{
"cells": [
{
"cell_type": "markdown",
"id": "d4962fd2",
"metadata": {},
"source": [
"# Waveguide crossing based on cosine tapers"
]
},
{
"cell_type": "markdown",
"id": "5e5b9158",
"metadata": {},
"source": [
"To achieve a high integration density on a photonic chip, efficient routing of light with low loss using compact junctions is necessary. Therefore, waveguide crossings are crucial building blocks in high performance integrated circuits. \n",
"\n",
"This example model demonstrates the simulation of a waveguide crossing based on cosine tapers. The convex cosine taper focuses the guided mode at the center of the crossing junction. This ensures the light is efficiently transmitted into the through port instead of scattered into the cross ports. The device achieves an insertion loss of ~0.2 dB and crosstalk ~-30 dB in the O-band (1260 nm -1360 nm). The design is adapted from [Sujith Chandran, et al. \"Beam shaping for ultra-compact waveguide crossings on monolithic silicon photonics platform,\" Opt. Lett. 45, 6230-6233 (2020)](https://opg.optica.org/ol/abstract.cfm?uri=ol-45-22-6230).\n",
"\n",
""
]
},
{
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"execution_count": 1,
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"outputs": [
{
"data": {
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"
[21:42:50] WARNING This version of Tidy3D was pip installed from the 'tidy3d-beta' repository on __init__.py:103\n",
" PyPI. Future releases will be uploaded to the 'tidy3d' repository. From now on, \n",
" please use 'pip install tidy3d' instead. \n",
"
\n"
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"\u001b[2;36m[21:42:50]\u001b[0m\u001b[2;36m \u001b[0m\u001b[31mWARNING \u001b[0m This version of Tidy3D was pip installed from the \u001b[32m'tidy3d-beta'\u001b[0m repository on \u001b]8;id=300549;file:///Users/twhughes/Documents/Flexcompute/tidy3d-docs/tidy3d/tidy3d/__init__.py\u001b\\\u001b[2m__init__.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=116576;file:///Users/twhughes/Documents/Flexcompute/tidy3d-docs/tidy3d/tidy3d/__init__.py#103\u001b\\\u001b[2m103\u001b[0m\u001b]8;;\u001b\\\n",
"\u001b[2;36m \u001b[0m PyPI. Future releases will be uploaded to the \u001b[32m'tidy3d'\u001b[0m repository. From now on, \u001b[2m \u001b[0m\n",
"\u001b[2;36m \u001b[0m please use \u001b[32m'pip install tidy3d'\u001b[0m instead. \u001b[2m \u001b[0m\n"
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INFO Using client version: 1.9.0rc1 __init__.py:121\n",
"
\n"
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"\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Using client version: \u001b[1;36m1.9\u001b[0m.0rc1 \u001b]8;id=755083;file:///Users/twhughes/Documents/Flexcompute/tidy3d-docs/tidy3d/tidy3d/__init__.py\u001b\\\u001b[2m__init__.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=554769;file:///Users/twhughes/Documents/Flexcompute/tidy3d-docs/tidy3d/tidy3d/__init__.py#121\u001b\\\u001b[2m121\u001b[0m\u001b]8;;\u001b\\\n"
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"metadata": {},
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}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import tidy3d as td\n",
"import tidy3d.web as web\n",
"from scipy.optimize import fsolve\n"
]
},
{
"cell_type": "markdown",
"id": "290a838f",
"metadata": {},
"source": [
"## Simulation Setup"
]
},
{
"cell_type": "markdown",
"id": "85200028",
"metadata": {},
"source": [
"Define geometric parameters and materials. In this device, the Si waveguide has a thickness of 161 nm and a width of 350 nm. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "2f5c50ea",
"metadata": {
"execution": {
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"outputs": [],
"source": [
"h = 0.161 # waveguide thickness\n",
"w_in = 0.35 # input taper width\n",
"w_out = 1.1 # output taper width\n",
"w_m = 0.75 # amplitude of the cos function\n",
"l_t = 5.3 # taper length\n",
"inf_eff = (\n",
" 1000 # effective infinity used to make sure the waveguides extend into the pml\n",
")\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "4b92b8e9",
"metadata": {
"execution": {
