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1007008950‐wong chi yan‐201308‐phd‐fulltext.pdf
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1007008950‐wong chi yan‐201308‐phd‐fulltext.pdf
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1007008950‐wong chi yan‐201308‐phd‐thesis (updated).docx
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1007008950‐wong chi yan‐201308‐phd‐thesis (updated).docx
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mathematica_code.txt
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mathematica_code.txt
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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:
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(* This code solves the NLS equation with the split-step Fourier method
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based on Govind P. Agrawal in March 2005 for the NLFO book
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*)
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ClearAll["Global`*"]
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(*---Specify input parameters*)
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distance = 150.;(*Enter fiber length (in units of L_c)=*)
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kappa = -0.001 ;(*Normalized 2nd-dispersion: kappa=beta2*f^2*L/2): \
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+ve for normal,-ve for anomalous*)
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sigma = 0.; (*Normalized 3rd-dispersion: sigma=beta3*f^3*L/6 *)
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G = 1.0;(*small signal gain of Ramam Amp: G=g*L *)
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Is = 1.; (*gain saturation parameter*)
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alpha = 0.4; (*Normalized fiber amplitude absorption coeff: alpha=l*L*)
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n = 2.^0.5;(*Nonlinear parameter n=') \
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sqrt(L_D/L_NL)=sqrt(gamma*P0*T0^2/|beta2|) or QT: n=kappa^0.5*)
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(*---Specify filter parameters*)
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bdwidth = 2. Pi*6.;
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delta = 2. Pi*0.5;
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a = Log[Sqrt[0.95]];
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perta = 0.3;
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pertfsr = 0.17;
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T = 0.2;
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t = Sqrt[T];
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r = I*Sqrt[1 - T];
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(*---Specify input parameters*)
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mshape = -1.;(*m=0 for sech,m>0 for super-Gaussian=*)
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chirp0 = 0. ;(*% input pulse chirp (default value)*)
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(*
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P = 1/(gamma*L); (P is the ref peak power);
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uu = A/sqrt(P);
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z = z0/L_c; (z0 is the real length, L_c is the cavity length);
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tau = f*t; (t is the time of reference traveling frame);
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*)
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(*---set simulation parameters*)
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nt = 2^13; (*% FFT points (powers of 2)*)
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Tmax = 100.; (*(half) window size*)
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stepno = 1*Round[20*distance*n^2];(*No.of z steps to*)
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dz = distance/stepno;(*step size in z*)
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dtau = (2.*Tmax)/nt ;(*step size in tau*)
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Twin = 5.;
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fmax = (1./(2. Tmax))*nt/2.;
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fwin = 5.;
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filterz = 0.5;
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plotz = 5;
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(*---tau and omega arrays*)
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tau = N[Range[-nt/2, nt/2 - 1]]*dtau ;(*temporal grid*)
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omega = (1. \[Pi]/Tmax)*
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N[Join[Range[0, nt/2 - 1],
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Range[-nt/2, -1]]];(*[(0:nt/2-1) (-nt/2:-1)]*)
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(*frequency grid*)
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delaytau = dtau*Range[-Round[Twin/dtau], Round[Twin/dtau]];
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(*Input Field profile*)
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If[mshape == 0,
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(*;% soliton*)
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uu = Sech[tau]*Exp[-0.5 I*chirp0*tau^2.],
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If[ mshape > 0 ,
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(* super-Gaussian*)
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uu = Exp[-0.5*(1. + 1. I*chirp0)*tau^(2.*mshape)],
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(*White noise*)
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uu = (RandomReal[NormalDistribution[0, 1], nt] +
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I*RandomReal[NormalDistribution[0, 1], nt])*Sqrt[1./2.]
