission and no phase). Let's do something about the phase calculation. To do this, we need to find the effective index of the waveguide in relation to its parameters. We can use meow to obtain the waveguide effective index. Let's first create a find_waveguide_modes:

def find_waveguide_modes(
    wl: float = 1.55,
    n_box: float = 1.4,
    n_clad: float = 1.4,
    n_core: float = 3.4,
    t_slab: float = 0.1,
    t_soi: float = 0.22,
    w_core: float = 0.45,
    du=0.02,
    n_modes: int = 10,
    cache_path: str | Path = "modes",
    *,
    replace_cached: bool = False,
):
    length = 10.0
    delta = 10 * du
    env = mw.Environment(wl=wl)
    cache_path = Path(cache_path).resolve()
    cache_path.mkdir(exist_ok=True)
    fn = f"{wl=:.2f}-{n_box=:.2f}-{n_clad=:.2f}-{n_core=:.2f}-{t_slab=:.3f}-{t_soi=:.3f}-{w_core=:.3f}-{du=:.3f}-{n_modes=}.json"
    path = cache_path / fn
    if not replace_cached and path.exists():
        return [mw.Mode.model_validate(mode) for mode in json.loads(path.read_text())]

    # fmt: off
    m_core = mw.SampledMaterial(name="slab", n=np.asarray([n_core, n_core]), params={"wl": np.asarray([1.0, 2.0])}, meta={"color": (0.9, 0, 0, 0.9)})
    m_clad = mw.SampledMaterial(name="clad", n=np.asarray([n_clad, n_clad]), params={"wl": np.asarray([1.0, 2.0])})
    m_box = mw.SampledMaterial(name="box", n=np.asarray([n_box, n_box]), params={"wl": np.asarray([1.0, 2.0])})
    box = mw.Structure(material=m_box, geometry=mw.Box(x_min=- 2 * w_core - delta, x_max= 2 * w_core + delta, y_min=- 2 * t_soi - delta, y_max=0.0, z_min=0.0, z_max=length))
    slab = mw.Structure(material=m_core, geometry=mw.Box(x_min=-2 * w_core - delta, x_max=2 * w_core + delta, y_min=0.0, y_max=t_slab, z_min=0.0, z_max=length))
    clad = mw.Structure(material=m_clad, geometry=mw.Box(x_min=-2 * w_core - delta, x_max=2 * w_core + delta, y_min=0, y_max=3 * t_soi + delta, z_min=0.0, z_max=length))
    core = mw.Structure(material=m_core, geometry=mw.Box(x_min=-w_core / 2, x_max=w_core / 2, y_min=0.0, y_max=t_soi, z_min=0.0, z_max=length))

    cell = mw.Cell(structures=[box, clad, slab, core], mesh=mw.Mesh2D( x=np.arange(-2*w_core, 2*w_core, du), y=np.arange(-2*t_soi, 3*t_soi, du) ), z_min=0.0, z_max=10.0)
    cross_section = mw.CrossSection.from_cell(cell=cell, env=env)
    modes = mw.compute_modes(cross_section, num_modes=n_modes)
    # fmt: on

    path.write_text(json.dumps([json.loads(mode.model_dump_json()) for mode in modes]))

    return modes

We can also create a rudimentary model for the silicon refractive index:

def silicon_index(wl):
    """A rudimentary silicon refractive index model"""
    a, b = 0.2411478522088102, 3.3229394315868976
    return a / wl + b

We can now easily calculate the modes of a strip waveguide:

modes = find_waveguide_modes(wl=1.5, n_core=silicon_index(wl=1.5))

/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))

The fundamental mode is the mode with index 0:

mw.visualize(modes[0])

wavelengths, widths = np.mgrid[1.5:1.6:10j, 0.4:0.6:5j]
neffs = np.zeros_like(wavelengths)
neffs_ = neffs.ravel()

for i, (wl, w) in enumerate(
    zip(tqdm(wavelengths.ravel()), widths.ravel(), strict=False)
):
    modes = find_waveguide_modes(
        wl=wl, n_core=silicon_index(wl), w_core=w, replace_cached=False
    )
    neffs_[i] = np.real(modes[0].neff)

