commit da45f5edf455efa605620b1c680cf04612cb8c30 Author: Chris Wong Date: Mon Dec 17 09:29:53 2018 +0800 first commit diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000..7e7a77f Binary files /dev/null and b/.DS_Store differ diff --git a/1007008950‐wong chi yan‐201308‐phd‐fulltext.pdf b/1007008950‐wong chi yan‐201308‐phd‐fulltext.pdf new file mode 100755 index 0000000..6f4eaeb Binary files /dev/null and b/1007008950‐wong chi yan‐201308‐phd‐fulltext.pdf differ diff --git a/1007008950‐wong chi yan‐201308‐phd‐thesis (updated).docx b/1007008950‐wong chi yan‐201308‐phd‐thesis (updated).docx new file mode 100755 index 0000000..a268653 Binary files /dev/null and b/1007008950‐wong chi yan‐201308‐phd‐thesis (updated).docx differ diff --git a/mathematica_code.txt b/mathematica_code.txt new file mode 100644 index 0000000..6b55a83 --- /dev/null +++ b/mathematica_code.txt @@ -0,0 +1,210 @@ +In this appendix, we show how to use the model based on Schröder et al. to simulate the DFWM mode-locked fiber laser. The following code is based on [65] and written in Mathematica 9.0: + (* This code solves the NLS equation with the split-step Fourier method +based on Govind P. Agrawal in March 2005 for the NLFO book +*) + +ClearAll["Global`*"] + +(*---Specify input parameters*) +distance = 150.;(*Enter fiber length (in units of L_c)=*) +kappa = -0.001 ;(*Normalized 2nd-dispersion: kappa=beta2*f^2*L/2): \ ++ve for normal,-ve for anomalous*) +sigma = 0.; (*Normalized 3rd-dispersion: sigma=beta3*f^3*L/6 *) +G = 1.0;(*small signal gain of Ramam Amp: G=g*L *) +Is = 1.; (*gain saturation parameter*) +alpha = 0.4; (*Normalized fiber amplitude absorption coeff: alpha=l*L*) + + +n = 2.^0.5;(*Nonlinear parameter n=') \ +sqrt(L_D/L_NL)=sqrt(gamma*P0*T0^2/|beta2|) or QT: n=kappa^0.5*) + +(*---Specify filter parameters*) +bdwidth = 2. Pi*6.; +delta = 2. Pi*0.5; +a = Log[Sqrt[0.95]]; +perta = 0.3; +pertfsr = 0.17; +T = 0.2; +t = Sqrt[T]; +r = I*Sqrt[1 - T]; + +(*---Specify input parameters*) +mshape = -1.;(*m=0 for sech,m>0 for super-Gaussian=*) +chirp0 = 0. ;(*% input pulse chirp (default value)*) + +(* +P = 1/(gamma*L); (P is the ref peak power); +uu = A/sqrt(P); +z = z0/L_c; (z0 is the real length, L_c is the cavity length); +tau = f*t; (t is the time of reference traveling frame); +*) + +(*---set simulation parameters*) +nt = 2^13; (*% FFT points (powers of 2)*) +Tmax = 100.; (*(half) window size*) +stepno = 1*Round[20*distance*n^2];(*No.of z steps to*) +dz = distance/stepno;(*step size in z*) +dtau = (2.*Tmax)/nt ;(*step size in tau*) + +Twin = 5.; +fmax = (1./(2. Tmax))*nt/2.; +fwin = 5.; + +filterz = 0.5; +plotz = 5; + +(*---tau and omega arrays*) +tau = N[Range[-nt/2, nt/2 - 1]]*dtau ;(*temporal grid*) +omega = (1. \[Pi]/Tmax)* + N[Join[Range[0, nt/2 - 1], + Range[-nt/2, -1]]];(*[(0:nt/2-1) (-nt/2:-1)]*) +(*frequency grid*) +delaytau = dtau*Range[-Round[Twin/dtau], Round[Twin/dtau]]; + + + +(*Input Field profile*) +If[mshape == 0, + (*;% soliton*) + uu = Sech[tau]*Exp[-0.5 I*chirp0*tau^2.], + If[ mshape > 0 , + (* super-Gaussian*) + uu = Exp[-0.5*(1. + 1. I*chirp0)*tau^(2.*mshape)], + (*White noise*) + uu = (RandomReal[NormalDistribution[0, 1], nt] + + I*RandomReal[NormalDistribution[0, 1], nt])*Sqrt[1./2.] + ] + ]; + +temp = RotateRight[ + InverseFourier[uu, FourierParameters -> {1, -1}]*(nt*dtau)/ + Sqrt[2.*Pi], nt/2.]; +tempomega = RotateRight[omega, nt/2]; + + +(*---store dispersive phase shifts to speedup code*) +dispersion = + Exp[(-alpha + I*kappa*omega^2. + I*sigma*omega^3.)* + dz];(*% nonlinear phase factor*) +(*comb filter type*) +(*original comb filter + BPF*) +(*filtert= \ +Exp[-omega^2./bdwidth^2.]*(t^2)/(1-r^2*Exp[-I*(omega+delta)+a]);*) +(*perturbated comb filter + BPF*) +filtert = Exp[-omega^2./bdwidth^2. - perta*Sin[0.5 + *omega/pertfsr]^2]*(t^2)/(1 - + r^2*Exp[-I*(omega + delta) + a]); + +p6 = ListLinePlot[ + Transpose[{tempomega/(2. Pi), + RotateRight[10.*Log10[Abs[filtert]^2], nt/2]}], + PlotRange -> {{-fwin, fwin}, {-30, 10}}, Frame -> True, + ImageSize -> Automatic]; + +(*%*********[Beginning of MAIN Loop]*********** +% scheme:1/2N\[Rule]D\[Rule]1/2N;first half step nonlinear*) +temp = uu* + Exp[(I*Abs[uu]^2. + G/(1.0 + Abs[uu]^2./Is))*dz/2.];(*% note hhz/2*) + +starttime = SessionTime[]; +timeused = SessionTime[] - starttime; +z = 0; + +Monitor[ (* Realtime monitoring the simulation progress*) + For[ i = 1, i <= stepno, i++, + If[Round[(Mod[z, 1] - filterz )/dz] == 0 , + ftemp = + InverseFourier[temp, FourierParameters -> {1, -1}]*filtert* + dispersion; + ftemp = + InverseFourier[temp, FourierParameters -> {1, -1}]*dispersion; + ] + uu = Fourier[ftemp, FourierParameters -> {1, -1}]; + temp = uu*Exp[(I*Abs[uu]^2. + G/(1.0 + Abs[uu]^2./Is))*dz]; + z = z + dz; + If[Round[Mod[z, plotz ]/dz] == 0 || + Round[(Mod[z, plotz ] - plotz )/dz] == 0 , + timeused = SessionTime[] - starttime; + p1 = ListLinePlot[Transpose[{tau, Abs[temp]^2.}], + PlotRange -> {{-Twin, Twin}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}} + ]; + ftemp0 = RotateRight[ftemp (nt*dtau)/Sqrt[2*Pi], nt/2]; + p2 = ListLinePlot[ + Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[ftemp0]^2.]}], + PlotRange -> {{-fwin, fwin}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{" Time = ", ToString[timeused]}]}} + ]; + p3 = ListLinePlot[Transpose[{tau, Abs[temp]^2}], + PlotRange -> {{-Tmax, Tmax}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}} + ]; + p4 = ListLinePlot[ + Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[ftemp0]^2.]}], + PlotRange -> {{-fmax, fmax}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{" Time = ", ToString[timeused]}]}} + ]; + autocorr0 = + RotateRight[ + InverseFourier[ + Fourier[Abs[temp]^2]*Conjugate[Fourier[Abs[temp]^2]]], nt/2]; + p5 = ListLinePlot[Transpose[{tau, autocorr0/Max[autocorr0]}], + PlotRange -> {{-Twin, Twin}, All}, Frame -> True]; + p = GraphicsGrid[{{p1, p2}, {p3, p4}, {p5, p6}}, ImageSize -> Full] + ]; + ], + p + ] + +uu = temp* + Exp[(I*Abs[uu]^2. + G/(1.0 + Abs[uu]^2./Is))* + dz/2.];(*% Final field*) +temp = RotateRight[ + InverseFourier[uu, FourierParameters -> {1, -1}]*(nt*dtau)/ + Sqrt[2*Pi], nt/2]; + +(*%Final spectrum*) +(*%***************[End of MAIN Loop]***************) +p1 = ListLinePlot[Transpose[{tau, Abs[uu]^2}], + PlotRange -> {{-Twin, Twin}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}} + ]; +p2 = ListLinePlot[ + Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[temp]^2.]}], + PlotRange -> {{-fwin, fwin}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{" Time = ", ToString[timeused]}]}} + ]; +p3 = ListLinePlot[Transpose[{tau, Abs[uu]^2}], + PlotRange -> {{-Tmax, Tmax}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}} + ]; +p4 = ListLinePlot[ + Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[temp]^2.]}], + PlotRange -> {{-fmax, fmax}, All}, Frame -> True, + FrameLabel -> {{Null, Null}, {Null, + StringJoin[{" Time = ", ToString[timeused]}]}} + ]; +autocorr0 = + RotateRight[ + InverseFourier[Fourier[Abs[uu]^2]*Conjugate[Fourier[Abs[uu]^2]]], + nt/2]; +p5 = ListLinePlot[Transpose[{tau, autocorr0/Max[autocorr0]}], + PlotRange -> {{-Twin, Twin}, All}, Frame -> True]; +p = GraphicsGrid[{{p1, p2}, {p3, p4}, {p5, p6}}, ImageSize -> Full] + +(*Exporting results*) +fname = "2nd_01(0.18)"; (*file name*) +Export[StringJoin[{fname , "_time.dat"}], + Transpose[{tau, Re[uu], Im[uu], Abs[uu]^2}]]; +Export[StringJoin[{fname , "_freq.dat"}], + Transpose[{tempomega/(2. Pi), Re[temp], Im[temp], Abs[temp]^2, + RotateRight[Abs[filtert]^2, nt/2]}]]; +Export[StringJoin[{fname , "_autocorr.dat"}], + Transpose[{tau, autocorr0, autocorr0/Max[autocorr0]}]]; \ No newline at end of file diff --git a/microring_dynamics.ipynb b/microring_dynamics.ipynb new file mode 100644 index 0000000..f2e5a50 --- /dev/null +++ b/microring_dynamics.ipynb @@ -0,0 +1,253 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ring Resonator Dynamics\n", + "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", + "\n", + "P.S.: We split the time to discrete step of each round trip of light in the ring." