254 lines
78 KiB
Plaintext
254 lines
78 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Ring Resonator Dynamics\n",
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"The following analysis is base on the model from Yariv's PTL, \"Critical Coupling and Its Control in Optical Waveguide-Ring Resonator Systems\", in 2002. We mainly focus on the dynamic of how it reach the static state. We start from the light reach the coupler at the bus wavguide.\n",
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"\n",
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"P.S.: We split the time to discrete step of each round trip of light in the ring."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline\n",
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"\n",
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"T = 0.99\n",
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"K = 1 - T\n",
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"Alpha = 0.99\n",
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"t = np.sqrt(T) + 0.0j\n",
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"k = 0.0 + 1j * np.sqrt(K)\n",
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"alpha = np.sqrt(Alpha)\n",
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"theta = 2.0 * np.pi"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We define a function to generate the time series of a1, a2, b1 & a2: \n",
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"**a[n] => [a1(n-step), a2(n-step)]** \n",
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"**b[n] => [b1(n-step), b2(n-step)]** "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.figure.Figure at 0x1cd14a583c8>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"def propagate_in_cycle(t, k, alpha, theta, num_cycle = 1000):\n",
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" a1_0 = 1.0 + 0.0j\n",
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" a2_0 = 0.0 + 0.0j\n",
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" a = np.zeros((num_cycle, 2), dtype=complex)\n",
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" b = np.zeros((num_cycle, 2), dtype=complex)\n",
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"\n",
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" a[0] = [a1_0, a2_0]\n",
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" \n",
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" coupler = np.array([[t, k],\n",
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" [-k.conjugate(), t.conjugate()]])\n",
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"\n",
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" for n in range(num_cycle - 1):\n",
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" b[n] = coupler@a[n]\n",
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" a[n+1] = np.array([a1_0, b[n][1] * alpha * np.exp(1.j * theta)])\n",
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"\n",
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" b[num_cycle - 1] = coupler@a[num_cycle - 1]\n",
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" \n",
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" return a, b\n",
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"\n",
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"a, b = propagate_in_cycle(t=t, k=k, alpha=alpha, theta=theta, num_cycle = 1000)\n",
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"plt.figure()\n",
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"plt.subplot(121)\n",
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"plt.plot(abs(a[:,0])**2, label='a1')\n",
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"\n",
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"plt.plot(abs(b[:,0])**2, label='b1')\n",
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"plt.yscale('log')\n",
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"plt.title('a1 & b1 in Bus WG')\n",
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"plt.legend()\n",
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"plt.subplot(122)\n",
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"plt.plot(abs(a[:,1])**2, label='a2')\n",
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"plt.plot(abs(b[:,1])**2, label='b2')\n",
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"plt.title('a2 & b2 in Resonator')\n",
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"plt.yscale('linear')\n",
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"plt.legend()\n",
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"\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"You can invitigate the change of bus waveguide output intensity & the ring intensity gain from the coupler by each cycle (normalized by the input intensity a1)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.figure.Figure at 0x1cd15ca4c88>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.figure()\n",
|
||
|
|
"bus_output = abs(b[:, 0]/a[:,0])**2\n",
|
||
|
|
"gain_per_cycle = (abs(b[:, 1])**2 - abs(a[:, 1])**2)/abs(a[:,0])**2\n",
|
||
|
|
"\n",
|
||
|
|
"plt.plot(bus_output, label='Bus WG Output')\n",
|
||
|
|
"plt.plot(gain_per_cycle, label='Energy gain of ring after coupler per cycle')\n",
|
||
|
|
"plt.plot(bus_output + gain_per_cycle, label=\"Sum of both\")\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"We can see that the bus waveguide output power: \n",
|
||
|
|
"**enegry loss from the ring via coupler + enegry from a1 does not coupled to the ring** \n",
|
||
|
|
"\n",
|
||
|
|
"is same as the enegry gain of the ring after coupler: \n",
|
||
|
|
"**enegry gain from bus waveguide + energy of the ring does not coupled out to bus waveguide** \n",
|
||
|
|
"\n",
|
||
|
|
"Therefore, when the distructive interference happened in bus output port (b1) of the coupler, the energy will transfer to the port of the ring (b2). It must be true since the coupler is lossless (coupler martrix is unitary, i.e., |t|^2 + |k|^2 = 1) \n",
|
||
|
|
"It is an interesting constructive & distructive interference porporty of wave 😉 "
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Play with other parameters\n",
|
||
|
|
"Enjoy~ 😊"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 4,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.figure.Figure at 0x1cd15c2b780>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"T2 = 0.999\n",
|
||
|
|
"K2 = 1 - T2\n",
|
||
|
|
"Alpha2 = 0.999\n",
|
||
|
|
"t2 = np.sqrt(T2) + 0.0j\n",
|
||
|
|
"k2 = 0.0 + 1j * np.sqrt(K2)\n",
|
||
|
|
"alpha2 = np.sqrt(Alpha2)\n",
|
||
|
|
"theta2 = 2.0 * np.pi\n",
|
||
|
|
"a2, b2 = propagate_in_cycle(t=t2, k=k2, alpha=alpha2, theta=theta2, num_cycle = 10000)\n",
|
||
|
|
"plt.figure()\n",
|
||
|
|
"plt.subplot(121)\n",
|
||
|
|
"plt.plot(abs(a2[:,0])**2, label='a1')\n",
|
||
|
|
"\n",
|
||
|
|
"plt.plot(abs(b2[:,0])**2, label='b1')\n",
|
||
|
|
"plt.yscale('log')\n",
|
||
|
|
"plt.title('a1 & b1 in Bus WG')\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.subplot(122)\n",
|
||
|
|
"plt.plot(abs(a2[:,1])**2, label='a2')\n",
|
||
|
|
"plt.plot(abs(b2[:,1])**2, label='b2')\n",
|
||
|
|
"plt.title('a2 & b2 in Resonator')\n",
|
||
|
|
"plt.yscale('linear')\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 5,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.figure.Figure at 0x1cd15b431d0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.figure()\n",
|
||
|
|
"bus_output = abs(b2[:, 0]/a2[:,0])**2\n",
|
||
|
|
"gain_per_cycle = (abs(b2[:, 1])**2 - abs(a2[:, 1])**2)/abs(a2[:,0])**2\n",
|
||
|
|
"\n",
|
||
|
|
"plt.plot(bus_output, label='Bus WG Output')\n",
|
||
|
|
"plt.plot(gain_per_cycle, label='Energy gain of ring after coupler per cycle')\n",
|
||
|
|
"plt.plot(bus_output + gain_per_cycle, label=\"Sum of both\")\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.6.4"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 2
|
||
|
|
}
|