  0%|          | 0/50 [00:00<?, ?it/s]


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))


/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:14: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:27: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dxb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Nx, Nx)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:42: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
/home/runner/work/sax/sax/.venv/lib/python3.12/site-packages/tidy3d/components/mode/derivatives.py:55: FutureWarning: Input has data type int64, but the output has been cast to float64.  In the future, the output data type will match the input. To avoid this warning, set the `dtype` parameter to `None` to have the output dtype match the input, or set it to the desired output data type.
  dyb = sp.csr_matrix(sp.diags([1, -1], [0, -1], shape=(Ny, Ny)))

This results in the following effective indices:

_wls = np.unique(wavelengths.ravel())
_widths = np.unique(widths.ravel())
plt.figure(figsize=(8, 3))
plt.plot(_wls * 1000, neffs)
plt.ylabel("neff")
plt.xlabel("λ [nm]")
plt.title("Effective Index")
plt.grid(True)
plt.figlegend(
    [f"{w=:.2f}um" for w in _widths], ncol=len(widths), bbox_to_anchor=(0.95, -0.05)
)
plt.show()

We can do a grid interpolation on those effective indices:

_grid = [jnp.sort(jnp.unique(wavelengths)), jnp.sort(jnp.unique(widths))]
_data = jnp.asarray(neffs)


@jax.jit
def _get_coordinate(arr1d: jnp.ndarray, value: jnp.ndarray):
    return jnp.interp(value, arr1d, jnp.arange(arr1d.shape[0]))


@jax.jit
def _get_coordinates(arrs1d: list[jnp.ndarray], values: jnp.ndarray):
    # don't use vmap as arrays in arrs1d could have different shapes...
    return jnp.array(
        [_get_coordinate(a, v) for a, v in zip(arrs1d, values, strict=False)]
    )


@jax.jit
def neff(wl=1.55, width=0.5):
    params = jnp.stack(jnp.broadcast_arrays(jnp.asarray(wl), jnp.asarray(width)), 0)
    coords = _get_coordinates(_grid, params)
    return jax.scipy.ndimage.map_coordinates(_data, coords, 1, mode="nearest")


neff(wl=[1.52, 1.58], width=[0.5, 0.55])

Array([2.61246994, 2.59526173], dtype=float64)

wavelengths_ = np.linspace(wavelengths.min(), wavelengths.max(), 100)
widths_ = np.linspace(widths.min(), widths.max(), 100)
wavelengths_, widths_ = np.meshgrid(wavelengths_, widths_)
neffs_ = neff(wavelengths_, widths_)

plt.figure(figsize=(8, 3))
plt.pcolormesh(wavelengths_ * 1000, widths_, neffs_)
plt.ylabel("neff")
plt.xlabel("λ [nm]")
plt.title("Effective Index")
plt.grid(True)
plt.figlegend(
    [f"{w=:.2f}um" for w in _widths], ncol=len(_widths), bbox_to_anchor=(0.95, -0.05)
)
plt.show()

def straight(wl=1.55, length=10.0, width=0.5):
    S = {
        ("o1", "o2"): jnp.exp(2j * np.pi * neff(wl=wl, width=width) / wl * length),
    }
    return sax.reciprocal(S)

Even though this still is lossless transmission, we're at least modeling the phase correctly.

straight()

{('o1', 'o2'): Array(-0.38310141-0.92370629j, dtype=complex128),
 ('o2', 'o1'): Array(-0.38310141-0.92370629j, dtype=complex128)}

Simulate MZI again

models["straight"] = straight
mzi2, _ = sax.circuit(mzi.get_netlist(recursive=True), models=models)
mzi2()

inst_name: bend_btm1
inst_name: bend_btm2
inst_name: bend_btm3
inst_name: bend_btm4
inst_name: bend_top1
inst_name: bend_top2
inst_name: bend_top3
inst_name: bend_top4
inst_name: mmi_in
inst_name: mmi_out
inst_name: straight
inst_name: straight2