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "T = 0.99\n", + "K = 1 - T\n", + "Alpha = 0.99\n", + "t = np.sqrt(T) + 0.0j\n", + "k = 0.0 + 1j * np.sqrt(K)\n", + "alpha = np.sqrt(Alpha)\n", + "theta = 2.0 * np.pi" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define a function to generate the time series of a1, a2, b1 & a2: \n", + "**a[n] => [a1(n-step), a2(n-step)]** \n", + "**b[n] => [b1(n-step), b2(n-step)]** " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def propagate_in_cycle(t, k, alpha, theta, num_cycle = 1000):\n", + " a1_0 = 1.0 + 0.0j\n", + " a2_0 = 0.0 + 0.0j\n", + " a = np.zeros((num_cycle, 2), dtype=complex)\n", + " b = np.zeros((num_cycle, 2), dtype=complex)\n", + "\n", + " a[0] = [a1_0, a2_0]\n", + " \n", + " coupler = np.array([[t, k],\n", + " [-k.conjugate(), t.conjugate()]])\n", + "\n", + " for n in range(num_cycle - 1):\n", + " b[n] = coupler@a[n]\n", + " a[n+1] = np.array([a1_0, b[n][1] * alpha * np.exp(1.j * theta)])\n", + "\n", + " b[num_cycle - 1] = coupler@a[num_cycle - 1]\n", + " \n", + " return a, b\n", + "\n", + "a, b = propagate_in_cycle(t=t, k=k, alpha=alpha, theta=theta, num_cycle = 1000)\n", + "plt.figure()\n", + "plt.subplot(121)\n", + "plt.plot(abs(a[:,0])**2, label='a1')\n", + "\n", + "plt.plot(abs(b[:,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(a[:,1])**2, label='a2')\n", + "plt.plot(abs(b[:,1])**2, label='b2')\n", + "plt.title('a2 & b2 in Resonator')\n", + "plt.yscale('linear')\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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)." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "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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\n", + "text/plain": [ + "" + ] + }, + "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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\n", + "text/plain": [ + "" + ] + }, + "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 +} diff --git a/microring_dynamics.py b/microring_dynamics.py new file mode 100644 index 0000000..3eda9ca --- /dev/null +++ b/microring_dynamics.py @@ -0,0 +1,21 @@ +import numpy as np + +a1 = 1.0 + 0.0j +a2 = 0.0 + 0.0j +T = 0.9 +K = 0.1 +t = np.sqrt(T) + 0.0j +k = 0.0 - 1j * np.sqrt(K) + +Coupler = np.array([[t, k], + [k.conjugate(), -t.conjugate()]]) + +num_cycle = 1000 +a = np.zeros((num_cycle, 2), dtype=complex) +b = np.zeros((num_cycle, 2), dtype=complex) + +a[0, 0] = a1 +a[0, 1] = a2 + +for n in range(num_cycle): + pass diff --git a/microring_dynamics_v2.ipynb b/microring_dynamics_v2.ipynb new file mode 100644 index 0000000..7ee1c48 --- /dev/null +++ b/microring_dynamics_v2.ipynb @@ -0,0 +1,287 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ring Resonator Dynamics\n", + "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", + "\n", + "P.S.: We split the time to discrete step of each round trip of light in the ring." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "T = 0.99\n", + "K = 1 - T\n", + "Alpha = 0.99\n", + "t = np.sqrt(T) + 0.0j\n", + "k = 0.0 + 1j * np.sqrt(K)\n", + "alpha = np.sqrt(Alpha)\n", + "theta = 2.0 * np.pi" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define a function to generate the time series of a1, a2, b1 & a2: \n", + "**a[n] => [a1(n-step), a2(n-step)]** \n", + "**b[n] => [b1(n-step), b2(n-step)]** " + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ZY7znq4RF/4C598D+bVR0G8P7mRfzp4IOrP7gAGlJ+xjTtwMTBnTkjN7tSU2y764XIj8RAGTmw/g/wqvXwry/wsgbvI7IGLN9Bbw6DTYvoLLTUF7t8Tt+sySD0uXlDMxJ4I8XDOS8EzqRlhQdq6FIFj3/gRMvhVVvwfu/he6joeNAryMyJjb5fPDJgzD3HjS5FZ8OuodpS3uwe10FZ/ZuzXVjejIkz87yCyfRkwhE4LwZ8MgI+M+VMPUDSEzxOipjYsvBXfDyVVDwDqVdJ3Jt6aV88jkM75bOLeP7ckLn1l5HaGoQXUdiWrSFSX9zzkZ4/zdeR2NMbClZBY+djq77gP/1+CVDV11Kwf5kHrrkRGZdOdySQBiLni2CKj3HHqs67nkWdA9UEbYxplabPoN/XowvLpHbM+/jua+zmDgom3smDyQjLdHr6Ew9omuLoMpZv4F2veCVa5xNVWNM8KydC89O4khyJhdX/IYXt3XgvgsH8dcpgy0JRIjoTARVVccHtsMbP/e7fKsxJqA2fgrPf48DLbswevev2KjteeGqEVw0tLMVfUWQ6EwE4FYd3wLLXoKl//Y6GmOiz9Yl8Nx3OZjakbN3/pTU1h2YPW2UHQuIQNGbCABG/RQ6D3e2Cko3eR2NMdFjXzHMuoTDCS04Z9dNtGqbw/NTh9Mxw87Ui0TRnQiqqo7V51yl1NesgdGMMeBcL+j57+E7uIvv7f8pLdp1ZtaVw2nbMtnryEwTRXciALfq+F7Y+LFTdWyMaZ45v4LNC5iu09ia2pNnfjSMzBY2UmAki/5EAHDi96DveU7V8bal9U9vjKnZitdhwVO8lPId3qr8Fs9cPsx2B0WB2EgEInDuQ5DWxqk6Li/zOiJjIs/eLTB7GltSezG9dDJ//u6J9OrQyuuoTADERiIAp+p4clXV8V1eR2NMZFGFN35OxZFDfL90Kpef3oez+nXwOioTILGTCAB6jIVhU51roq+d63U0xkSOFa/Bqjd5qPJC2uT156aze3kdkQmg2EoEAGPvsqpjYxqjbC/61s1sTOrO05Xjuf+iE0iIj71VRzSLvf9mUhqc/4Rbdfwzqzo2pj4f3gf7tnHdvh/y83P6k9+uhdcRmQCLvUQA0OlEOPNXsOxlWPKC19EYE752b0TnP8rrcjpxuSfxw1PyvY7IBEFsJgKAkTc6Yxy/eZNVHRtTm//+lgqfcE/ZBdz17f7Exdn1g6JR7CaCuHj4zqPOriGrOjbmeFsWw9J/80TFeE496QS7hlAUi91EAMfGOt74MXz6F6+jMSa8fHgfB+NaMjNuMr84p4/X0Zggiu1EAG7V8bfhv79zrqZojIHiZbDydR47fA4Xj+pPViu7jlA0s0QgAuc9BGlt4aWpVnVsDMBHf+KQpPFS4kSuGNXV62hMkFkiAOfSE5MftqpjYwB2rkW/fon/Kx/LJaefQEaqjTIW7SwRVPlG1fF/vY7GGO/Mf4wKEvh3wnlcZqeLxgRLBP7G3gXtelvVsYldZXvxLXqO1ypPZsKIQbRMTvA6IhMClgj8HR3ruARe/6lVHZvY89Us4sr385yO57IR+V5HY0LEEkF1VVXHy1+BJf/yOhpjQsfno/Kzx1isPeh2wqm0T7dxBmKFJYKaHK06/oVVHZvYseEj4nev5Znys/nxqd28jsaEkCWCmnyj6vhqqzo2R4nIT0VkmYh8LSKzRCRFRLqKyHwRKRCRf4lIRI7bqIv/wX7SKOl8Dr072oAzscQSQW0y82HCvbDxE6s6NgCISA5wPTBUVQcA8cAlwB+BB1S1J7AbuMK7KJuobC++ZbN5pWIEFw7v4XU0JsQsEdTlhCl+VcdfeR2NCQ8JQKqIJABpwFZgNPCi+/eZwGSPYmu6ZS8TX1nG2wljGD8g2+toTIhZIqjLcVXHh7yOyHhIVTcD9wObcBLAHmAhUKqqFe5kRUBOTa8XkakiskBEFpSUlIQi5AYr//IfrNVO9BxyOimJ8V6HY0LMEkF9jlYdr4T3rOo4lolIJjAJ6Ap0AloA42uYtMbzjlX1cVUdqqpDs7KyghdoY+1aR+Lmz/l3xWlcPCzP62iMB0KaCERksog8ISKvisjZoVx2s/QYC8OugvmPWNVxbBsLrFfVElUtB14CTgFau7uKAHKBLV4F2CTLXgFgeduz6NMx3eNgjBcanAhE5GkR2S4iX1drHyciq0RkjYhMr2seqvqKql4J/BC4uEkRe+Usqzo2bAKGi0iaiAgwBlgOzAUudKe5DHjVo/ia5MiSl1js686IIYO9DsV4pDFbBM8A4/wbRCQeeBhn87gfMEVE+onIQBF5vdqtvd9Lb3NfFzkSU63qOMap6nycg8JfAktxvj+PA78EfiYia4C2wFOeBdlYu9aRVLKUNypP5rwT7CBxrGrwhURU9UMRya/WPAxYo6rrAETkeWCSqv4eOLf6PNxfUX8A3lLVL5satGc6nQhn3upcoXTJv+CES7yOyISYqt4B3FGteR3OdyHyuLuFijqdTW5mmsfBGK809xhBDlDo97zWMyZc1+HsZ71QRK6uaYJwPrMCgJE3QN4pTtXx7o1eR2NMs5R95ewWOsV2C8W05iaCmkayrnWfiarOUNWTVPVqVX20lmnC88yKKlZ1bKJF6SZSdizlLd8wxlntQExrbiIoAjr7PY+8MyaaIrMLTLgPNn0Kn87wOhpjmmb1HAC2dBhtQ1HGuOYmgi+Anu61VpJwyu1nNz+sCHDCJdBvEvz3bqs6NhGpbPmbrPd1YMDAIV6HYjzWmNNHZwHzgN4iUiQiV7jVlNOAOcAK4AVVXRacUMOMCJz7oFUdm8h05ACJmz5mrm8wZ/Xv6HU0xmMNTgSqOkVVs1U1UVVzVfUpt/1NVe2lqt1V9e7ghRqG0trA5L+5Vcd3eh2NMQ23/kPifUdYmX4K3bJaeh2N8ZhdYqK5eoyBk6+G+Y9a1bGJGIeXv8V+TSFrwGivQzFhwBJBIIy9E7L6WNWxiQyq+FbP4SPfQEb3r+tsbxMrLBEEwtGq4x3w+o1WdWzC247VpB7axvz4wZyQ29rraEwYsEQQKNknuGMdvwpfPe91NMbUStd9AEBll9NIiLdVgLFEEFhWdWwiwIGV71Poy6Jf/xO8DsWECUsEgVRVdQxWdWzCk6+SxMJP+cTXn1N7tvM6GhMmLBEEmlUdm3C2dTHJFftY0/Iku8icOcoSQTBY1bEJU+VrPgAgueeZ3gZiwoolgmCoqjpu0Q7+c6VVHZuwcWDl+6z0dWZw315eh2LCiCWCYKmqOt6xyqqOTXioOEzL4gV86uvPt7q28ToaE0YsEQRT99HHqo7XvO91NCbWbVlEgu8wmzNOIiM10etoTBixRBBsY++0qmMTFio2zAMgpfspHkdiwo0lgmCrqjo+uNOqjo2n9hd8xFpfNgN79fA6FBNmLBGEQvYJMPpWqzo23vH5SN66gAW+3gyz4wOmGksEoXLK9VZ1bLyzs4DUij0UtRpEmxZJXkdjwowlglD5RtXxVVZ1bEKqYqNzfCAhf4THkZhwZIkglDK7wMT7YdM8+OQhr6MxMWTvqo/Yoel072PXFzLHs0QQaoMuhn6TYe49VnVsQiahaD4Lfb04Kd+OD5jjWSIINRE49wGrOjahs3876YcKWZXUj+yMVK+jMWHIEoEX/KuO373D62hMtNu8EIAjHU/yOBATriwReKX7aDj5J/D5Y1Z1bILq4PrPqVShTY+hXodiwpQlAi+NvcOqjk3QHdzwBas1l4FdO3kdiglTlgi8lJgK5z/hVB2/doNVHZvAUyVtxxK+1u4M6JThdTQmTFki8Fr2IBh9G6yYDV/N8joaE212byCtYg/b0/uTmhTvdTQmTFkiCAenXAddRsKbN8PuDV5HY+ogIq1F5EURWSkiK0RkhIi0EZF3RaTAvc/0Os4qvs1fAhCXO8TjSEw4s0QQDqqqjkVsrOPw9xDwtqr2AU4AVgDTgfdVtSfwvvs8LOxe8xmHNYHsXpYITO0sEYSL1nnuWMfz4JMHvY7G1EBE0oHTgKcAVPWIqpYCk4CZ7mQzgcneRHi8ysIvWa75DMxr73UoJoxZIggngy6G/t9xqo63LPY6GnO8bkAJ8H8iskhEnhSRFkAHVd0K4N7XuNYVkakiskBEFpSUlAQ/Wl8lGaXLWC7d6dq2RfCXZyKWJYJwIgIT/wwt2sNLU63qOPwkAEOAR1R1MHCARuwGUtXHVXWoqg7NysoKVozH7FhNsu8Qu1sPJC5Ogr88E7EsEYQbqzoOZ0VAkarOd5+/iJMYikUkG8C93+5RfN/g2+Jcyyouxy40Z+pmiSAcdT/Tr+r4Pa+jMS5V3QYUikhvt2kMsByYDVzmtl0GvOpBeMfZs/5LDmsiHbsO9DoUE+YsEYSrsXdAVl945VqrOg4v1wHPicgS4ETgHuAPwFkiUgCc5T73XPmWJazWHPp3bud1KCbMWSIIV4mpcIFVHYcbVV3s7ucfpKqTVXW3qu5U1TGq2tO99z5zq9Ji90pWkU/3LDtQbOpmiSCcdRxoVcemafZto0XFbnan9yEh3r7mpm7WQ8KdVR2bJvBtXQKAdLTjA6Z+lgjCnX/V8Us21rFpmD3rFwHQpttgjyMxkSCkiUBEWojIQhE5N5TLjXit82DC/VD4mVUdmwY5VLiIQl8Wvbrkeh2KiQANSgQi8rSIbBeRr6u1jxORVSKyRkQaUljzS+CFpgQa8wZ916qOTYMl71zBCrrQq0Mrr0MxEaChWwTPAOP8G0QkHngYGA/0A6aISD8RGSgir1e7tReRsTjnXBcHMP7Y8Y2q4yvhyEGvIzLh6sgBMss2UZzak6QE2/tr6tegXqKqHwLVT4kbBqxR1XWqegR4HpikqktV9dxqt+3AmcBw4HvAlSJS47JDfj2WSHK06ng1vGdVx6YWxcuJQylr28/rSEyEaM7PhRyg0O95kdtWI1W9VVVvBP4JPKGqvlqmC+31WCJN9zNh+DXw+eNWdWxqVFbk7DpMzrVLS5iGaU4iqOkqVvVWPanqM6r6ejOWa8ZUVR1fAwd2eh2NCTN7Ny1hv6aQk9+7/omNoXmJoAjo7Pc8F9jSvHBMgySmuFXHu+B1qzo23+QrXsEazaF3drrXoZgI0ZxE8AXQU0S6ikgScAnOxbdMKHQcCGNuhxWvweJ/eh2NCSMt965hvXQmp3Wq16GYCNHQ00dnAfOA3iJSJCJXqGoFMA2YgzNc3wuquix4oZrjjJgGXUbBW7+0qmPjOLCTlhW72dOqByI2BoFpmIaeNTRFVbNVNVFVc1W1aqi+N1W1l6p2V9W7gxuqOU5cPHznEas6Nkfp9uXOfVYfjyMxkcROMo50rfNg4p+cquOPH/A6GuOxvYVOzWerznaNIdNwlgiiwcCLoP/58MHvYcsir6MxHtpfuJS9mkrnLj28DsVEEEsE0UAEzvUb69iqjmNXySrWaA59sjO8jsREEEsE0SI10zleYFXHMS193xqKErqQkZbodSgmglgiiCbdzoDh1zpVxwVWdRxzDuygVWUp+9Ntt5BpHEsE0WbMr6F9P3jVqo5jja/YOWMIO2PINJIlgmiTmALnPw6HdlvVcYzZs3EpAGm5AzyOxEQaSwTR6OhYx1Z1HEsObv6avZpKTl53r0MxEcYSQbQaMQ3yT4W3boZd672OxoRA3I5VFGguPdrbYDSmcSwRRKu4eJj8CEg8vHy1VR3HgBb711MUn0tmiySvQzERxhJBNGvdGSbeb1XHseDwPtIrdnGgRRevIzERyBJBtLOq49iwax0A2qabx4GYSGSJINpVVR237AD/sbGOo9X+LasASO3Yy+NITCSyRBALUjOdsY53FsC7v/Y6GhMEpUUrAGjXpa/HkZhIZIkgVnQ7w6k6/uIJKHjX62hMgJVvX8M2zaRrdnuvQzERyBJBLDladXytVR1HmYTSdWwi20YlM01iiSCW+Fcdv3a9VR1HkYxDhexKySUuzkYlM41niSDWdBwIo2+Hla/D4ue8jsYEwqFS0n17ONyqq9eRmAhliSAWHa06/qVVHTeSiMSLyCIRed193lVE5otIgYj8S0RCXs1VVlwAQHxWz1Av2kQJSwSxKC7Or+r4Kqis8DqiSHIDsMLv+R+BB1S1J7C2p2RzAAAU0UlEQVQbuCLUAe3Y5Fx1tFVO71Av2kQJSwSxqnVnd6zj+fCJVR03hIjkAhOBJ93nAowGXnQnmQlMDnVc+7eswqdCdr6dOmqaxhJBLBt0EQy4AD74A2z+0utoIsGDwM2Az33eFihV1apNqiIgp7YXi8hUEVkgIgtKSkoCFpTuXMtW2tKlY5uAzdPEFksEsW7in5yqYxvruE4ici6wXVUX+jfXMGmtp2Kp6uOqOlRVh2ZlZQUsttR9G9ka34nkhPiAzdPEFksEse4bVce3ex1NOBsJfFtENgDP4+wSehBoLSIJ7jS5wJZQB9b2cCF7UvNCvVgTRSwRGKfqeMQ0+OJJqzquhareoqq5qpoPXAL8V1UvBeYCF7qTXQa8GtK4Duykle7nSIadOmqazhKBcYy+Hdr3t6rjxvsl8DMRWYNzzOCpUC5872bnBKb4LBuw3jSdJQLjsKrjBlPVD1T1XPfxOlUdpqo9VPUiVT0cylh2FTqJID3Hrjpqms4SgTmm4wDnekQrX4dF//A6GtMAZdsKqFShg1111DSDJQLzTcOvdaqO355uVccRQHatYzNZ5LbL8DoUE8EsEZhviouD7zxqVccRIm3/BrYl5JAYb19l03TWe8zxMnKt6jgSqNLucBF70+zUUdM8lghMzQZdBAMutKrjMKb7t5PGIcrt1FHTTJYITO0m3m9Vx2GstGglAIl21VHTTJYITO1SM52rlFrVcViqOnW0Va5dddQ0jyUCU7dupx+rOl79jtfRGD+Hiwso13iy8ywRmOYJWSIQkTgRuVtE/iIil4VquSYAvlF1vMPraIwrbvc6isiiU5uWXodiIlyDEoGIPC0i20Xk62rt40RklYisEZHp9cxmEs4lestxLtdrIkViClzwBJSVwms3WNVxmGixfyPFCTkk2Kmjppka2oOeAcb5N4hIPPAwMB7oB0wRkX4iMlBEXq92aw/0Buap6s+AnwTuLZiQ6NDfqo7DiSpZR4rYl9bF60hMFEiofxJQ1Q9FJL9a8zBgjaquAxCR54FJqvp74Nzq8xCRIuCI+7SytmWJyFRgKkBenp0fHVaGXwur5zhVx/kjoU03ryOKWb49W0jhMBWZduqoab7mbFPmAIV+z+scnQl4CThHRP4CfFjbRMEavMMEgH/V8UtWdeyl3UXOGUNJ7e3UUdN8zUkEjR2d6aCqXqGq16nqw81YrvFSRi6c+2co+hw+tqpjr+x2awgycvt4HImJBs1JBEVAZ7/nnozOZDww8EKn6vh/VnXslSPFazisCWTn2RaBab7mJIIvgJ4i0lVEknBGbZodmLBM2DtadXwlHDngdTQxJ373WgrpQHbrFl6HYqJAQ08fnQXMA3qLSJGIXKGqFcA0YA6wAnhBVZcFL1QTVlIzneMFO9fCO1Z1HGotD2xie2IOcXE17aE1pnEaetbQlFra3wTeDGhEJnJ0PQ1GXAvz/gq9xkGvs72OKDb4fLQr38KyjG95HYmJElaJYppnzK+t6jjEKvcUkcwRKjPt9F0TGJYITPMkJFvVcYjt3OScOppsp46aALFEYJqvQ38Yc4dbdfx3r6OJenvs1FETYJYITGAMv8Y5ZvDWdNi1zutoolr59gLKNJGcvO5eh2KihCUCExhxcc7YBfEJVnUcZAml69lERzpkpHodiokSlghM4GTkwkSrOg62Vgc2UpKUi4idOmoCwxKBCayBF8LAi+CD38PmhV5HE30qK2hXsZX9LeyqoyZwLBGYwJtwP7TKdsc6tqrjQKosLSSRCioz7fiACRxLBCbwUlvDdx6xquMg2LVpOQDJHXp4HImJJpYITHB0PQ1OmQYLnnLGMDABsWezc+po69y+HkdiooklAhM8o2+HDgPg1WlWdRwg5dvXsF9TyMnN9zoUE0UsEZjgSUiG8x93qo5nX29VxwFw7NTRFK9DMVHEEoEJrqqq41VvRHzVsYh0FpG5IrJCRJaJyA1uexsReVdECtz7zGDFkH5wEzuScuzUURNQlghM8PlXHe9c63U0zVEB/FxV+wLDgWtFpB8wHXhfVXsC77vPA6+ynHYVWznQIj8oszexyxKBCb64OJj8qFN1/HLkVh2r6lZV/dJ9vA9nHI4cYBIw051sJjA5GMuv3LWReHz42thVR01gWSIwoZGR41YdfwEf/9nraJpNRPKBwcB8oIOqbgUnWQDta3nNVBFZICILSkpKGr3MXYV21VETHJYITOgcrTr+AxRFbtWxiLQE/gPcqKp7G/o6VX1cVYeq6tCsrKxGL3dv1amjne2qoyawLBGY0DpadRyZYx2LSCJOEnhOVV9ym4tFJNv9ezawPRjLLt9ewF5NJTcnLxizNzHMEoEJrdTWzljHu9bBO7d5HU2jiHOqzlPAClX13781G7jMfXwZ8Gowlp+4Zz0bybZTR03AWSIwodf1VLfq+OlIqzoeCfw/YLSILHZvE4A/AGeJSAFwlvs84JxTR+2qoybwGjR4vTEBN/p2WDvXGev4J/OgZeP3mYeaqn4M1LYWHhPUhVccpk3Fdg5knh3UxZjYZFsExhtHq473wmtWdVyfyp3r3FNH7aqjJvAsERjvdOgPY++AVW/Cl896HU1Y2330qqO9PY7ERCNLBMZbJ/8Eup4Ob98S6VXHQbXPPXW0TZ6dOmoCzxKB8Zb/WMcRXHUcbBUlBZRoBp2zs70OxUQhSwTGexk5cO4DTtXxR3/yOpqwlFR16mh6stehmChkicCEhwEXwMDvwv/+GNFVx8HS+uAGdqbk2amjJigi7vTR8vJyioqKKCsr8zqUJklJSSE3N5fExESvQwk/E+6DjZ86VcdXfwRJLbyOKDwcKiXDV0pZq65eRxJ1bH3iiLhEUFRURKtWrcjPz4+4X0eqys6dOykqKqJrV/tSH6eq6njmeU7V8bkPeB1RWCgrLiAFiMuyi80Fmq1PHBG3a6isrIy2bdtG3D8NQERo27ZtxP76CImup8Ip1zlVx6ve9jqasLBjo3PqaKscO2Mo0Gx94oi4RABE5D+tSiTHHjKjb4MOA2H2NNjf+Ms1R5uDW1dSqUKHLpYIgiGSv5OBij0iE4GJclZ1/A26Yw1FZJHfoY3XoZgoZYkggG699VY6d+5My5YtvQ4l8nXoB2PvtKpjIG3fBrbG55CaFO91KCZEDh48yMSJE+nTpw/9+/dn+vTgjH5axRJBAJ133nl8/vnnXocRPU6+2qqOfT7aHd7E3rQuXkdiQuymm25i5cqVLFq0iE8++YS33noraMuKuLOG/N312jKWb2nwAFEN0q9TOnec17/e6SZPnkxhYSFlZWXccMMNTJ06leHDhwc0lphXVXX8yAh4aSpcPsepQI4hvtJNpFLGkTZ2jaFgC7f1yZlnnglAUlISQ4YMoaioKKCx+QvZFoGI5InIbBF5WkSCu50TAk8//TQLFy5kwYIFzJgxg507d3odUnSqqjrevCAmq453bVwCQFKnfh5HYoKprvVJaWkpr732GmPGBO9K5w36eSUiTwPnAttVdYBf+zjgISAeeFJV6xqQoxfwhqo+JiIB2enbkEwbLDNmzODll18GoLCwkIKCAtq2betZPFFtwAXOADb/+yP0GAu5J3kdUcjs3biUdkDrLid4HUrUC8f1SUVFBVOmTOH666+nW7duQVt+Q7cIngHG+TeISDzwMDAe6AdMEZF+IjJQRF6vdmsPLAIuEZH/AnMD9xZC74MPPuC9995j3rx5fPXVVwwePNhqA4Jtwn2Q3ilixzpuqopty9mmmXTr3MnrUEyQ1LU+mTp1Kj179uTGG28MagwNSgSq+iGwq1rzMGCNqq5T1SPA88AkVV2qqudWu20HfgTcoaqjgYm1LUtEporIAhFZUFISnueQ79mzh8zMTNLS0li5ciWfffaZ1yFFv5SMY2Mdz7nV62hCJrW0gA1xebRraRebi1a1rU9uu+029uzZw4MPPhj0GJpzjCAHKPR7XuS21eZt4HoReRTYUNtEqvq4qg5V1aFZWeE5fOG4ceOoqKhg0KBB3H777UcPEt98883k5uZy8OBBcnNzufPOO70NNNrkj3Kqjhf+X2xUHft8ZJVtoLRF8HYJGO/VtD4pKiri7rvvZvny5QwZMoQTTzyRJ598MmgxNOcUjJpK2mqt/FHVr4ELm7G8sJGcnFzjqVxnnHEG9957rwcRxZDRtzljHc+eFjFjHTdVxa4NpHCYynZWURzNaluffP/73w9ZDM3ZIigCOvs9zwW2NC8cY+qRkAwXPOFUHc++LqqrjrevXQxAWo53BzFNbGhOIvgC6CkiXUUkCbgEmB2YsIypQ/u+TtXx6rfgy5leRxM0+9cvwKdC+55DvQ7FRLkGJQIRmQXMA3qLSJGIXKGqFcA0YA6wAnhBVZcFL1Rj/BytOv5V1FYdxxUvYS2d6J7T3utQTJRr6FlDU1Q1W1UTVTVXVZ9y299U1V6q2l1V7w5uqMb4OTrWcaJTdRyFYx232bucTUk9SUm0awyZ4LJrDZnI9Y2q4/u9jiagdN822lTu5FC7AfVPbEwzWSIwkW3A+TDoYvjfvVC0wOtoAqZ4lXPxwtQusVNFbbxjiaAJNmzYwIABx/9S++tf/0qPHj0QEXbs2OFBZDHqaNXx1KipOi5d/QmVKuT2tQsZRrva1ieXXnopvXv3ZsCAAVx++eWUl5cHLQZLBAE0cuRI3nvvPbp0sUsGh1QUVh0nb/6MFXSle25Hr0MxHrn00ktZuXIlS5cu5dChQ2FbUOa9t6bDtqWBnWfHgTC+rmvnOSoqKrjssstYtGgRvXr14tlnn2Xw4MGBjcU0XP4oGHk9fPIQ9DoHeo/3OqKmKy8j58Ay5mZMYkC8/VYLmTBbn0yYMOHo34cNGxYdl6GONqtWrWLq1KksWbKE9PR0/va3v3kdkjnzVnes4+sieqzjkhUfkUQ5cfkjvQ7FhEhd65Py8nL+/ve/M27cuDrm0DyRvUXQgEwbLJ07d2bkSOeL+v3vf58ZM2Zw0003eRaP4VjV8WOnO8lgyiyIwIHJdyx8mXRNpMu3JtQ/sQmcMF2fXHPNNZx22mmceuqpQVu+bRE0kVRbwVR/bjzSvi+cdZdTdbzwmZAtVkTGicgqEVnTrIGXfJVkFb7Dl4kn0jO3QwAjNOGstvXJXXfdRUlJCX/+85+DunxLBE20adMm5s2bB8CsWbMYNWqUxxGZo4ZdBd3OgDmhqTqubWyOpsxr40f/pJ2vhD29v2s/LmJITeuTJ598kjlz5jBr1izi4oK7qrZE0ER9+/Zl5syZDBo0iF27dvGTn/yEGTNmkJubS1FREYMGDeLHP/6x12HGpqNVx0mhqjqucWyOxs5k6Ycv0XbuLyggj5ETfxDwIE34qml9cvXVV1NcXMyIESM48cQT+c1vfhO05Uf2MQKP5Ofns3z58uPar7/+eq6//noPIjLHSe/kVB2vmwu+8mAPel/T2BwnV59IRKYCUwHy8vKOm0mrnH6sSxtEyqQHaJWWEqRQTbipbX1SURG6y6ZYIjDRa8D5zi34GjQ2h6o+DjwOMHTo0OP+nt+9D9z8TuCjM6YetmvImOazsTlMRIvIRKARPBhJJMduamVjc0SwSP5OBir2iEsEKSkp7Ny5MyL/earKzp07SUmx/b/RxMbmiFy2PnFE3DGCqrNySkois3I0JSWF3Nxcr8MwAaaqbwJveh2HaRxbnzgiLhEkJibStWtXr8MwxkQBW584Im7XkDHGmMCyRGCMMTHOEoExxsQ4Ceej5SJSAmys5c/tgHAYBixc4gCLpSZ1xdFFVbNCGUyVOvp2uHxuYLHUJFzigAD27bBOBHURkQWqOtTiOMZiCd84Giqc4rVYwjcOCGwstmvIGGNinCUCY4yJcZGcCB73OgBXuMQBFktNwiWOhgqneC2W44VLHBDAWCL2GIExxpjAiOQtAmOMMQFgicAYY2JcxCWCgA0S3vDldRaRuSKyQkSWicgNbvudIrJZRBa7twl+r7nFjW+ViJwTwFg2iMhSd3kL3LY2IvKuiBS495luu4jIDDeOJSIyJIBx9PZ734tFZK+I3Biqz0REnhaR7SLytV9boz8HEbnMnb5ARC5rTkyBEMq+HU792p13zPdtT/u1qkbMDYgH1gLdgCTgK6BfkJeZDQxxH7cCVuMMUH4ncFMN0/dz40oGurrxxgcolg1Au2pt9wLT3cfTgT+6jycAb+GMnjUcmB/E/8k2oEuoPhPgNGAI8HVTPwegDbDOvc90H2fGSt8Op35tfdv7fh1pWwQBGSS8MVR1q6p+6T7eh3O9+Zw6XjIJeF5VD6vqemCNG3ewTAJmuo9nApP92p9Vx2dAaxHJDsLyxwBrVbW2CvCqWAL2majqh8CuGpbRmM/hHOBdVd2lqruBd4FxTY0pAELatyOgX1ctM2b6tpf9OtISQU2DhNfVeQNKRPKBwcB8t2mau1n2dNUmW5BjVOAdEVkozkDoAB1UdSs4X26gfQji8HcJMMvveag/kyqN/Rw87Us18CyeMOjXYH27NiHp15GWCBo0SHhQFizSEvgPcKOq7gUeAboDJwJbgT+FIMaRqjoEGA9cKyKn1RVyEONwFuAMy/ht4N9ukxefSX1qW7aXMdXEk3jCpF+D9e3GCmi/jrRE4Mkg4SKSiPNleU5VXwJQ1WJVrVRVH/AExzYHgxajqm5x77cDL7vLLK7aLHbvtwc7Dj/jgS9VtdiNK+SfiZ/Gfg7hNuB8yOMJl37tLtf6ds1C0q8jLRGEfJBwERHgKWCFqv7Zr91/n+R3gKoj/bOBS0QkWUS6Aj2BzwMQRwsRaVX1GDjbXeZsoOrMgMuAV/3i+IF7dsFwYE/VJmYATcFv0znUn0k1jf0c5gBni0imu5l/ttvmlZD27XDp1+4yrW/XLjT9uqlH1L264RwtX41zdP7WECxvFM6m1RJgsXubAPwdWOq2zway/V5zqxvfKmB8gOLohnN2wlfAsqr3DrQF3gcK3Ps2brsAD7txLAWGBvhzSQN2Ahl+bSH5THC+oFuBcpxfQFc05XMALsc5uLcG+FEs9e1w6dfWt8OjX9slJowxJsZF2q4hY4wxAWaJwBhjYpwlAmOMiXGWCIwxJsZZIjDGmBhnicAYY2KcJQJjjIlx/x+osh/9UI54mwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def propagate_in_cycle(t, k, alpha, theta, num_cycle = 1000):\n", + " a1_0 = 1.0 + 0.0j\n", + " a2_0 = 0.0 + 0.0j\n", + " a = np.zeros((num_cycle, 2), dtype=complex)\n", + " b = np.zeros((num_cycle, 2), dtype=complex)\n", + "\n", + " a[0] = [a1_0, a2_0]\n", + " \n", + " coupler = np.array([[t, k],\n", + " [-k.conjugate(), t.conjugate()]])\n", + "\n", + " for n in range(num_cycle - 1):\n", + " b[n] = coupler@a[n]\n", + " a[n+1] = np.array([a1_0, b[n][1] * alpha * np.exp(1.j * theta)])\n", + "\n", + " b[num_cycle - 1] = coupler@a[num_cycle - 1]\n", + " \n", + " return a, b\n", + "\n", + "a, b = propagate_in_cycle(t=t, k=k, alpha=alpha, theta=theta, num_cycle = 1000)\n", + "plt.figure()\n", + "plt.subplot(121)\n", + "plt.plot(abs(a[:,0])**2, label='a1')\n", + "\n", + "plt.plot(abs(b[:,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(a[:,1])**2, label='a2')\n", + "plt.plot(abs(b[:,1])**2, label='b2')\n", + "plt.title('a2 & b2 in Resonator')\n", + "plt.yscale('linear')\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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)." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "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": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "# plt.semilogy((abs(a[1:,1])**2 + (abs(a[1:,0])**2 - abs(b[1:,0])**2))/abs(b[:-1,1])**2 - 1)\n", + "# plt.semilogy(abs(a[1:,1])**2 * T + abs(a[1:,0])**2 * K - 2 * np.real(np.conj(a[1:,1]) * a[1:,0] * k.conjugate() * t) - abs(b[:-1,1])**2)\n", + "# plt.semilogy(abs(b[1:,1])**2 - abs(b[:-1,1])**2)\n", + "plt.plot(- 2 * np.real(np.conj(a[1:,1]) * a[1:,0] * k.conjugate() * t))\n", + "plt.plot(abs(a[1:,1])**2 * T + abs(a[1:,0])**2 * K - abs(b[:-1,1])**2)\n", + "# plt.plot(abs(a[1:,0]) * abs(b[:-1,1]) * np.sqrt(K*T*0.999))\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "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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cKzm3aIDfoZkQEuPaR30Gwbm/g81L4F+3+x2NMQZoqdvJ2ocvo/fjZ9Jr7yaeKb6BlGuWcP7lt1BmCSFmxf+WQsC4L8ExX/NOUx1xJgw73u+IjEla21e8hj59BWVN23gxZxYjvvoLzist9jss0wWJsaUQMP1X0HcoPDMbDuzxOxpjkk9LC+ueupm8v5zPvqYUXpv6BDOu/yOjLSHEjcRKCpl94PwHYOcmeOnGzqc3xoSNHthD+T3nc8TKu3k983S44k3OOuscKxqLM4mVFOBgtfOS/4VVz/sdjTFJoXFPDZW/PZ2ybW/wzMCrmPqDpygZXNj5C03MSbykAF61c9HR8Nw1sKfa72iMSWgHdm5m65wvUFD/CS8edSezrvwFWRmJc7gy2SRmUkjLgPMf8i6H++x3gy5Ha4wJp4ZdW6m9+yzyGqr41+R7OOcr37TdRXEuMZMCHKx2Ln/Fq3Y2xoRVS/1equ77EnmNW3j7xPv54rn/4XdIJgwSNymAV+084gtetfO2tX5HY0ziaGlm/X1fpXj/al478ld8Ydp5fkdkwiSxk0Kg2jk926t2bm70OyJjEsLqP/+QEbve5oVhP2D6Vy7zOxwTRomdFMCqnY0Js01v/4Ux5Q/yaq/pTP/GzXYMIcEkflIAV+18sVftvOldv6MxJm7t2/oJeS9fwyo5gqNn309aanKsQpJJ8vxHp1m1szE90tJC1WOXItpC4/l/ZEC/vn5HZCIgeZJCVq5VOxvTA2v+cScj9n3Am8O/x4SjjvY7HBMhyZMUwKqdjemmPdXrGbb4dt5Pm8TpF13vdzgmgpIrKYBVOxvTDZVPfh9V6P3lu8lMt2rlRJZ8SSEwtnPDPqt2NqYLKha9wNgdr/PmoK8zbux4v8MxEZZ8SQGgYDSc9Quv2nnRw35HY0zM0qYG5KUfUsFAjrvov/wOx0RBciYFOFjtPP8Wq3Y2ph1r5j9AcdMmyifeRP++uX6HY6IgeZOCVTsb06GWhnr6L76LFSmjmDrj636HY6IkeZMCWLWzMR1Y9fzvKGypofb4H5KRnup3OCZKkjspgFU7GxNCy4E6ipbdy5LUozjpzC/7HY6JIksK4Kqdi63a2Rhn1fz76a87qTvpelJT7NpGycSSAnjVzucFqp1v8jsaY/zV0kz/jx5gpYzk+M+f63c0JsosKQSUnOiqnZ+wameT1MrffIqi5s1UH3U5aWl2LCHZWFIIZtXOxsDbc6ikkONnfMPvSIwPLCkEs2pnk+SqVy9kxIGVrCn9Gr2yMv0Ox/jAkkJbBaPhzJ9btbNJSlteu5/9msHYaVf4HYrxiSWFUKZcbtXOJuk01u1ixNYXWdznNAYPGuR3OMYnlhRCsWrnpCYi3xORFSKyXETmikiWiJSJyLsislZE/k9EMty0me5xuXu+1N/ou2/NPx+lN/VkTrnU71CMjywptMeqnZOSiAwBrgEmq+qRQCpwAXA7cKeqjgR2AIHR6i8DdqjqCOBON11c6rXsCcqlhElTz/I7FOMjSwodsWrnZJUGZItIGtALqAJOB/7qnn8MmOXuz3SPcc+fIXE4kv22dR8yvHEtFSVfJtXGXU5q9t/vjFU7JxVV/RT4DbAJLxnsAhYDO1W1yU1WCQxx94cAFe61TW76/FDzFpHZIrJIRBbV1NRE7k10Q8WCx2nSFIafZhe+S3aWFDpj1c5JRUTy8H79lwGDgd7A9BCTBs5XDrVVEPJcZlV9QFUnq+rkgoKCcIQbHqoUVTzP0oxjKCkp8zsa47OoJgURmSUiD4rIsyISPzsurdo5mXwB+ERVa1S1EXgaOAno53YnARQDm939SmAogHu+L1Ab3ZB7pnLpGwxqqWbvyPP8DsXEgC4nBRF5RES2isjyNu3TRGSNO/vixo7moap/V9XLgW8A/9GtiP1i1c7JYhNwgoj0cscGzgBWAq8DX3HTXAI86+7Pc49xz7+mGl9VjzVv/4l6TWfsGRf5HYqJAYezpfAoMC24QURSgXvwNq/HAReKyDgROUpEnm9zKwx66S3udfHDqp2Tgqq+i3fA+ANgGd535AHgh8D3RaQc75hBoLLxYSDftX8f6PCHUazR5kZKq1/mo14nUpA/wO9wTAxI63wSj6ouCHEO9hSgXFXXA4jIk8BMVf0lcE7bebhfXr8CXlTVD7obtG8C1c4v/qdX7Xzct/yOyESAqv4E+Emb5vV4/b3ttPXAV6MRVyRs/PB1StlF45iZfodiYkRPjym0nnnhBJ+VEcrVePtsvyIiV4aaIJbP0AC8aucjzrBqZ5MQahc/wwFNZ8zJdjzBeHqaFLp85gWAqs5R1WNV9UpV/UM708TmGRoBrdXOWVbtbOKbKoO3vMryzGMYkB/yLFqThHqaFFrPvHCCz8pIXLlFcO4cV+18h9/RGNMtW9YuZlBLNfvKvuh3KCaG9DQpvA+MdNeFycC7HMC8nocVB1qrnX9j1c4mLm1+56+0qFB20lc6n9gkjcM5JXUusBAYLSKVInKZq+C8CpgPrAKeUtUVkQk1Blm1s4ljeRUvsyptDEOtYM0E6XJSUNULVbVIVdNVtVhVH3btL6jqKFU9QlVvi1yoMciqnU2c2rutgrLGddQMPs3vUEyMsctc9FTJiTD1Oqt2NnHlk3e9vpo3IdQVPEwys6QQDqfeZNXOJq40r32VbdqXscec5HcoJsZYUggHq3Y2cURbminZ+S5rc44jI73L9asmSVhSCBcb29nEiU9XvUseu2kefqrfoZgYZEkhnKza2cSB6iX/AKB0ypd8jsTEIksK4WTVziYO9K5YwNqUMoqHlvgdiolBlhTCLbcoaGxnq3Y2saWpfi9H1K+gKv9Ev0MxMcqSQiSMm3mw2rniPb+jMabVho/eIF2ayRp5it+hmBhlSSFSAtXOT19u1c4mZuxc+QbNKpRN+oLfoZgYZUkhUqza2cSgnC3vUJ46nIIBMXgFYhMTLClEklU7mxjSdKCOsvrVbM2f7HcoJoZZUog0q3Y2MWLj0gVkSiMZwz/ndygmhllSiLTgaud5V1m1s/HNjpWve5fKPvZMv0MxMcySQjQEqp3XvmzVzsY3vaveZX1qKYWFg/wOxcQwSwrRYtXOxkctjQ2U1q+gut8kv0MxMc6SQrRYtbPx0acfLyKbBlJKTvA7FBPjLClEk1U7G59sW/UWAIPG20Fm0zFLCtE2biYcfZFVO5vo+nQRNfSjpGy035GYGGdJwQ/Tb3fVzja2s4mOwl1L2Zg9jpRU+8qbjlkP8UNrtfNGq3Y2EbdvRzVDWqrYX2gHmU3nLCn4xaqdTZRsWroAgJwRdpDZdM6Sgp+s2tlEwd51C2nSFMqOOtnvUEwcsKTgJ6t2NlHQe+sSPkktpV+/PL9DMXHAkoLfCkbDmT9z1c6P+B2NSTDa3MSw+lVs7TvB71BMnLCkEAuOC1Q732zVzjFARPqJyF9FZLWIrBKRE0Wkv4i8IiJr3d88N62IyBwRKReRpSISU0dzazauJIf9MCSmwjIxzJJCLEhJsWrn2PI74CVVHQMcDawCbgReVdWRwKvuMcB0YKS7zQbui3647duy5l0A8kZM8TkSEy8sKcQKq3aOCSKSC5wCPAygqg2quhOYCTzmJnsMmOXuzwQeV887QD8RKYpy2O1qqFhCvaZTNsa2FEzXWFKIJVbtHAuGAzXAH0VkiYg8JCK9gYGqWgXg/ha66YcAFUGvr3RthxCR2SKySEQW1dTURO4dBOldu4INaWVkZ2VGZXkm/llSiDWfqXbe63c0ySgNmATcp6oTgX0c3FUUioRoC3kamao+oKqTVXVyQUEUhsNUpbj+Y7bnjon8skzCsKQQa7Jy4bz7vWrn+Vbt7INKoFJV33WP/4qXJKoDu4Xc361B0w8Nen0xsDlKsXZoe8Ua+lCHDjrG71BMHLGkEItKTvKqnT943Kqdo0xVtwAVIhK4ctwZwEpgHnCJa7sEeNbdnwd83Z2FdAKwK7CbyW+bV78DQN6I43yOxMSTNL8DMO049SZY96pX7Vx8HPQZ6HdEyeRq4E8ikgGsB76J9wPqKRG5DNgEfNVN+wIwAygH6ty0MaF+0xIaNJXSMcf6HYqJI5YUYlWg2vn+U7xq54ue8gbqMRGnqh8Ck0M8dUaIaRX4bsSD6obs7cvZmFrCyN69/Q7FxBHbfRTLrNrZdJcqQ/Z/zLY+dpDZHB5LCrHuuMvhiNPh5VtgW7nf0Zg4UVv1CXnspmXQ0X6HYuKMJYVYl5ICM++FtEyrdjZdtmWNV+fSp9SK1szhiWpSEJHeIrJYRM6J5nLjXmu18wdW7Wy6pK5iKQBDRttBZnN4upQUROQREdkqIsvbtE8TkTXuYmAdFfgE/BB4qjuBJj2rdjaHIXXbKiopJL9/vt+hmDjT1S2FR4FpwQ0ikgrcg3dBsHHAhSIyTkSOEpHn29wKReQLeOd722gy3WXVzqaL8veVU511hN9hmDjUpaSgqguA2jbNU4ByVV2vqg3Ak8BMVV2mque0uW0FTgNOAC4CLheRkMv24/owcSNQ7bxjg1U7m3Y1N9QzuKmS/XmjO5/YmDZ6ckyhyxcCA1DVm1X1OuDPwIOq2tLOdNG9Pky8KTkJTv6eV+28+h9+R2Ni0OZ1H5EmLaQWjfc7FBOHepIUunwhsM9MoPqoqtq1G3oiMLbzvKttbGdziO3rlgAwYPhEnyMx8agnSSFmLwSW8GxsZ9OBxqrlHNA0ho44yu9QTBzqSVJ4HxgpImXuGjEX4F0czESDVTubdmTXrqYidShZWVl+h2LiUFdPSZ0LLARGi0iliFymqk3AVcB8vOEKn1LVFZEL1RzCqp1NCIX169ne2848Mt3T1bOPLlTVIlVNV9ViVQ0MVfiCqo5S1SNU9bbIhmoOYdXOpo19O7dRqNtpzB/rdygmTtllLuJdbhGcc5dX7bzg135HY3z26ceLAMgutuMJpnssKSSC8bO8aucFv7Zq5yS3e8NHAAwcadc8Mt1jSSFRWLWzAahZxW7txeBiO6ZguseSQqKwamcD9N69jsq0YaSk2lfbdI/1nERSchKc7MZ2Xv2C39EYHxQe2MTu3mV+h2HimCWFRHPqj2DQBK/aee9Wv6MxUVS3axv57KQpf6TfoZg4Zkkh0aRlwJcfgoa98KxVOyeTqnXeQeasIjsd1XSfJYVE1FrtPN+qnZPI7k1e7Wh+qZ2OarrPkkKismrnpNNUvYYDms6Q0jF+h2LimCWFRGXVzkknc1c5lamDychI9zsUE8csKSQyq3ZOKgP2b6A22848Mj1jSSHRtVY729jOiayxfh+DWqo50G+E36GYOGdJIRlMvx36DrFq5wRWtX4FKaKkD7QhOE3PWFJIBlbtnPBqNy4HoN+wI32OxMQ7SwrJwqqdE1rDllW0qDDERlszPWRJIZlYtXPCSq9dy2YpJCenj9+hmDhnSSGZtI7tbNXOiaZf3Qa2ZZX4HYZJAJYUkk3hmIPVzov/6Hc0Jgy0uYnBTZXU5drlsk3PWVJIRoFq5/k3W7VzO0QkVUSWiMjz7nGZiLwrImtF5P9EJMO1Z7rH5e750mjHuv3TcjKlEQpGRXvRJgFZUkhGVu3cFdcCq4Ie3w7cqaojgR3AZa79MmCHqo4A7nTTRdW2TasB6DXIkoLpOUsKycqqndslIsXA2cBD7rEApwN/dZM8Bsxy92e6x7jnz3DTR82+qjUAFAwbF83FmgRlSSGZjZ8FR1/oqp3f9zuaWHIXcAPQ4h7nAztVtck9rgSGuPtDgAoA9/wuN/0hRGS2iCwSkUU1NTVhC7Zl+zr2aSYDh9iBZtNzlhSS3fQ7XLXz5VbtDIjIOcBWVV0c3BxiUu3Cc59tVH1AVSer6uSCgoIeRnpQ1u4NVKUOJi0tNWzzNMnLkkKys2rntqYCXxKRDcCTeLuN7gL6iUiam6YY2OzuVwJDAdzzfYHaaAacV1/JzqziaC7SJDBLCsaqnYOo6k2qWqyqpcAFwGuqejHwOvAVN9klwLPu/jz3GPf8a6rRKwDR5kYGNm+hPrc0Wos0Cc6SgvFYtXNnfgh8X0TK8Y4ZPOzaHwbyXfv3gRujGdS2ynWkSzMp+VajYMLDkoLxWLXzIVT1DVU9x91fr6pTVHWEqn5VVQ+49nr3eIR+N4p5AAATDElEQVR7fn00Y6zZ5J0123uwXR3VhIclBXNQ4Rj4wk+t2jmO1LnTUQcMG+tzJCZRWFIwnzVltlU7xxHdvo69msWgwXY6qgkPSwrms6zaOa5k7dlAVWoRqan2VTbhYT3JHMqqneNGXn0lO7OH+h2GSSCWFExoVu0c81qaGhnYXE1Dn1K/QzEJxJKCad/02yHXqp1j1bZP15IuzciAEX6HYhKIJQXTvqy+cH6g2vlHfkdj2ti20TsdNafITkc14WNJwXSstdr5saSvdo41dVUfAzCgZIzPkZhEErWkICIpInKbiPxeRC7p/BUmZli1c0zSWnc6atEwv0MxCaRLSUFEHhGRrSKyvE37NBFZ40ad6qy8fybeZYYb8S4iZuKFVTvHpGx3ddQUOx3VhFFXe9OjwLTgBhFJBe4BpgPjgAtFZJyIHCUiz7e5FQKjgYWq+n3g2+F7CyYqrNo55uQdqGRntm0lmPBK63wSUNUFIcaenQKUB671IiJPAjNV9ZfAOW3nISKVQIN72NzdgI2PpsyGj1/yqp1LTwE768U3LY0NDGyuZkPuWX6HYhJMT7Y7W0eccoJHowrlaeCLIvJ7YEF7E0VqdCoTBikpMOs+r9r5mdlW7eyjrZVrSZMWUiwxmzDrSVLo8ohTAKpap6qXqerVqnpPB9NFZHQqEyaBaudPF1u1s49qN60EIKdolM+RmETTk6TQOuKUEzwalUlkVu3su7otawEoKB3ncyQm0fQkKbwPjBSRMhHJwBulal54wjIxz6qdfeVdHTWbwoE2DKcJr66ekjoXWAiMFpFKEblMVZuAq4D5wCrgKVVdEblQTUyxamdfZe/ZaKejmojo6tlHF7bT/gJgZa7JquQkmHot/PsuGDUNxszwO6KkkVdfweZeVslsws9+ZpieOe1mGHSUVTtHUXNjAwNbttLQt8zvUEwCsqRgeiYtA85/yKqdo6imYo13Omr+EX6HYhKQJQXTc1btHFXbN60GIGewnY5qws+SggmPKbNh+Gk2tnMU1G3xro5aaKejmgiwpGDCIyUFZt0LqRlW7Rxp29exR7MpKOzoAgLGdI8lBRM+uYPh3N+5auff+B1Nwsreu4GqtCF2OqqJCOtVJrxaq51/bdXOEdK//lN2Zg/tfEJjusGSggk/q3aOmObGAwxsqbbTUU3EWFIw4WfVzhGzddMaUkVJs9NRTYRYUjCREah2trGdw6p20yoAcoaM9jkSk6gsKZjIsWrnsGu9OmqJnY5qIsOSgomc4GrneVdbtXM41K5jl/amsLDI70hMgrKkYCIrUO388UtxUe0sIkNF5HURWSUiK0TkWtfeX0ReEZG17m+eaxcRmSMi5SKyVEQmRTK+7D0bqU4rQlLsq2siw3qWibz4qnZuAn6gqmOBE4Dvisg44EbgVVUdCbzqHgNMB0a622zgvkgGl3+ggl3ZwyK5CJPkLCmYyIujamdVrVLVD9z9PXhjhQwBZgKPuckeA2a5+zOBx9XzDtBPRCKyb6fpwH4KW2rsdFQTUZYUTHTkDoZz74qramcRKQUmAu8CA1W1CrzEARS6yYYAFUEvq3RtoeY3W0QWiciimpqaw46n2p2OmjpgxGG/1piusqRgomf8eXFT7SwiOcDfgOtUdXdHk4ZoC3lEXVUfUNXJqjq5oKDgsGMKnI7ax05HNRFkScFEVxxUO4tIOl5C+JOqPu2aqwO7hdzfwDm2lUDwNSeKgc2RiKveXR11YOn4SMzeGMCSgom2GK92FhEBHgZWqepvg56aB1zi7l8CPBvU/nV3FtIJwK7Abqawx7ZjPTs1h/yCgZGYvTGAJQXjh9iudp4K/D/gdBH50N1mAL8CzhSRtcCZ7jF4Y5SvB8qBB4HvRCqw7D0b2JI+BC9vGRMZaX4HYJLUaTfDule9orbiyZBT2PlrokBV3yL0cQKAM0JMr8B3IxqUM6Chko05E6OxKJPEbEvB+CMtA85/EA7ssWrnLmjYv4+Buo3GfnY6qoksSwrGP4Vj4cyfuWrnR/2OJqZVb/TOPEovsNNRTWRZUjD+aq12/lE8VDv7ZkeFlxRyi8f4HIlJdJYUjL/iqNrZT/XV3tVR7XRUE2mWFIz/4rDaOdqkdj215JLXf4DfoZgEZ0nBxIbx58GEC7xq58pFfkcTc3rv3Uh1WsirZxgTVnF3SmpjYyOVlZXU19f7HUq3ZGVlUVxcTHp6ut+hxJ4Zd8DGt71q5yvehMwcvyOKGQUNlXzSd4rfYSQcW58cKu6SQmVlJX369KG0tDTuinhUle3bt1NZWUlZmZ1aeIisvnDeH+DRs+Hlm+Hc3/kdUUyo37ebAmpZa6ejhp2tTw4Vd7uP6uvryc/Pj7t/IICIkJ+fH7e/SqKidKpX7bz40VisdvbFlvXLAUgrHOVzJInH1ieHirukAMTlPzAgnmOPGhvb+TN2bPSSQv+SI32OJDHF83cyErHHZVIwCc6qnT+jsXoVTZpC8Yij/A7FJAFLCmF08803M3ToUHJy7ABpjxWOhTN/atXOQMaOtWxOGURWVrbfoZgoqaur4+yzz2bMmDGMHz+eG2+8sfMXhYklhTA699xzee+99/wOI3FMueJgtfP2dX5H45u8ug1syyr1OwwTZddffz2rV69myZIl/Pvf/+bFF1+MynLj7uyjYD99bgUrN3c0KNbhGzc4l5+c23nV6KxZs6ioqKC+vp5rr72W2bNnc8IJJ4Q1lqQXqHa+90TvNNVL50Nqcp3K29zYwODmzXza91S/Q0l4sbY+Oe200wDIyMhg0qRJVFZWhjW29tiWQjc98sgjLF68mEWLFjFnzhy2b9/ud0iJKcmrnbdsWEm6NJM60IbgTGQdrU927tzJc889xxlnHHLl9oiI2paCiAwD7ga2AR+r6q86eUmnupKBI2XOnDk888wzAFRUVLB27Vry8/N9iyehjT8P1rzkVTuPPNMbfyFJbNuwnCFA7lA78yjSYnF90tTUxIUXXsg111zD8OHDoxJLl7YUROQREdkqIsvbtE8TkTUiUi4inR0JGQX8Q1UvBcZ1M96Y8MYbb/DPf/6ThQsX8tFHHzFx4kSrPYi0GXfE/NjOkVBf5V0ddfCIo32OxERKR+uT2bNnM3LkSK677rqoxdPV3UePAtOCG0QkFbgHmI63kr9QRMaJyFEi8nybWyGwBLhARF4DXg/fW4i+Xbt2kZeXR69evVi9ejXvvPOO3yElvkC1c+0nXrVzkkjdvpZq+tO3X3+/QzER0t765JZbbmHXrl3cddddUY2nS0lBVRcAtW2apwDlqrpeVRuAJ4GZqrpMVc9pc9sKfBP4iaqeDpzd3rJEZLaILBKRRTU1Nd17VxE2bdo0mpqamDBhAj/+8Y9bDzDfcMMNFBcXU1dXR3FxMbfeequ/gSaa4GrnNdE5E8Nv+Xs/ZktmdHYbGH+EWp9UVlZy2223sXLlSiZNmsQxxxzDQw89FJV4enJMYQhQEfS4Eji+g+lfAm4VkYuADe1NpKoPAA8ATJ48OSarljIzM0OeHnbqqadyxx13+BBREgmM7fzsVfCdhTEztnMkNDXUM6RpE1UFJ/sdiomg9tYnX/va13yIpmdnH4Wqr253Ja6qy1X1K6p6pape34PlmmSWRNXOlWs/IkOaSRsywe9QTBLpSVKoBIYGPS4GNvcsHGO6IEmqnWvXLQZgwIhjfY7EJJOeJIX3gZEiUiYiGcAFwLzwhGVMJ6ZcAcNPTehq58bNS6nXdIbaNY9MFHX1lNS5wEJgtIhUishlqtoEXAXMB1YBT6nqisiFakyQlBSYdZ83tvPTlyfk2M45O1axMa2U9PQMv0MxSaSrZx9dqKpFqpquqsWq+rBrf0FVR6nqEap6W2RDNaaNBK521pZmhh5Yy47cMX6HYpKMXebCxLcEHdv50/Kl5LIPio/zOxSTZCwpdMOGDRs48shDLztw9913M2LECESEbdu2+RBZkkrAauctKxYAMHD8KT5HYiKtvfXJxRdfzOjRoznyyCO59NJLaWyMzi5SSwphNHXqVP75z39SUlLidyjJJQGrnXXTe+yiNyUj7XTUZHXxxRezevVqli1bxv79++OieM1/L94IW5aFd56DjoLpnV+rr6mpiUsuuYQlS5YwatQoHn/8cSZOnBjeWEzXlU6FqdfAv38Ho6bB6Ol+R9QjRbs+4JOsIzkmNdXvUJJHjK1PZsyY0fr8lClT7NLZsW7NmjXMnj2bpUuXkpuby7333ut3SCYwtvOzV8X12M5Vn6ykuGUzdcM+73coJko6Wp80NjbyxBNPMG3atA7mED7xvaXQhQwcKUOHDmXq1KmAV44+Z84crr/eCrV9lZbpVTvf/3mv2vnCJyEOB2WveO85ioAhk8/1O5TkEqPrk+985zuccsopfO5zn4tKLLal0E3SZmXT9rHxiU/Vzod5GfkO9S1/hg0pQxk2wsZQSBbtrU9++tOfUlNTw29/+9uoxWJJoZs2bdrEwoULAZg7dy4nn2wXLYsZUa52bu8y8t2Z17oPFzC6cRWbS7+MpNjXM1mEWp889NBDzJ8/n7lz55ISxb5gva6bxo4dy2OPPcaECROora3l29/+NnPmzKG4uJjKykomTJjAt771Lb/DTE6fqXaeDc1NkV5iyMvIH+5Mlv3rafr//SK20Y8jZ14b9iBN7Aq1Prnyyiuprq7mxBNP5JhjjuFnP/tZVGKJ72MKPiktLWXlypWHtF9zzTVcc801PkRkDpE7GM65E9a/Di2NkBrRrt6ly8iLyGxgNsCwYcMOmUnfwSPY2Osocqb9FyP62qA6yaK99UlTU8R/zIRkScEkriPP926R16XLyHc2VsiwkRMYdkNyDB5kYpftPjKm5+wy8iZhxGVS0DgeWCWeYzftssvIx7F4/k5GIva4SwpZWVls3749Lv+Rqsr27dvJysryOxQTRnYZ+fhl65NDxd0xhcDZPTU1NX6H0i1ZWVkUFxf7HYYJM1V9AXjB7zjM4bH1yaHiLimkp6dTVlbmdxjGmARg65NDxd3uI2OMMZFjScEYY0wrSwrGGGNaSSwfdReRGmBjO08PAGJheLNYiQMsllA6iqNEVQuiGUxAB307Vj43sFhCiZU4IEJ9O6aTQkdEZJGqTrY4DrJYYjeOroqleC2W2I0DIheL7T4yxhjTypKCMcaYVvGcFB7wOwAnVuIAiyWUWImjq2IpXovlULESB0Qolrg9pmCMMSb84nlLwRhjTJhZUjDGGNMq7pJCOAdI72AZQ0XkdRFZJSIrRORa136riHwqIh+624yg19zkYlojIl8MV7wiskFElrnlLXJt/UXkFRFZ6/7muXYRkTluWUtFZFLQfC5x068VkUu6EcfooPf9oYjsFpHrovWZiMgjIrJVRJYHtYXtcxCRY93nXO5eG2rgnIiKdN+OpX7t5uF737Z+HYKqxs0NSAXWAcOBDOAjYFwEllMETHL3+wAf4w3IfitwfYjpx7lYMoEyF2NqOOIFNgAD2rTdAdzo7t8I3O7uzwBexBsJ7ATgXdfeH1jv/ua5+3k9/D9sAUqi9ZkApwCTgOWR+ByA94AT3WteBKYnWt+OpX4di33b+rV3i7cthbAMkN4ZVa1S1Q/c/T1418gf0sFLZgJPquoBVf0EKHexRiremcBj7v5jwKyg9sfV8w7QT0SKgC8Cr6hqraruAF4BpvVg+WcA61S1vWrzQCxh+0xUdQFQG2IZPf4c3HO5qrpQvW/S40HzipaI9+046NeBZfrVt61fE3+7j0INkN5Rp+4xESkFJgLvuqar3KbbI4HNug7iCke8CrwsIovFG/gdYKCqVoH3RQcKoxBHsAuAuUGPo/2ZBITrcxji7ocjpu6Kat+OgX4Nsde3rV8Tf0mhSwOkh21hIjnA34DrVHU3cB9wBHAMUAX8TydxhSPeqao6CZgOfFdETuko5AjG4S3AG27yS8BfXJMfn0mnYR7msqPar9oRtRhipF9DDPVt69cHxVtSiNoA6SKSjvfF+ZOqPg2gqtWq2qyqLcCDeJuMHcXV43hVdbP7uxV4xi2z2m0a4v5ujXQcQaYDH6hqtYsr6p9JkHB9DpXufjhi6q6o9O1Y6dduubHUt61fB3R20CGWbngjxa3HO8ATOJgzPgLLEbz9b3e1aS8Kuv89vH2LAOP57MGn9XgHnnoUL9Ab6BN0/228/aW/5rMHou5w98/mswei3tODB6I+wTsIlefu9+/mZ/Mk8E0/PhOglM8ekAvb5wC876YNHJCbkWh9O1b6dSz2bevXQfFEs+OHqWPPwDtrYh1wc4SWcTLeZtZS4EN3mwE8ASxz7fPadJybXUxrCDrC35N48c5k+MjdVgReD+QDrwJr3d9ABxDgHresZcDkoHldindQrDy48x9mPL2A7UDfoLaofCZ4+3qrgEa8X0CXhfNzACYDy91r7sZV+ydS346Vfh1rfdv69WdvdpkLY4wxreLtmIIxxpgIsqRgjDGmlSUFY4wxrSwpGGOMaWVJwRhjTCtLCsYYY1pZUjDGGNPq/wOgSJqQfLC7JQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "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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\n", + "text/plain": [ + "" + ] + }, + "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 +} diff --git a/notebook.tex b/notebook.tex new file mode 100644 index 0000000..61af298 --- /dev/null +++ b/notebook.tex @@ -0,0 +1,456 @@ + +% Default to the notebook output style + + + + +% Inherit from the specified cell style. + + + + + +\documentclass[11pt]{article} + + + + \usepackage[T1]{fontenc} + % Nicer default font (+ math font) than Computer Modern for most use cases + \usepackage{mathpazo} + + % Basic figure setup, for now with no caption control since it's done + % automatically by Pandoc (which extracts ![](path) syntax from Markdown). + \usepackage{graphicx} + % We will generate all images so they have a width \maxwidth. This means + % that they will get their normal width if they fit onto the page, but + % are scaled down if they would overflow the margins. + \makeatletter + \def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth + \else\Gin@nat@width\fi} + \makeatother + \let\Oldincludegraphics\includegraphics + % Set max figure width to be 80% of text width, for now hardcoded. + \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} + % Ensure that by default, figures have no caption (until we provide a + % proper Figure object with a Caption API and a way to capture that + % in the conversion process - todo). + \usepackage{caption} + \DeclareCaptionLabelFormat{nolabel}{} + \captionsetup{labelformat=nolabel} + + \usepackage{adjustbox} % Used to constrain images to a maximum size + \usepackage{xcolor} % Allow colors to be defined + \usepackage{enumerate} % Needed for markdown enumerations to work + \usepackage{geometry} % Used to adjust the document margins + \usepackage{amsmath} % Equations + \usepackage{amssymb} % Equations + \usepackage{textcomp} % defines textquotesingle + % Hack from http://tex.stackexchange.com/a/47451/13684: + \AtBeginDocument{% + \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code + } + \usepackage{upquote} % Upright quotes for verbatim code + \usepackage{eurosym} % defines \euro + \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support + \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document + \usepackage{fancyvrb} % verbatim replacement that allows latex + \usepackage{grffile} % extends the file name processing of package graphics + % to support a larger range + % The hyperref package gives us a pdf with properly built + % internal navigation ('pdf bookmarks' for the table of contents, + % internal cross-reference links, web links for URLs, etc.) + \usepackage{hyperref} + \usepackage{longtable} % longtable support required by pandoc >1.10 + \usepackage{booktabs} % table support for pandoc > 1.12.2 + \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) + \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) + % normalem makes italics be italics, not underlines + + + + + % Colors for the hyperref package + \definecolor{urlcolor}{rgb}{0,.145,.698} + \definecolor{linkcolor}{rgb}{.71,0.21,0.01} + \definecolor{citecolor}{rgb}{.12,.54,.11} + + % ANSI colors + \definecolor{ansi-black}{HTML}{3E424D} + \definecolor{ansi-black-intense}{HTML}{282C36} + \definecolor{ansi-red}{HTML}{E75C58} + \definecolor{ansi-red-intense}{HTML}{B22B31} + \definecolor{ansi-green}{HTML}{00A250} + \definecolor{ansi-green-intense}{HTML}{007427} + \definecolor{ansi-yellow}{HTML}{DDB62B} + \definecolor{ansi-yellow-intense}{HTML}{B27D12} + \definecolor{ansi-blue}{HTML}{208FFB} + \definecolor{ansi-blue-intense}{HTML}{0065CA} + \definecolor{ansi-magenta}{HTML}{D160C4} + \definecolor{ansi-magenta-intense}{HTML}{A03196} + \definecolor{ansi-cyan}{HTML}{60C6C8} + \definecolor{ansi-cyan-intense}{HTML}{258F8F} + \definecolor{ansi-white}{HTML}{C5C1B4} + \definecolor{ansi-white-intense}{HTML}{A1A6B2} + + % commands and environments needed by pandoc snippets + % extracted from the output of `pandoc -s` + \providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} + \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} + % Add ',fontsize=\small' for more characters per line + \newenvironment{Shaded}{}{} + \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}} + \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + 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+\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} + +\def\PYZbs{\char`\\} +\def\PYZus{\char`\_} +\def\PYZob{\char`\{} +\def\PYZcb{\char`\}} +\def\PYZca{\char`\^} +\def\PYZam{\char`\&} +\def\PYZlt{\char`\<} +\def\PYZgt{\char`\>} +\def\PYZsh{\char`\#} +\def\PYZpc{\char`\%} +\def\PYZdl{\char`\$} +\def\PYZhy{\char`\-} +\def\PYZsq{\char`\'} +\def\PYZdq{\char`\"} +\def\PYZti{\char`\~} +% for