{
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"source": [
"# Multimode simulations\n",
"> SAX can handle multiple modes too!"
]
},
{
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"execution_count": null,
"id": "1",
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"source": [
"from itertools import combinations_with_replacement, product\n",
"\n",
"import jax.numpy as jnp\n",
"import sax"
]
},
{
"cell_type": "markdown",
"id": "2",
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"source": [
"## Ports and modes per port"
]
},
{
"cell_type": "markdown",
"id": "3",
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"source": [
"Let's denote a combination of a port and a mode by a string of the following format: `\"{port}@{mode}\"`. We can obtain all possible port-mode combinations with some magic itertools functions:"
]
},
{
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"source": [
"ports = [\"in0\", \"out0\"]\n",
"modes = [\"TE\", \"TM\"]\n",
"portmodes = [\n",
" (f\"{p1}@{m1}\", f\"{p2}@{m2}\")\n",
" for (p1, m1), (p2, m2) in combinations_with_replacement(product(ports, modes), 2)\n",
"]\n",
"portmodes"
]
},
{
"cell_type": "markdown",
"id": "5",
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"source": [
"If we would disregard any backreflection, this can be further simplified:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6",
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"source": [
"portmodes_without_backreflection = [\n",
" (p1, p2) for p1, p2 in portmodes if p1.split(\"@\")[0] != p2.split(\"@\")[0]\n",
"]\n",
"portmodes_without_backreflection"
]
},
{
"cell_type": "markdown",
"id": "7",
"metadata": {
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},
"source": [
"Sometimes cross-polarization terms can also be ignored:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8",
"metadata": {
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"source": [
"portmodes_without_crosspolarization = [\n",
" (p1, p2) for p1, p2 in portmodes if p1.split(\"@\")[1] == p2.split(\"@\")[1]\n",
"]\n",
"portmodes_without_crosspolarization"
]
},
{
"cell_type": "markdown",
"id": "9",
"metadata": {
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"tags": []
},
"source": [
"## Multimode waveguide"
]
},
{
"cell_type": "markdown",
"id": "10",
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"source": [
"Let's create a waveguide with two ports (`\"in\"`, `\"out\"`) and two modes (`\"te\"`, `\"tm\"`) without backreflection. Let's assume there is 5% cross-polarization and that the `\"tm\"`->`\"tm\"` transmission is 10% worse than the `\"te\"`->`\"te\"` transmission. Naturally in more realisic waveguide models these percentages will be length-dependent, but this is just a dummy model serving as an example."
]
},
{
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"execution_count": null,
"id": "11",
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"source": [
"def waveguide(wl=1.55, wl0=1.55, neff=2.34, ng=3.4, length=10.0, loss=0.0):\n",
" \"\"\"a simple straight waveguide model\n",
"\n",
" Args:\n",
" wl: wavelength\n",
" neff: waveguide effective index\n",
" ng: waveguide group index (used for linear neff dispersion)\n",
" wl0: center wavelength at which neff is defined\n",
" length: [m] wavelength length\n",
" loss: [dB/m] waveguide loss\n",
" \"\"\"\n",
" dwl = wl - wl0\n",
" dneff_dwl = (ng - neff) / wl0\n",
" neff = neff - dwl * dneff_dwl\n",
" phase = 2 * jnp.pi * neff * length / wl\n",
" transmission = 10 ** (-loss * length / 20) * jnp.exp(1j * phase)\n",
" sdict = sax.reciprocal(\n",
" {\n",
" (\"in0@TE\", \"out0@TE\"): 0.95 * transmission, # 5% lost to cross-polarization\n",
" (\"in0@TE\", \"out0@TM\"): 0.05 * transmission, # 5% cross-polarization\n",
" (\"in0@TM\", \"out0@TM\"): 0.85 * transmission, # 10% worse tm->tm than te->te\n",
" (\"in0@TM\", \"out0@TE\"): 0.05 * transmission, # 5% cross-polarization\n",
" }\n",
" )\n",
" return sdict\n",
"\n",
"\n",
"waveguide()"
]
},
{
"cell_type": "markdown",
"id": "12",
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},
"source": [
"## Multimode Coupler"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "13",
"metadata": {
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"source": [
"def coupler():\n",
" return {\n",
" (\"in0@TE\", \"out0@TE\"): 0.45**0.5,\n",
" (\"in0@TE\", \"out1@TE\"): 1j * 0.45**0.5,\n",
" (\"in1@TE\", \"out0@TE\"): 1j * 0.45**0.5,\n",
" (\"in1@TE\", \"out1@TE\"): 0.45**0.5,\n",
" (\"in0@TM\", \"out0@TM\"): 0.45**0.5,\n",
" (\"in0@TM\", \"out1@TM\"): 1j * 0.45**0.5,\n",
" (\"in1@TM\", \"out0@TM\"): 1j * 0.45**0.5,\n",
" (\"in1@TM\", \"out1@TM\"): 0.45**0.5,\n",
" (\"in0@TE\", \"out0@TM\"): 0.01**0.5,\n",
" (\"in0@TE\", \"out1@TM\"): 1j * 0.01**0.5,\n",
" (\"in1@TE\", \"out0@TM\"): 1j * 0.01**0.5,\n",
" (\"in1@TE\", \"out1@TM\"): 0.01**0.5,\n",
" (\"in0@TM\", \"out0@TE\"): 0.01**0.5,\n",
" (\"in0@TM\", \"out1@TE\"): 1j * 0.01**0.5,\n",
" (\"in1@TM\", \"out0@TE\"): 1j * 0.01**0.5,\n",
" (\"in1@TM\", \"out1@TE\"): 0.01**0.5,\n",
" }"
]
},
{
"cell_type": "markdown",
"id": "14",
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"tags": []
},
"source": [
"## Multimode MZI"
]
},
{
"cell_type": "markdown",
"id": "15",
"metadata": {
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"source": [
"We can now combine these models into a circuit in much the same way as before. We just need to add the `modes=` keyword:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "16",
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"source": [
"mzi, _ = sax.circuit(\n",
" netlist={\n",
" \"instances\": {\n",
" \"lft\": \"coupler\", # single mode models will be automatically converted to multimode models without cross polarization.\n",
" \"top\": {\"component\": \"straight\", \"settings\": {\"length\": 25.0}},\n",
" \"btm\": {\"component\": \"straight\", \"settings\": {\"length\": 15.0}},\n",
" \"rgt\": \"coupler\", # single mode models will be automatically converted to multimode models without cross polarization.\n",
" },\n",
" \"connections\": {\n",
" \"lft,out0\": \"btm,in0\",\n",
" \"btm,out0\": \"rgt,in0\",\n",
" \"lft,out1\": \"top,in0\",\n",
" \"top,out0\": \"rgt,in1\",\n",
" },\n",
" \"ports\": {\n",
" \"in0\": \"lft,in0\",\n",
" \"in1\": \"lft,in1\",\n",
" \"out0\": \"rgt,out0\",\n",
" \"out1\": \"rgt,out1\",\n",
" },\n",
" },\n",
" models={\n",
" \"coupler\": coupler,\n",
" \"straight\": waveguide,\n",
" },\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "17",
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"outputs": [],
"source": [
"mzi()"
]
},
{
"cell_type": "markdown",
"id": "18",
"metadata": {
"papermill": {
"duration": 0.006007,
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"source": [
"we can convert this model back to a singlemode `SDict` as follows:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "19",
"metadata": {
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},
"outputs": [],
"source": [
"mzi_te = sax.singlemode(mzi, mode=\"TE\")\n",
"mzi_te()"
]
}
],
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"display_name": "Python 3 (ipykernel)",
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