{('o1', 'o1'): Array(0.+0.j, dtype=complex128),
 ('o1', 'o2'): Array(0.25085186-0.28844437j, dtype=complex128),
 ('o1', 'o3'): Array(-0.60638585+0.69725847j, dtype=complex128),
 ('o2', 'o1'): Array(0.25085186-0.28844437j, dtype=complex128),
 ('o2', 'o2'): Array(0.+0.j, dtype=complex128),
 ('o2', 'o3'): Array(0.+0.j, dtype=complex128),
 ('o3', 'o1'): Array(-0.60638585+0.69725847j, dtype=complex128),
 ('o3', 'o2'): Array(0.+0.j, dtype=complex128),
 ('o3', 'o3'): Array(0.+0.j, dtype=complex128)}

wl = jnp.linspace(1.51, 1.59, 1000)
S = mzi2(wl=wl)
plt.plot(wl, abs(S["o1", "o2"]) ** 2)
plt.ylim(-0.05, 1.05)
plt.xlabel("λ [μm]")
plt.ylabel("T")
plt.ylim(-0.05, 1.05)
plt.grid(True)
plt.show()

Optimize MZI

We'd like to optimize an MZI such that one of the minima is at 1550nm. To do this, we need to define a loss function for the circuit at 1550nm. This function should take the parameters that you want to optimize as positional arguments:

@jax.jit
def loss_fn(delta_length):
    S = mzi2(
        wl=1.55,
        straight_top1={"length": delta_length / 2},
        straight_top2={"length": delta_length / 2},
    )
    return jnp.mean(jnp.abs(S["o1", "o2"]) ** 2)

We can use this loss function to define a grad function which works on the parameters of the loss function:

grad_fn = jax.jit(
    jax.grad(
        loss_fn,
        argnums=0,  # JAX gradient function for the first positional argument, jitted
    )
)

Next, we need to define a JAX optimizer. We'll use optax, a gradient processing and optimization library for JAX.

loss_fn(20.0)

Array(0.14612682, dtype=float64)

initial_delta_length = 10.0
optimizer = optax.adam(learning_rate=0.1)
params = {"delta_length": jnp.array(initial_delta_length)}
opt_state = optimizer.init(params)

Given all this, a single training step can be defined:

@jax.jit
def step_fn(params, opt_state):
    loss, grads = jax.value_and_grad(lambda p: loss_fn(p["delta_length"]))(params)
    updates, opt_state = optimizer.update(grads, opt_state, params)
    params = optax.apply_updates(params, updates)
    return loss, params, opt_state

And we can use this step function to start the training of the MZI:

for step in (
    pb := trange(300)
):  # the first two iterations take a while because the circuit is being jitted...
    loss, params, opt_state = step_fn(params, opt_state)
    pb.set_postfix(loss=f"{loss:.6f}")

  0%|          | 0/300 [00:00<?, ?it/s]

delta_length = params["delta_length"]
delta_length

Array(10., dtype=float64)

Let's see what we've got over a range of wavelengths:

S = mzi2(
    wl=wl,
    straight_top1={"length": delta_length / 2},
    straight_top2={"length": delta_length / 2},
)
plt.plot(wl * 1e3, abs(S["o1", "o2"]) ** 2)
plt.xlabel("λ [nm]")
plt.ylabel("T")
plt.plot([1550, 1550], [-1, 2], ls=":", color="black")
plt.ylim(-0.05, 1.05)
plt.grid(True)
plt.show()

Note that we could've just as well optimized the waveguide width:

@jax.jit
def loss_fn(width):
    S = mzi2(
        wl=1.55,
        straight_top1={"width": width},
        straight_top2={"width": width},
    )
    return jnp.mean(jnp.abs(S["o1", "o2"]) ** 2)


grad_fn = jax.jit(
    jax.grad(
        loss_fn,
        argnums=0,  # JAX gradient function for the first positional argument, jitted
    )
)

initial_width = 0.5
optimizer = optax.adam(learning_rate=0.01)
params = {"width": jnp.array(initial_width)}
opt_state = optimizer.init(params)