compatibility with earlier versions +\def\PYZat{@} +\def\PYZlb{[} +\def\PYZrb{]} +\makeatother + + + % Exact colors from NB + \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} + \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} + + + + + % Prevent overflowing lines due to hard-to-break entities + \sloppy + % Setup hyperref package + \hypersetup{ + breaklinks=true, % so long urls are correctly broken across lines + colorlinks=true, + urlcolor=urlcolor, + linkcolor=linkcolor, + citecolor=citecolor, + } + % Slightly bigger margins than the latex defaults + + \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} + + + + \begin{document} + + + \maketitle + + + + + \section{Ring Resonator Dynamics}\label{ring-resonator-dynamics} + +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. + +P.S.: We split the time to discrete step of each round trip of light in +the ring. + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}1}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} + \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} + \PY{o}{\PYZpc{}}\PY{k}{matplotlib} inline + + \PY{n}{T} \PY{o}{=} \PY{l+m+mf}{0.99} + \PY{n}{K} \PY{o}{=} \PY{l+m+mi}{1} \PY{o}{\PYZhy{}} \PY{n}{T} + \PY{n}{Alpha} \PY{o}{=} \PY{l+m+mf}{0.99} + \PY{n}{t} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{n}{T}\PY{p}{)} \PY{o}{+} \PY{l+m+mf}{0.0}\PY{n}{j} + \PY{n}{k} \PY{o}{=} \PY{l+m+mf}{0.0} \PY{o}{+} \PY{l+m+mi}{1}\PY{n}{j} \PY{o}{*} \PY{n}{np}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{)} + \PY{n}{alpha} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{n}{Alpha}\PY{p}{)} + \PY{n}{theta} \PY{o}{=} \PY{l+m+mf}{2.0} \PY{o}{*} \PY{n}{np}\PY{o}{.}\PY{n}{pi} +\end{Verbatim} + + + We define a function to generate the time series of a1, a2, b1 \& a2:\\ +\textbf{a{[}n{]} =\textgreater{} {[}a1(n-step), a2(n-step){]}}\\ +\textbf{b{[}n{]} =\textgreater{} {[}b1(n-step), b2(n-step){]}} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}2}]:} \PY{k}{def} \PY{n+nf}{propagate\PYZus{}in\PYZus{}cycle}\PY{p}{(}\PY{n}{t}\PY{p}{,} \PY{n}{k}\PY{p}{,} \PY{n}{alpha}\PY{p}{,} \PY{n}{theta}\PY{p}{,} \PY{n}{num\PYZus{}cycle} \PY{o}{=} \PY{l+m+mi}{1000}\PY{p}{)}\PY{p}{:} + \PY{n}{a1\PYZus{}0} \PY{o}{=} \PY{l+m+mf}{1.0} \PY{o}{+} \PY{l+m+mf}{0.0}\PY{n}{j} + \PY{n}{a2\PYZus{}0} \PY{o}{=} \PY{l+m+mf}{0.0} \PY{o}{+} \PY{l+m+mf}{0.0}\PY{n}{j} + \PY{n}{a} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{p}{(}\PY{n}{num\PYZus{}cycle}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{complex}\PY{p}{)} + \PY{n}{b} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{p}{(}\PY{n}{num\PYZus{}cycle}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{complex}\PY{p}{)} + + \PY{n}{a}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{=} \PY{p}{[}\PY{n}{a1\PYZus{}0}\PY{p}{,} \PY{n}{a2\PYZus{}0}\PY{p}{]} + + \PY{n}{coupler} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{k}\PY{p}{]}\PY{p}{,} + \PY{p}{[}\PY{o}{\PYZhy{}}\PY{n}{k}\PY{o}{.}\PY{n}{conjugate}\PY{p}{(}\PY{p}{)}\PY{p}{,} \PY{n}{t}\PY{o}{.}\PY{n}{conjugate}\PY{p}{(}\PY{p}{)}\PY{p}{]}\PY{p}{]}\PY{p}{)} + + \PY{k}{for} \PY{n}{n} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{num\PYZus{}cycle} \PY{o}{\PYZhy{}} \PY{l+m+mi}{1}\PY{p}{)}\PY{p}{:} + \PY{n}{b}\PY{p}{[}\PY{n}{n}\PY{p}{]} \PY{o}{=} \PY{n}{coupler}\PY{n+nd}{@a}\PY{p}{[}\PY{n}{n}\PY{p}{]} + \PY{n}{a}\PY{p}{[}\PY{n}{n}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{a1\PYZus{}0}\PY{p}{,} \PY{n}{b}\PY{p}{[}\PY{n}{n}\PY{p}{]}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{*} \PY{n}{alpha} \PY{o}{*} \PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{l+m+mf}{1.}\PY{n}{j} \PY{o}{*} \PY{n}{theta}\PY{p}{)}\PY{p}{]}\PY{p}{)} + + \PY{n}{b}\PY{p}{[}\PY{n}{num\PYZus{}cycle} \PY{o}{\PYZhy{}} \PY{l+m+mi}{1}\PY{p}{]} \PY{o}{=} \PY{n}{coupler}\PY{n+nd}{@a}\PY{p}{[}\PY{n}{num\PYZus{}cycle} \PY{o}{\PYZhy{}} \PY{l+m+mi}{1}\PY{p}{]} + + \PY{k}{return} \PY{n}{a}\PY{p}{,} \PY{n}{b} + + \PY{n}{a}\PY{p}{,} \PY{n}{b} \PY{o}{=} \PY{n}{propagate\PYZus{}in\PYZus{}cycle}\PY{p}{(}\PY{n}{t}\PY{o}{=}\PY{n}{t}\PY{p}{,} \PY{n}{k}\PY{o}{=}\PY{n}{k}\PY{p}{,} \PY{n}{alpha}\PY{o}{=}\PY{n}{alpha}\PY{p}{,} \PY{n}{theta}\PY{o}{=}\PY{n}{theta}\PY{p}{,} \PY{n}{num\PYZus{}cycle} \PY{o}{=} \PY{l+m+mi}{1000}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{121}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{a}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{b}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{yscale}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{log}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a1 \PYZam{} b1 in Bus WG}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{122}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{a}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a2}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{b}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b2}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a2 \PYZam{} b2 in Resonator}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{yscale}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{linear}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)} + + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} +\end{Verbatim} + + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_3_0.png} + \end{center} + { \hspace*{\fill} \\} + + 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). + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}3}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{p}{)} + \PY{n}{bus\PYZus{}output} \PY{o}{=} \PY{n+nb}{abs}\PY{p}{(}\PY{n}{b}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{o}{/}\PY{n}{a}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} + \PY{n}{gain\PYZus{}per\PYZus{}cycle} \PY{o}{=} \PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{b}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} \PY{o}{\PYZhy{}} \PY{n+nb}{abs}\PY{p}{(}\PY{n}{a}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{/}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{a}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} + + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{bus\PYZus{}output}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Bus WG Output}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{gain\PYZus{}per\PYZus{}cycle}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Energy gain of ring after coupler per cycle}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{bus\PYZus{}output} \PY{o}{+} \PY{n}{gain\PYZus{}per\PYZus{}cycle}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Sum of both}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} +\end{Verbatim} + + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_5_0.png} + \end{center} + { \hspace*{\fill} \\} + + We can see that the bus waveguide output power:\\ +\textbf{enegry loss from the ring via coupler + enegry from a1 does not +coupled to the ring} + +is same as the enegry gain of the ring after coupler:\\ +\textbf{enegry gain from bus waveguide + energy of the ring does not +coupled out to bus waveguide} + +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., \textbar{}t\textbar{}\^{}2 + \textbar{}k\textbar{}\^{}2 = +1)\\ +It is an interesting constructive \& distructive interference porporty +of wave 😉 + + \subsubsection{Play with other +parameters}\label{play-with-other-parameters} + +Enjoy\textasciitilde{} 😊 + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}4}]:} \PY{n}{T2} \PY{o}{=} \PY{l+m+mf}{0.999} + \PY{n}{K2} \PY{o}{=} \PY{l+m+mi}{1} \PY{o}{\PYZhy{}} \PY{n}{T2} + \PY{n}{Alpha2} \PY{o}{=} \PY{l+m+mf}{0.999} + \PY{n}{t2} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{n}{T2}\PY{p}{)} \PY{o}{+} \PY{l+m+mf}{0.0}\PY{n}{j} + \PY{n}{k2} \PY{o}{=} \PY{l+m+mf}{0.0} \PY{o}{+} \PY{l+m+mi}{1}\PY{n}{j} \PY{o}{*} \PY{n}{np}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{n}{K2}\PY{p}{)} + \PY{n}{alpha2} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{n}{Alpha2}\PY{p}{)} + \PY{n}{theta2} \PY{o}{=} \PY{l+m+mf}{2.0} \PY{o}{*} \PY{n}{np}\PY{o}{.