"iopub.execute_input": "2023-02-03T03:42:51.037911Z",
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"shell.execute_reply": "2023-02-03T03:42:51.044601Z"
}
},
"outputs": [],
"source": [
"si = td.Medium(permittivity=3.67**2)\n",
"sio2 = td.Medium(permittivity=1.45**2)\n"
]
},
{
"cell_type": "markdown",
"id": "718becc3",
"metadata": {},
"source": [
"The taper width is described by a cosine function $w(x)=w_m cos(ax+b)$. To determine the parameters $a$ and $b$, we solve a system of equations to ensure $w(x)=w_{in}/2$ at the beginning of the taper and $w(x)=w_{out}/2$ at the end of the taper. This can be easily done using fsolve from Scipy.\n",
"\n",
"After we obtain $w(x)$, vertices can be generated and the taper can be made using PolySlab. Once the first taper is made, the rest three tapers can be made by manipulating the vertices with the symmetry relation."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0e2ef818",
"metadata": {
"execution": {
"iopub.execute_input": "2023-02-03T03:42:51.049232Z",
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}
},
"outputs": [],
"source": [
"# numerically solve for the cos function that describes the taper shape\n",
"def equations(x0):\n",
" a, b = x0\n",
" return (\n",
" w_m * np.cos(a * (-w_out / 2) + b) - w_out / 2,\n",
" w_m * np.cos(a * (-w_out / 2 - l_t) + b) - w_in / 2,\n",
" )\n",
"\n",
"\n",
"a, b = fsolve(equations, (0.5, 2))\n",
"\n",
"x = np.linspace(-w_out / 2 - l_t, -w_out / 2, 30)\n",
"w = w_m * np.cos(a * x + b)\n",
"\n",
"# using the calculated taper shape to construct the taper as a PolySlab\n",
"vertices = np.zeros((2 * len(x), 2))\n",
"vertices[:, 0] = np.concatenate((x, np.flipud(x)))\n",
"vertices[:, 1] = np.concatenate((w, -np.flipud(w)))\n",
"taper_1 = td.Structure(\n",
" geometry=td.PolySlab(vertices=vertices, axis=2, slab_bounds=(-h / 2, h / 2)),\n",
" medium=si,\n",
")\n",
"\n",
"# creating the other four tapers by manipulating the vertices of the first taper\n",
"vertices[:, 0] = -vertices[:, 0]\n",
"taper_2 = td.Structure(\n",
" geometry=td.PolySlab(vertices=vertices, axis=2, slab_bounds=(-h / 2, h / 2)),\n",
" medium=si,\n",
")\n",
"\n",
"vertices[:, [1, 0]] = vertices[:, [0, 1]]\n",
"taper_3 = td.Structure(\n",
" geometry=td.PolySlab(vertices=vertices, axis=2, slab_bounds=(-h / 2, h / 2)),\n",
" medium=si,\n",
")\n",
"\n",
"vertices[:, 1] = -vertices[:, 1]\n",
"taper_4 = td.Structure(\n",
" geometry=td.PolySlab(vertices=vertices, axis=2, slab_bounds=(-h / 2, h / 2)),\n",
" medium=si,\n",
")\n",
"\n",
"# creating the center crossing junction using a Box\n",
"corner = 0\n",
"center = td.Structure(\n",
" geometry=td.Box.from_bounds(\n",
" rmin=(-w_out / 2 - corner, -w_out / 2 - corner, -h / 2),\n",
" rmax=(w_out / 2 + corner, w_out / 2 + corner, h / 2),\n",
" ),\n",
" medium=si,\n",
")\n",
"\n",
"# creating the input port and through port\n",
"horizontal_wg = td.Structure(\n",
" geometry=td.Box.from_bounds(\n",
" rmin=(-inf_eff, -w_in / 2, -h / 2), rmax=(inf_eff, w_in / 2, h / 2)\n",
" ),\n",
" medium=si,\n",
")\n",
"\n",
"# creating the cross ports\n",
"vertical_wg = td.Structure(\n",
" geometry=td.Box.from_bounds(\n",
" rmin=(-w_in / 2, -inf_eff, -h / 2), rmax=(w_in / 2, inf_eff, h / 2)\n",
" ),\n",
" medium=si,\n",
")\n"
]
},
{
"cell_type": "markdown",
"id": "074d7cde",
"metadata": {},
"source": [
"Set up simulation domain, source, and monitors. A mode source is used to excite the input waveguide. A field monitor at $z=0$ plane is added to monitor the field propagation. Two flux monitors are added at the through port and cross port to monitor the transmission and crosstalk levels.\n",
"\n",
"Before running the simulation, we can use the plot method to ensure the geometry, source, and monitors are set up correctly."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "54a54758",
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"outputs": [
{
"data": {
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""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
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\n",
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