@jax.jit
def step_fn(params, opt_state):
    loss, grads = jax.value_and_grad(lambda p: loss_fn(p["width"]))(params)
    updates, opt_state = optimizer.update(grads, opt_state, params)
    params = optax.apply_updates(params, updates)
    return loss, params, opt_state


for step in (
    pb := trange(300)
):  # the first two iterations take a while because the circuit is being jitted...
    loss, params, opt_state = step_fn(params, opt_state)
    pb.set_postfix(loss=f"{loss:.6f}")

optim_width = params["width"]
S = Sw = mzi2(
    wl=wl,
    straight_top1={"width": optim_width},
    straight_top2={"width": optim_width},
)
plt.plot(wl * 1e3, abs(S["o1", "o2"]) ** 2)
plt.xlabel("λ [nm]")
plt.ylabel("T")
plt.plot([1550, 1550], [-1, 2], color="black", ls=":")
plt.ylim(-0.05, 1.05)
plt.grid(True)
plt.show()

  0%|          | 0/300 [00:00<?, ?it/s]

Layout-aware Monte Carlo

Let's assume the waveguide width changes with a certain correlation length. We can create a 'wafermap' of width variations by randomly varying the width and low pass filtering with a spatial frequency being the inverse of the correlation length (there are probably better ways to do this, but this works for this tutorial).

def create_wafermaps(
    placements, correlation_length=1.0, num_maps=1, mean=0.0, std=1.0, seed=None
):
    dx = dy = correlation_length / 200
    xs = [p["x"] for p in placements.values()]
    ys = [p["y"] for p in placements.values()]
    xmin, xmax, ymin, ymax = min(xs), max(xs), min(ys), max(ys)
    wx, wy = xmax - xmin, ymax - ymin
    xmin, xmax, ymin, ymax = xmin - wx, xmax + wx, ymin - wy, ymax + wy
    x, y = np.arange(xmin, xmax + dx, dx), np.arange(ymin, ymax + dy, dy)
    r = np.random if seed is None else np.random.RandomState(seed=seed)
    W0 = r.randn(num_maps, x.shape[0], y.shape[0])

    fx = fftshift(fftfreq(x.shape[0], d=x[1] - x[0]))
    fy = fftshift(fftfreq(y.shape[0], d=y[1] - y[0]))
    fY, fX = np.meshgrid(fy, fx)

    fW = fftshift(fft2(W0))

    if correlation_length >= min(x.shape[0], y.shape[0]):
        fW = np.zeros_like(fW)
    else:
        fW = np.where(np.sqrt(fX**2 + fY**2)[None] > 1 / correlation_length, 0, fW)

    W = np.abs(fftshift(ifft2(fW))) ** 2

    mean_ = W.mean(1, keepdims=True).mean(2, keepdims=True)

    std_ = W.std(1, keepdims=True).std(2, keepdims=True)
    if (std_ == 0).all():
        std_ = 1

    W = (W - mean_) / std_

    W = W * std + mean

    return x, y, W

placements = mzi.get_netlist()["placements"]
xm, ym, wmaps = create_wafermaps(
    placements,
    correlation_length=100,
    mean=0.5,
    std=0.002,
    num_maps=100,
    seed=42,
)

for i, wmap in enumerate(wmaps):
    if i > 1:
        break
    plt.imshow(wmap, cmap="RdBu")
    plt.show()

inst_name: bend_btm1
inst_name: bend_btm2
inst_name: bend_btm3
inst_name: bend_btm4
inst_name: bend_top1
inst_name: bend_top2
inst_name: bend_top3
inst_name: bend_top4
inst_name: mmi_in
inst_name: mmi_out
inst_name: straight
inst_name: straight2

def widths(xw, yw, wmaps, x, y):
    _wmap_grid = [xw, yw]
    params = jnp.stack(jnp.broadcast_arrays(jnp.asarray(x), jnp.asarray(y)), 0)
    coords = _get_coordinates(_wmap_grid, params)

    map_coordinates = partial(
        jax.scipy.ndimage.map_coordinates, coordinates=coords, order=1, mode="nearest"
    )
    w = jax.vmap(map_coordinates)(wmaps)
    return w