}\PY{n}{pi} + \PY{n}{a2}\PY{p}{,} \PY{n}{b2} \PY{o}{=} \PY{n}{propagate\PYZus{}in\PYZus{}cycle}\PY{p}{(}\PY{n}{t}\PY{o}{=}\PY{n}{t2}\PY{p}{,} \PY{n}{k}\PY{o}{=}\PY{n}{k2}\PY{p}{,} \PY{n}{alpha}\PY{o}{=}\PY{n}{alpha2}\PY{p}{,} \PY{n}{theta}\PY{o}{=}\PY{n}{theta2}\PY{p}{,} \PY{n}{num\PYZus{}cycle} \PY{o}{=} \PY{l+m+mi}{10000}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{121}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{a2}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{b2}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{yscale}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{log}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a1 \PYZam{} b1 in Bus WG}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{subplot}\PY{p}{(}\PY{l+m+mi}{122}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{a2}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a2}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{b2}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b2}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{a2 \PYZam{} b2 in Resonator}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{yscale}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{linear}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)} + + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} +\end{Verbatim} + + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_8_0.png} + \end{center} + { \hspace*{\fill} \\} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}5}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{p}{)} + \PY{n}{bus\PYZus{}output} \PY{o}{=} \PY{n+nb}{abs}\PY{p}{(}\PY{n}{b2}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{o}{/}\PY{n}{a2}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} + \PY{n}{gain\PYZus{}per\PYZus{}cycle} \PY{o}{=} \PY{p}{(}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{b2}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} \PY{o}{\PYZhy{}} \PY{n+nb}{abs}\PY{p}{(}\PY{n}{a2}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{/}\PY{n+nb}{abs}\PY{p}{(}\PY{n}{a2}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} + + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{bus\PYZus{}output}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Bus WG Output}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{gain\PYZus{}per\PYZus{}cycle}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Energy gain of ring after coupler per cycle}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{bus\PYZus{}output} \PY{o}{+} \PY{n}{gain\PYZus{}per\PYZus{}cycle}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Sum of both}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} +\end{Verbatim} + + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_9_0.png} + \end{center} + { \hspace*{\fill} \\} + + + % Add a bibliography block to the postdoc + + + + \end{document} diff --git a/output_3_0.png b/output_3_0.png new file mode 100644 index 0000000..3f12a88 Binary files /dev/null and b/output_3_0.png differ diff --git a/output_5_0.png b/output_5_0.png new file mode 100644 index 0000000..850e247 Binary files /dev/null and b/output_5_0.png differ diff --git a/output_8_0.png b/output_8_0.png new file mode 100644 index 0000000..128e1db Binary files /dev/null and b/output_8_0.png differ diff --git a/output_9_0.png b/output_9_0.png new file mode 100644 index 0000000..2027728 Binary files /dev/null and b/output_9_0.png differ diff --git a/ref/simple_anim.py b/ref/simple_anim.py new file mode 100644 index 0000000..59552cd --- /dev/null +++ b/ref/simple_anim.py @@ -0,0 +1,41 @@ +""" +================== +Animated line plot +================== + +""" + +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.animation as animation + +fig, ax = plt.subplots() + +x = np.arange(0, 2*np.pi, 0.01) +line, = ax.plot(x, np.sin(x)) + + +def init(): # only required for blitting to give a clean slate. + line.set_ydata([np.nan] * len(x)) + return line, + + +def animate(i): + line.set_ydata(np.sin(x + i / 100)) # update the data. + return line, + + +ani = animation.FuncAnimation( + fig, animate, init_func=init, interval=2, blit=True, save_count=50) + +# To save the animation, use e.g. +# +# ani.save("movie.mp4") +# +# or +# +# from matplotlib.animation import FFMpegWriter +# writer = FFMpegWriter(fps=15, metadata=dict(artist='Me'), bitrate=1800) +# ani.save("movie.mp4", writer=writer) + +plt.show() diff --git a/ref/strip_chart.py b/ref/strip_chart.py new file mode 100644 index 0000000..8e9bf2d --- /dev/null +++ b/ref/strip_chart.py @@ -0,0 +1,62 @@ +""" +============ +Oscilloscope +============ + +Emulates an oscilloscope. +""" + +import numpy as np +from matplotlib.lines import Line2D +import matplotlib.pyplot as plt +import matplotlib.animation as animation + + +class Scope(object): + def __init__(self, ax, maxt=2, dt=0.02): + self.ax = ax + self.dt = dt + self.maxt = maxt + self.tdata = [0] + self.ydata = [0] + self.line = Line2D(self.tdata, self.ydata) + self.ax.add_line(self.line) + self.ax.set_ylim(-.1, 1.1) + self.ax.set_xlim(0, self.maxt) + + def update(self, y): + lastt = self.tdata[-1] + if lastt > self.tdata[0] + self.maxt: # reset the arrays + self.tdata = [self.tdata[-1]] + self.ydata = [self.ydata[-1]] + self.ax.set_xlim(self.tdata[0], self.tdata[0] + self.maxt) + self.ax.figure.canvas.draw() + + t = self.tdata[-1] + self.dt + self.tdata.append(t) + self.ydata.append(y) + self.line.set_data(self.tdata, self.ydata) + return self.line, + + +def emitter(p=0.03): + 'return a random value with probability p, else 0' + while True: + v = np.random.rand(1) + if v > p: + yield 0. + else: + yield np.random.rand(1) + +# Fixing random state for reproducibility +np.random.seed(19680801) + + +fig, ax = plt.subplots() +scope = Scope(ax) + +# pass a generator in "emitter" to produce data for the update func +ani = animation.FuncAnimation(fig, scope.update, emitter, interval=10, + blit=True) + +plt.show() diff --git a/result_autocorr.csv b/result_autocorr.csv new file mode 100644 index 0000000..0daf5a2 --- /dev/null +++ b/result_autocorr.csv @@ -0,0 +1,3 @@ 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diff --git a/result_freq.dat b/result_freq.dat new file mode 100644 index 0000000..78f99ad --- /dev/null +++ b/result_freq.dat @@ -0,0 +1,5 @@ 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diff --git a/result_time.csv b/result_time.csv new file mode 100644 index 0000000..57bee74 --- /dev/null +++ b/result_time.csv @@ -0,0 +1,4 @@ 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diff --git a/result_time.dat b/result_time.dat new file mode 100644 index 0000000..c6c6664 --- /dev/null +++ b/result_time.dat @@ -0,0 +1,4 @@ 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diff --git a/split_step_fourier_method.py b/split_step_fourier_method.py new file mode 100644 index 0000000..4435d86 --- /dev/null +++ b/split_step_fourier_method.py @@ -0,0 +1,193 @@ +# -*- coding: utf-8 -*- +""" +Created on Sun Mar 18 00:49:54 2018 + +@author: chris + +This code solves the NLS equation with the split-step Fourier method based +on Govind P. Agrawal in March 2005 for the Nonlinear fiber optics book (Appendix B) +""" +import numpy as np +import matplotlib.pyplot as plt +import time + +# ---Specify input parameters +distance = 150. # Enter fiber length (in units of L_c)= +# Normalized 2nd-dispersion: kappa=beta2*f^2*L/2): +# +ve for normal,-ve for anomalous*) +kappa = -0.001 +sigma = 0. # Normalized 3rd-dispersion: sigma=beta3*f^3*L/6 +G = 1. # small signal gain of Ramam Amp: G=g*L +Is = 1. # gain saturation parameter +alpha = 0.4 # Normalized fiber amplitude absorption coeff: alpha=l*L + +# Nonlinear parameter n=') +# sqrt(L_D/L_NL)=sqrt(gamma*P0*T0^2/|beta2|) or QT: n=kappa^0.5 +n = 2. ** 0.5 + +# ---Specify filter parameters +bdwidth = 2. * np.pi * 6. +delta = 2. * np.pi * 0.5 +a = np.log(np.sqrt(0.95)) +perta = 0.3 +pertfsr = 0.17 +T = 0.2 +t = np.sqrt(T) +r = 1.j * np.sqrt(1. - T) + +# ---Specify input parameters +mshape = -1. # m=0 for sech,m>0 for super-Gaussian= +chirp0 = 0. # % input pulse chirp (default value) + +# P = 1/(gamma*L); (P is the ref peak power); +# uu = A/sqrt(P); +# z = z0/L_c; (z0 is the real length, L_c is the cavity length); +# tau = f*t; (t is the time of reference traveling frame); + + +# ---set simulation parameters +nt = 2 ** 13 # % FFT points (powers of 2) +Tmax = 100. # (half) window size +stepno = 1 * round(20 * distance * n ** 2) # No.of z steps to +dz = distance / stepno # step size in z +dtau = (2. * Tmax) / nt # step size in tau + +Twin = 5. +fmax = (1. / (2. * Tmax)) * nt / 2. +fwin = 5. + +filterz = 0.5 +plotz = 5 + +# ---tau and omega arrays +tau = np.arange(-nt / 2., nt / 2.) * dtau # temporal grid +# [(0:nt/2-1) (-nt/2:-1)] +omega = (np.pi / Tmax) * \ + np.append(np.arange(0.0, nt / 2.), np.arange(-nt / 2., 0.0)) + +# frequency grid +delaytau = dtau * np.arange(-round(Twin / dtau), round(Twin / dtau) + 1) + +# Input Field profile +if mshape == 0: + # ;% soliton + uu = np.exp(-0.5j * chirp0 * tau ** 2.) / np.cosh(tau) +elif mshape > 0: + # super-Gaussian + uu = np.exp(-0.5 * (1. + 1.j * chirp0) * tau ** (2. * mshape)) +else: + # White noise + uu = (np.random.randn(nt) + 1.j * np.random.randn(nt)) * np.sqrt(0.5) + +# temp = np.fft.fftshift(np.fft.ifft(uu) * (nt * dtau) / np.sqrt(2. * np.pi)) +tempomega = np.fft.fftshift(omega) + +# ---store dispersive phase shifts to speedup code +# % nonlinear phase