Lithium niobate phase-shifter

Contents

Lithium niobate phase-shifter#

Reproducing [1]

Hide code cell source 
from collections import OrderedDict

import matplotlib.pyplot as plt
import numpy as np
from shapely.geometry import box
from skfem import Basis, ElementDG, ElementTriP0, ElementTriP1
from skfem.io import from_meshio
from tqdm import tqdm

from femwell.coulomb import solve_coulomb
from femwell.maxwell.waveguide import compute_modes
from femwell.mesh import mesh_from_OrderedDict

core_width = 1.532
electrode_start_x = core_width / 2 + 2.629
electrode_width = 4.4

electrode_left = box(-electrode_start_x - electrode_width, 0.5, -electrode_start_x, 0.5 + 1.8)
electrode_right = box(electrode_start_x, 0.5, electrode_start_x + electrode_width, 0.5 + 1.8)
slab = box(-10, 0, 10, 0.5)
core = box(-core_width / 2, 0.5, core_width / 2, 0.8)
env = slab.buffer(20, resolution=8)

polygons = OrderedDict(
    electrode_left=electrode_left,
    electrode_right=electrode_right,
    slab=slab,
    core=core,
    env=env,
)

resolutions = dict(
    slab={"resolution": 0.1, "distance": 4},
    core={"resolution": 0.1, "distance": 4},
)

mesh = from_meshio(
    mesh_from_OrderedDict(polygons, resolutions, filename="mesh.msh", default_resolution_max=3)
)

basis = Basis(mesh, ElementTriP1(), intorder=4)
basis_epsilon_r = basis.with_element(ElementTriP0())

epsilon_dc = basis_epsilon_r.zeros() + 3.9
epsilon_dc[basis_epsilon_r.get_dofs(elements="slab")] = 28.4
epsilon_dc[basis_epsilon_r.get_dofs(elements="core")] = 7.5
# basis.plot(epsilon).show()

basis_u, u = solve_coulomb(
    basis_epsilon_r,
    epsilon_dc,
    {"electrode_left___slab": 1, "electrode_right___slab": 0},
)

fig, ax = plt.subplots()
for subdomain in basis_epsilon_r.mesh.subdomains.keys() - {"gmsh:bounding_entities"}:
    basis_epsilon_r.mesh.restrict(subdomain).draw(ax=ax, boundaries_only=True)
basis_u.plot(u, ax=ax, shading="gouraud", colorbar=True)
# basis_vec.plot(-u_grad, ax=ax)
plt.show()

fig, ax = plt.subplots()
for subdomain in basis_epsilon_r.mesh.subdomains.keys() - {"gmsh:bounding_entities"}:
    basis_epsilon_r.mesh.restrict(subdomain).draw(ax=ax, boundaries_only=True)
basis_grad = basis_u.with_element(ElementDG(basis_u.elem))
e_x = basis_u.project(-basis_epsilon_r.interpolate(epsilon_dc) * basis_u.interpolate(u).grad[0])
basis_u.plot(e_x, ax=ax, shading="gouraud", colorbar=True)
plt.show()

voltages = np.linspace(0, 100, 5)
voltages_neffs = []

for voltage in tqdm(voltages):
    refractive_index_optical = basis_epsilon_r.zeros() + 1.445
    refractive_index_optical[basis_epsilon_r.get_dofs(elements="core")] = 1.989
    refractive_index_optical[basis_epsilon_r.get_dofs(elements="slab")] = (
        2.211
        + 0.5
        * 2.211**3
        * 31e-6
        * basis_epsilon_r.project(-basis_u.interpolate(u).grad[0])[
            basis_epsilon_r.get_dofs(elements="slab")
        ]
        * voltage
    )
    # basis_epsilon_r.plot(refractive_index, colorbar=True).show()

    modes = compute_modes(basis_epsilon_r, refractive_index_optical**2, wavelength=1.55)
    voltages_neffs.append(modes[0].n_eff)

    # from mode_solver import plot_mode
    # plot_mode(basis_modes, modes[0])
    # plt.show()

plt.plot(voltages, np.real(voltages_neffs))
plt.xlabel("Voltage / V")
plt.ylabel("Effective refractive index")
plt.show()
../../_images/2af6833e11f7df78b412de2d6038c115ccc4f305d7d6dd95592def85467f04d7.png ../../_images/820415d00aa2fc8e9f6af01d2dcafc4c85ed8b05f2bc504cf18f9bb40409bd5a.png ../../_images/5cf7af4fde1de287402f7d7cf8309f4273709926fa96a2898f17293a4c9365ef.png

Bibliography#

[1]

Huangpu Han, Fan Yang, Chenghao Liu, Zhengfang Wang, Yunpeng Jiang, Guangyue Chai, Shuangchen Ruan, and Bingxi Xiang. High-performance electro-optical mach–zehnder modulators in a silicon nitride–lithium niobate thin-film hybrid platform. Photonics, 9(7):500, July 2022. URL: https://doi.org/10.3390/photonics9070500, doi:10.3390/photonics9070500.

Contents