Let's now sample the MZI width variation on the wafer map (let's assume a single width variation per point):

mzi_params = sax.get_settings(mzi2)
placements = mzi.get_netlist()["placements"]
width_params = {
    k: {"width": widths(xm, ym, wmaps, v["x"], v["y"])}
    for k, v in placements.items()
    if "width" in mzi_params[k]
}

S0 = mzi2(wl=wl)
S = mzi2(
    wl=wl[:, None],
    **width_params,
)
ps = plt.plot(wl * 1e3, abs(S["o1", "o2"]) ** 2, color="C0", lw=1, alpha=0.1)
nps = plt.plot(wl * 1e3, abs(S0["o1", "o2"]) ** 2, color="C1", lw=2, alpha=1)
plt.xlabel("λ [nm]")
plt.ylabel("T")
plt.plot([1550, 1550], [-1, 2], color="black", ls=":")
plt.ylim(-0.05, 1.05)
plt.grid(True)
plt.figlegend([*ps[-1:], *nps], ["MC", "nominal"], bbox_to_anchor=(1.1, 0.9))
rmse = jnp.mean(
    jnp.abs(jnp.abs(S["o1", "o2"]) ** 2 - jnp.abs(S0["o1", "o2"][:, None]) ** 2) ** 2
)
plt.title(f"{rmse=}")
plt.show()

inst_name: bend_btm1
inst_name: bend_btm2
inst_name: bend_btm3
inst_name: bend_btm4
inst_name: bend_top1
inst_name: bend_top2
inst_name: bend_top3
inst_name: bend_top4
inst_name: mmi_in
inst_name: mmi_out
inst_name: straight
inst_name: straight2

Compact MZI

Let's see if we can improve variability (i.e. the RMSE w.r.t. nominal) by making the MZI more compact:

@gf.cell
def compact_mzi():
    c = gf.Component()

    # instances
    mmi_in = gf.components.mmi1x2()
    mmi_out = gf.components.mmi2x2()
    bend = gf.components.bend_euler()
    half_delay_straight = gf.components.straight()
    middle_straight = gf.components.straight(length=6.0)
    half_middle_straight = gf.components.straight(3.0)

    # references (sax convention: vars ending in underscore are references)
    mmi_in = c.add_ref(mmi_in, name="mmi_in")

    bend_top1 = c.add_ref(bend, name="bend_top1")
    straight_top1 = c.add_ref(half_delay_straight, name="straight_top1")
    bend_top2 = c.add_ref(bend, name="bend_top2").dmirror()
    straight_top2 = c.add_ref(middle_straight, name="straight_top2")
    bend_top3 = c.add_ref(bend, name="bend_top3").dmirror()
    straight_top3 = c.add_ref(half_delay_straight, name="straight_top3")
    bend_top4 = c.add_ref(bend, name="bend_top4")

    straight_btm1 = c.add_ref(half_middle_straight, name="straight_btm1")
    bend_btm1 = c.add_ref(bend, name="bend_btm1")
    bend_btm2 = c.add_ref(bend, name="bend_btm2").dmirror()
    bend_btm3 = c.add_ref(bend, name="bend_btm3").dmirror()
    bend_btm4 = c.add_ref(bend, name="bend_btm4")
    straight_btm2 = c.add_ref(half_middle_straight, name="straight_btm2")

    mmi_out = c.add_ref(mmi_out, name="mmi_out")

    # connections
    bend_top1.connect("o1", mmi_in.ports["o2"])
    straight_top1.connect("o1", bend_top1.ports["o2"])
    bend_top2.connect("o1", straight_top1.ports["o2"])
    straight_top2.connect("o1", bend_top2.ports["o2"])
    bend_top3.connect("o1", straight_top2.ports["o2"])
    straight_top3.connect("o1", bend_top3.ports["o2"])
    bend_top4.connect("o1", straight_top3.ports["o2"])

    straight_btm1.connect("o1", mmi_in.ports["o3"])
    bend_btm1.connect("o1", straight_btm1.ports["o2"])
    bend_btm2.connect("o1", bend_btm1.ports["o2"])
    bend_btm3.connect("o1", bend_btm2.ports["o2"])
    bend_btm4.connect("o1", bend_btm3.ports["o2"])
    straight_btm2.connect("o1", bend_btm4.ports["o2"])

    mmi_out.connect("o1", straight_btm2.ports["o2"])