factor +dispersion = np.exp((-alpha + 1.j * kappa * omega ** 2. + + 1.j * sigma * omega ** 3.) * dz) + +# comb filter type +# original comb filter + BPF +# filtert = np.exp(-omega ** 2. / bdwidth ** 2.) * (t ** 2.) / \ +# (1 - r ** 2 * np.exp(-1.j * (omega + delta) + a)) + +# perturbated comb filter + BPF +filtert = np.exp(-omega ** 2. / bdwidth ** 2. - + perta * np.sin(0.5 * omega / pertfsr) ** 2) * \ + (t ** 2) / (1.0 - r ** 2 * np.exp(-1.j * (omega + delta) + a)) + +fig1 = plt.figure() +plt.plot(tempomega / (2. * np.pi), + np.fft.fftshift(10. * np.log10(np.abs(filtert) ** 2.))) +plt.title("Perturbated comb filter + BPF") +plt.xlim(-fwin, fwin) +plt.xlim(-fwin, fwin) +plt.ylim(-30., 10.) +plt.show() + +# %*********[Beginning of MAIN Loop]*********** +# % scheme:1/2N\[Rule]D\[Rule]1/2N;first half step nonlinear +temp = uu * np.exp((1.j * np.abs(uu) ** 2. + + G / (1.0 + np.abs(uu) ** 2. / Is)) * dz / 2.) +# % note hhz/2 + +start_time = time.time() +time_used = time.time() - start_time +z = 0 + +# Realtime monitoring the simulation progress +plt.figure() +fig2, ((ax1, ax2), (ax3, ax4), (ax5, ax6)) = plt.subplots(3, 2) +plt.tight_layout() +abs_temp = np.abs(temp) +autocorr0 = None +line1, = ax1.plot(abs_temp) +line2, = ax2.plot(abs_temp) +line3, = ax3.plot(abs_temp) +line4, = ax4.plot(abs_temp) +line5, = ax5.plot(abs_temp) +plt.ion() + +for i in range(stepno): + if round((z % 1 - filterz) / dz) == 0: + ftemp = np.fft.ifft(temp) * filtert * dispersion + else: + ftemp = np.fft.ifft(temp) * dispersion + + uu = np.fft.fft(ftemp) + temp = uu * np.exp((1.j * np.abs(uu) ** 2. + G / (1.0 + np.abs(uu) ** 2 / Is)) * dz) + z = z + dz + + if round((z % plotz) / dz) == 0 or round(((z % plotz) - plotz) / dz) == 0: + time_used = time.time() - start_time + print("Z: " + str(z)) + # fig2.suptitle("i = " + str(i) + ", z = " + str(z) + " Time: " + str(time_used)) + + line1.set_data(tau, np.abs(temp) ** 2.) + ax1.relim() + ax1.autoscale_view(True, True, True) + ax1.set_xlim([-Twin, Twin]) + ax1.set_title("Time domain (Magnified)") + + ftemp0 = np.fft.fftshift(ftemp * (nt * dtau) / np.sqrt(2 * np.pi)) + + line2.set_data(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0) ** 2.)) + # + ax2.relim() + ax2.autoscale_view(True, True, True) + ax2.set_xlim([-fwin, fwin]) + ax2.set_title("Spectrum (Magnified)") + + line3.set_data(tau, np.abs(temp) ** 2) + ax3.relim() + ax3.autoscale_view(True, True, True) + ax3.set_xlim([-Tmax, Tmax]) + ax3.set_title("Time domain (Full Scale)") + + line4.set_data(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0) ** 2.)) + ax4.relim() + ax4.autoscale_view(True, True, True) + ax4.set_xlim([-fmax, fmax]) + ax4.set_title("Spectrum (Full Scale)") + + autocorr0 = np.fft.fftshift( + np.fft.ifft(np.fft.fft(np.abs(temp) ** 2) * np.conjugate(np.fft.fft(np.abs(temp) ** 2)))) + + line5.set_data(tau, np.abs(autocorr0) / max(np.abs(autocorr0))) + ax5.relim() + ax5.autoscale_view(True, True, True) + ax5.set_xlim([-Twin, Twin]) + ax5.set_title("Autocorrelation") + + plt.pause(0.1) +plt.ioff() +plt.show() + + +# Exporting results +fname = "result" # file name +np.savetxt(fname + "_time.csv", (tau, np.real(uu), np.imag(uu), np.abs(uu) ** 2), delimiter=",") +np.savetxt(fname + "_freq.csv", (tempomega / (2. * np.pi), np.real(temp), np.imag(temp), + np.abs(temp) ** 2, np.fft.fftshift(np.abs(filtert) ** 2.)), delimiter=",") +np.savetxt(fname + "_autocorr.csv", (tau, np.abs(autocorr0), np.abs(autocorr0) / max(np.abs(autocorr0))), delimiter=",") diff --git a/split_step_fourier_method_v0.py b/split_step_fourier_method_v0.py new file mode 100644 index 0000000..7270a7c --- /dev/null +++ b/split_step_fourier_method_v0.py @@ -0,0 +1,177 @@ +# -*- coding: utf-8 -*- +""" +Created on Sun Mar 18 00:49:54 2018 + +@author: chris + +This code solves the NLS equation with the split-step Fourier method based +on Govind P. Agrawal in March 2005 for the NLFO book +""" +import numpy as np +import matplotlib.pyplot as plt +import time + +# ---Specify input parameters +distance = 150. # Enter fiber length (in units of L_c)= +# Normalized 2nd-dispersion: kappa=beta2*f^2*L/2): +# +ve for normal,-ve for anomalous*) +kappa = -0.001 +sigma = 0. # Normalized 3rd-dispersion: sigma=beta3*f^3*L/6 +G = 1. # small signal gain of Ramam Amp: G=g*L +Is = 1. # gain saturation parameter +alpha = 0.4 # Normalized fiber amplitude absorption coeff: alpha=l*L + + +# Nonlinear parameter n=') +# sqrt(L_D/L_NL)=sqrt(gamma*P0*T0^2/|beta2|) or QT: n=kappa^0.5 +n = 2. ** 0.5 + + +# ---Specify filter parameters +bdwidth = 2. * np.pi * 6. +delta = 2. * np.pi * 0.5 +a = np.log(np.sqrt(0.95)) +perta = 0.3 +pertfsr = 0.17 +T = 0.2 +t = np.sqrt(T) +r = 1.j * np.sqrt(1. - T) + + +# ---Specify input parameters +mshape = -1. # m=0 for sech,m>0 for super-Gaussian= +chirp0 = 0. # % input pulse chirp (default value) + + +# P = 1/(gamma*L); (P is the ref peak power); +# uu = A/sqrt(P); +# z = z0/L_c; (z0 is the real length, L_c is the cavity length); +# tau = f*t; (t is the time of reference traveling frame); + + +# ---set simulation parameters +nt = 2 ** 13 # % FFT points (powers of 2) +Tmax = 100. # (half) window size +stepno = 1 * round(20 * distance * n ** 2) # No.of z steps to +dz = distance / stepno # step size in z +dtau = (2. * Tmax) / nt # step size in tau + + +Twin = 5. +fmax = (1. / (2. * Tmax)) * nt / 2. +fwin = 5. + +filterz = 0.5 +plotz = 5 + +# ---tau and omega arrays +tau = np.arange(-nt / 2., nt / 2.) * dtau # temporal grid +# [(0:nt/2-1) (-nt/2:-1)] +omega = (np.pi / Tmax) * \ + np.append(np.arange(0.0 , nt / 2.), np.arange(-nt / 2., 0.0)) + + +# frequency grid +delaytau = dtau * np.arange(-round(Twin / dtau), round(Twin / dtau) + 1) + + +# Input Field profile +if mshape == 0: + # ;% soliton + uu = np.exp(-0.5j * chirp0 * tau ** 2.) / np.cosh(tau) +elif mshape > 0: + # super-Gaussian + uu = np.exp(-0.5 * (1. + 1.j * chirp0) * tau ** (2. * mshape)) +else: + # White noise + uu = (np.random.randn(nt) + 1.j * np.random.randn(nt)) * np.sqrt(0.5) + + +temp = np.fft.fftshift(np.fft.ifft(uu) * (nt * dtau) / np.sqrt(2.* np.pi)) +tempomega = np.fft.fftshift(omega) + + +# ---store dispersive phase shifts to speedup code +# % nonlinear phase factor +dispersion = np.exp((-alpha + 1.j * kappa * omega **2. + \ + 1.j * sigma * omega ** 3.) * dz) + +# comb filter type +# original comb filter + BPF +# filtert = np.exp(-omega ** 2. / bdwidth ** 2.) * (t ** 2.) / \ +# (1 - r ** 2 * np.exp(-1.j * (omega + delta) + a)) + +# perturbated comb filter + BPF +filtert = np.exp(-omega ** 2. / bdwidth ** 2. - \ + perta * np.sin(0.5 * omega / pertfsr) ** 2) * \ + (t ** 2) / (1.0 - r ** 2 * np.exp(-1.j*(omega + delta) + a)) + +plt.figure() +plt.plot(tempomega / (2. * np.pi), + np.fft.fftshift(10. * np.log10(np.abs(filtert) ** 2.))) +plt.xlim(-fwin, fwin) +plt.xlim(-fwin, fwin) +plt.ylim(-30., 10.) +plt.show() + +# %*********[Beginning of MAIN Loop]*********** +# % scheme:1/2N\[Rule]D\[Rule]1/2N;first half step nonlinear +temp = uu * np.exp((1.j * np.abs(uu) ** 2. + + G / (1.0 + np.abs(uu) ** 2. / Is )) * dz / 2.) +# % note hhz/2 + +start_time = time.time() +time_used = time.time() - start_time +z = 0 + + +# Realtime monitoring the simulation progress + + +plt.ion() +fig, ((ax1, ax2), (ax3, ax4), (ax5, ax6)) = plt.subplots(3, 2) +for i in range(stepno): + if round((z % 1 - filterz)/dz) == 0: + ftemp = np.fft.ifft(temp) * filtert * dispersion + else: + ftemp = np.fft.ifft(temp) * dispersion + + uu = np.fft.fft(ftemp) + temp = uu*np.exp((1.j * np.abs(uu)**2. + G / (1.0 + np.abs(uu)**2 / Is)) * dz) + z = z + dz + + if round((z % plotz) / dz) == 0 or round(((z % plotz) - plotz) / dz) == 0: + time_used = time.time() - start_time + print(i) + + ax1.clear() + ax1.plot(tau, np.abs(temp)**2.) + ax1.set_xlim([-Twin, Twin]) + ax1.set_title("i = " + str(i) + ", z = " + str(z)) + + ftemp0 = np.fft.fftshift(ftemp * (nt * dtau) / np.sqrt(2 * np.pi)) + + ax2.clear() + ax2.plot(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0)**2.)) + ax2.set_xlim([-fwin, fwin]) + ax2.set_title(" Time = " + str(time_used)) + + ax3.clear() + ax3.plot(tau, np.abs(temp)**2) + ax3.set_xlim([-Tmax, Tmax]) + ax3.set_title("i = " + str(i) + ", z = " + str(z)) + + ax4.clear() + ax4.plot(tempomega / (2. * np.pi), 10. * np.log10(np.abs(ftemp0)**2.)) + ax4.set_xlim([-fmax, fmax]) + ax4.set_title(" Time = " + str(time_used)) + + autocorr0 = np.fft.fftshift( + np.fft.ifft(np.fft.fft(np.abs(temp)**2) * np.conjugate(np.fft.fft(np.abs(temp)**2)))) + + ax5.clear() + ax5.plot(tau, autocorr0 / max(autocorr0)) + ax5.set_xlim([-Twin, Twin]) + fig.canvas.draw() + # PlotRange -> {{-Twin, Twin}, All}, Frame -> True]; + diff --git a/tmp.py b/tmp.py new file mode 100644 index 0000000..d480db8 --- /dev/null +++ b/tmp.py @@ -0,0 +1 @@ +print(1.3%1.0) \ No newline at end of file