{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Circuit optimization by backpropagation with PyTorch "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Python\n",
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Torch\n",
"import torch\n",
"\n",
"# PhotonTorch\n",
"import photontorch as pt\n",
"\n",
"# Progress Bars\n",
"from tqdm.notebook import tqdm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Michelson Interferometer Cavity\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation and Design Parameters"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"neff = np.sqrt(12.1)\n",
"wl = 1.55e-6\n",
"dt = 0.5e-9\n",
"total_time = 2e-6\n",
"time = np.arange(0,total_time,dt)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Network"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We define the network again in the standard way. However, sometimes it is useful to define components only once, but save copies of the component while setting it as an attribute of the network.\n",
"\n",
"Look for example at the line\n",
"```\n",
"self.m_west = self.m_north = self.m_east = self.m_south = pt.Mirror(R=0.9)\n",
"```\n",
"Note that the order of the detectors is defined by where they appear in the link."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"BoundedParameter in [0.00, 1.00] representing:\n",
"tensor(0.9000)\n",
"BoundedParameter in [0.00, 1.00] representing:\n",
"tensor(0.9000)\n",
"BoundedParameter in [0.00, 1.00] representing:\n",
"tensor(0.9000)\n",
"BoundedParameter in [0.00, 1.00] representing:\n",
"tensor(0.9000)\n"
]
}
],
"source": [
"# define network in the standard way:\n",
"class MichelsonCavity(pt.Network):\n",
" def __init__(self):\n",
" super(MichelsonCavity, self).__init__()\n",
" self.west = pt.Source()\n",
" self.north = self.east = self.south = pt.Detector()\n",
" self.m_west = pt.Mirror(R=0.9)\n",
" self.m_north = pt.Mirror(R=0.9)\n",
" self.m_east = pt.Mirror(R=0.9)\n",
" self.m_south = pt.Mirror(R=0.9)\n",
" self.wg_west = pt.Waveguide(0.43, neff=neff, trainable=False)\n",
" self.wg_north = pt.Waveguide(0.60, neff=neff, trainable=False)\n",
" self.wg_east = pt.Waveguide(0.95, neff=neff, trainable=False)\n",
" self.wg_south = pt.Waveguide(1.12, neff=neff, trainable=False)\n",
" self.dc = pt.DirectionalCoupler(coupling=0.5, trainable=False)\n",
" self.link('west:0','0:m_west:1', '0:wg_west:1', '0:dc:2', '0:wg_east:1', '0:m_east:1', '0:east')\n",
" self.link('north:0', '0:m_north:1', '0:wg_north:1', '1:dc:3', '0:wg_south:1', '0:m_south:1', '0:south')\n",
" \n",
"# create network\n",
"nw = MichelsonCavity()\n",
"\n",
"# print out the parameters of the network:\n",
"for p in nw.parameters():\n",
" print(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 1.1 s, sys: 59.7 ms, total: 1.16 s\n",
"Wall time: 581 ms\n"
]
}
],
"source": [
"%%time\n",
"with pt.Environment(wl=wl, t=time):\n",
" detected = nw(source=1)[:,0,:,0] # get all timesteps, the only wavelength, all detectors, the only batch"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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