    # ports
    c.add_port(
        "o1",
        port=mmi_in.ports["o1"],
    )
    c.add_port("o2", port=mmi_out.ports["o3"])
    c.add_port("o3", port=mmi_out.ports["o4"])
    return c

compact_mzi1 = compact_mzi()
compact_mzi1

placements = compact_mzi1.get_netlist()["placements"]
mzi3, _ = sax.circuit(compact_mzi1.get_netlist(recursive=True), models=models)
mzi3()

inst_name: bend_btm1
inst_name: bend_btm2
inst_name: bend_btm3
inst_name: bend_btm4
inst_name: bend_top1
inst_name: bend_top2
inst_name: bend_top3
inst_name: bend_top4
inst_name: mmi_in
inst_name: mmi_out
inst_name: straight
inst_name: straight2
inst_name: straight3
inst_name: straight4
inst_name: straight5
inst_name: bend_btm1
inst_name: bend_btm2
inst_name: bend_btm3
inst_name: bend_btm4
inst_name: bend_top1
inst_name: bend_top2
inst_name: bend_top3
inst_name: bend_top4
inst_name: mmi_in
inst_name: mmi_out
inst_name: straight
inst_name: straight2
inst_name: straight3
inst_name: straight4
inst_name: straight5





{('o1', 'o1'): Array(0.+0.j, dtype=complex128),
 ('o1', 'o2'): Array(0.27263693-0.26794761j, dtype=complex128),
 ('o1', 'o3'): Array(-0.65904702+0.64771151j, dtype=complex128),
 ('o2', 'o1'): Array(0.27263693-0.26794761j, dtype=complex128),
 ('o2', 'o2'): Array(0.+0.j, dtype=complex128),
 ('o2', 'o3'): Array(0.+0.j, dtype=complex128),
 ('o3', 'o1'): Array(-0.65904702+0.64771151j, dtype=complex128),
 ('o3', 'o2'): Array(0.+0.j, dtype=complex128),
 ('o3', 'o3'): Array(0.+0.j, dtype=complex128)}

mzi_params = sax.get_settings(mzi3)
placements = compact_mzi1.get_netlist()["placements"]
width_params = {
    k: {"width": widths(xm, ym, wmaps, v["x"], v["y"])}
    for k, v in placements.items()
    if "width" in mzi_params[k]
}

S0 = mzi3(wl=wl)
S = mzi3(
    wl=wl[:, None],
    **width_params,
)
ps = plt.plot(wl * 1e3, abs(S["o1", "o2"]) ** 2, color="C0", lw=1, alpha=0.1)
nps = plt.plot(wl * 1e3, abs(S0["o1", "o2"]) ** 2, color="C1", lw=2, alpha=1)
plt.xlabel("λ [nm]")
plt.ylabel("T")
plt.plot([1550, 1550], [-1, 2], color="black", ls=":")
plt.ylim(-0.05, 1.05)
plt.grid(True)
plt.figlegend([*ps[-1:], *nps], ["MC", "nominal"], bbox_to_anchor=(1.1, 0.9))
rmse = jnp.mean(
    jnp.abs(jnp.abs(S["o1", "o2"]) ** 2 - jnp.abs(S0["o1", "o2"][:, None]) ** 2) ** 2
)
plt.title(f"{rmse=}")
plt.show()

inst_name: bend_btm1
inst_name: bend_btm2
inst_name: bend_btm3
inst_name: bend_btm4
inst_name: bend_top1
inst_name: bend_top2
inst_name: bend_top3
inst_name: bend_top4
inst_name: mmi_in
inst_name: mmi_out
inst_name: straight
inst_name: straight2
inst_name: straight3
inst_name: straight4
inst_name: straight5