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]
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];
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temp = RotateRight[
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InverseFourier[uu, FourierParameters -> {1, -1}]*(nt*dtau)/
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Sqrt[2.*Pi], nt/2.];
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tempomega = RotateRight[omega, nt/2];
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(*---store dispersive phase shifts to speedup code*)
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dispersion =
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Exp[(-alpha + I*kappa*omega^2. + I*sigma*omega^3.)*
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dz];(*% nonlinear phase factor*)
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(*comb filter type*)
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(*original comb filter + BPF*)
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(*filtert= \
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Exp[-omega^2./bdwidth^2.]*(t^2)/(1-r^2*Exp[-I*(omega+delta)+a]);*)
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(*perturbated comb filter + BPF*)
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filtert = Exp[-omega^2./bdwidth^2. - perta*Sin[0.5
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*omega/pertfsr]^2]*(t^2)/(1 -
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r^2*Exp[-I*(omega + delta) + a]);
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p6 = ListLinePlot[
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Transpose[{tempomega/(2. Pi),
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RotateRight[10.*Log10[Abs[filtert]^2], nt/2]}],
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PlotRange -> {{-fwin, fwin}, {-30, 10}}, Frame -> True,
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ImageSize -> Automatic];
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(*%*********[Beginning of MAIN Loop]***********
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% scheme:1/2N\[Rule]D\[Rule]1/2N;first half step nonlinear*)
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temp = uu*
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Exp[(I*Abs[uu]^2. + G/(1.0 + Abs[uu]^2./Is))*dz/2.];(*% note hhz/2*)
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starttime = SessionTime[];
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timeused = SessionTime[] - starttime;
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z = 0;
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Monitor[ (* Realtime monitoring the simulation progress*)
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For[ i = 1, i <= stepno, i++,
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If[Round[(Mod[z, 1] - filterz )/dz] == 0 ,
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ftemp =
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InverseFourier[temp, FourierParameters -> {1, -1}]*filtert*
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dispersion;
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ftemp =
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InverseFourier[temp, FourierParameters -> {1, -1}]*dispersion;
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]
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uu = Fourier[ftemp, FourierParameters -> {1, -1}];
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temp = uu*Exp[(I*Abs[uu]^2. + G/(1.0 + Abs[uu]^2./Is))*dz];
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z = z + dz;
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If[Round[Mod[z, plotz ]/dz] == 0 ||
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Round[(Mod[z, plotz ] - plotz )/dz] == 0 ,
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timeused = SessionTime[] - starttime;
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p1 = ListLinePlot[Transpose[{tau, Abs[temp]^2.}],
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PlotRange -> {{-Twin, Twin}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}}
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];
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ftemp0 = RotateRight[ftemp (nt*dtau)/Sqrt[2*Pi], nt/2];
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p2 = ListLinePlot[
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Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[ftemp0]^2.]}],
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PlotRange -> {{-fwin, fwin}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{" Time = ", ToString[timeused]}]}}
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];
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p3 = ListLinePlot[Transpose[{tau, Abs[temp]^2}],
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PlotRange -> {{-Tmax, Tmax}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}}
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];
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p4 = ListLinePlot[
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Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[ftemp0]^2.]}],
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PlotRange -> {{-fmax, fmax}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{" Time = ", ToString[timeused]}]}}
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];
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autocorr0 =
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RotateRight[
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InverseFourier[
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Fourier[Abs[temp]^2]*Conjugate[Fourier[Abs[temp]^2]]], nt/2];
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p5 = ListLinePlot[Transpose[{tau, autocorr0/Max[autocorr0]}],
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PlotRange -> {{-Twin, Twin}, All}, Frame -> True];
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p = GraphicsGrid[{{p1, p2}, {p3, p4}, {p5, p6}}, ImageSize -> Full]
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];
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],
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p
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]
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uu = temp*
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Exp[(I*Abs[uu]^2. + G/(1.0 + Abs[uu]^2./Is))*
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dz/2.];(*% Final field*)
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temp = RotateRight[
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InverseFourier[uu, FourierParameters -> {1, -1}]*(nt*dtau)/
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Sqrt[2*Pi], nt/2];
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(*%Final spectrum*)
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(*%***************[End of MAIN Loop]***************)
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p1 = ListLinePlot[Transpose[{tau, Abs[uu]^2}],
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PlotRange -> {{-Twin, Twin}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}}
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];
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p2 = ListLinePlot[
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Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[temp]^2.]}],
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PlotRange -> {{-fwin, fwin}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{" Time = ", ToString[timeused]}]}}
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];
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p3 = ListLinePlot[Transpose[{tau, Abs[uu]^2}],
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PlotRange -> {{-Tmax, Tmax}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{"i = ", ToString[i], ", z = ", ToString[z]}]}}
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];
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p4 = ListLinePlot[
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Transpose[{tempomega/(2. Pi), 10.*Log10[Abs[temp]^2.]}],
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PlotRange -> {{-fmax, fmax}, All}, Frame -> True,
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FrameLabel -> {{Null, Null}, {Null,
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StringJoin[{" Time = ", ToString[timeused]}]}}
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];
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autocorr0 =
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RotateRight[
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InverseFourier[Fourier[Abs[uu]^2]*Conjugate[Fourier[Abs[uu]^2]]],
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nt/2];
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p5 = ListLinePlot[Transpose[{tau, autocorr0/Max[autocorr0]}],
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PlotRange -> {{-Twin, Twin}, All}, Frame -> True];
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p = GraphicsGrid[{{p1, p2}, {p3, p4}, {p5, p6}}, ImageSize -> Full]
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(*Exporting results*)
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fname = "2nd_01(0.18)"; (*file name*)
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Export[StringJoin[{fname , "_time.dat"}],
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Transpose[{tau, Re[uu], Im[uu], Abs[uu]^2}]];
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Export[StringJoin[{fname , "_freq.dat"}],
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Transpose[{tempomega/(2. Pi), Re[temp], Im[temp], Abs[temp]^2,
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RotateRight[Abs[filtert]^2, nt/2]}]];
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Export[StringJoin[{fname , "_autocorr.dat"}],
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Transpose[{tau, autocorr0, autocorr0/Max[autocorr0]}]];
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253
microring_dynamics.ipynb
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microring_dynamics.ipynb
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microring_dynamics.py
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microring_dynamics.py
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@ -0,0 +1,21 @@
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import numpy as np
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a1 = 1.0 + 0.0j
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a2 = 0.0 + 0.0j
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T = 0.9
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K = 0.1
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t = np.sqrt(T) + 0.0j
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k = 0.0 - 1j * np.sqrt(K)
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Coupler = np.array([[t, k],
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[k.conjugate(), -t.conjugate()]])
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num_cycle = 1000
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a = np.zeros((num_cycle, 2), dtype=complex)
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b = np.zeros((num_cycle, 2), dtype=complex)
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a[0, 0] = a1
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a[0, 1] = a2
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for n in range(num_cycle):
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pass
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287
microring_dynamics_v2.ipynb
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microring_dynamics_v2.ipynb
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File diff suppressed because one or more lines are too long
456
notebook.tex
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notebook.tex
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% Default to the notebook output style
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% Inherit from the specified cell style.
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\documentclass[11pt]{article}
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\usepackage[T1]{fontenc}
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% Nicer default font (+ math font) than Computer Modern for most use cases
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\usepackage{mathpazo}
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% Basic figure setup, for now with no caption control since it's done
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% automatically by Pandoc (which extracts  syntax from Markdown).
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\usepackage{graphicx}
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% We will generate all images so they have a width \maxwidth. This means
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% that they will get their normal width if they fit onto the page, but
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% are scaled down if they would overflow the margins.
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\makeatletter
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\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
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\else\Gin@nat@width\fi}
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\makeatother
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\let\Oldincludegraphics\includegraphics
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% Set max figure width to be 80% of text width, for now hardcoded.
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\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}}
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% Ensure that by default, figures have no caption (until we provide a
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% proper Figure object with a Caption API and a way to capture that
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% in the conversion process - todo).
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\usepackage{caption}
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\DeclareCaptionLabelFormat{nolabel}{}
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\captionsetup{labelformat=nolabel}
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\usepackage{adjustbox} % Used to constrain images to a maximum size
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\usepackage{xcolor} % Allow colors to be defined
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\usepackage{enumerate} % Needed for markdown enumerations to work
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\usepackage{geometry} % Used to adjust the document margins
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\usepackage{amsmath} % Equations
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\usepackage{amssymb} % Equations
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\usepackage{textcomp} % defines textquotesingle
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% Hack from http://tex.stackexchange.com/a/47451/13684:
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\AtBeginDocument{%
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\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
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}
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\usepackage{upquote} % Upright quotes for verbatim code
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\usepackage{eurosym} % defines \euro
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\usepackage[mathletters]{ucs} % Extended unicode (utf-8) support
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\usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document
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\usepackage{fancyvrb} % verbatim replacement that allows latex
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\usepackage{grffile} % extends the file name processing of package graphics
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% to support a larger range
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% The hyperref package gives us a pdf with properly built
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% internal navigation ('pdf bookmarks' for the table of contents,
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% internal cross-reference links, web links for URLs, etc.)
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\usepackage{hyperref}
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\usepackage{longtable} % longtable support required by pandoc >1.10
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\usepackage{booktabs} % table support for pandoc > 1.12.2
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\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
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\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
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% normalem makes italics be italics, not underlines
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% Colors for the hyperref package
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\definecolor{urlcolor}{rgb}{0,.145,.698}
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\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
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\definecolor{citecolor}{rgb}{.12,.54,.11}
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% ANSI colors
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\definecolor{ansi-black}{HTML}{3E424D}
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\definecolor{ansi-black-intense}{HTML}{282C36}
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\definecolor{ansi-red}{HTML}{E75C58}
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\definecolor{ansi-red-intense}{HTML}{B22B31}
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\definecolor{ansi-green}{HTML}{00A250}
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\definecolor{ansi-green-intense}{HTML}{007427}
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\definecolor{ansi-yellow}{HTML}{DDB62B}
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\definecolor{ansi-yellow-intense}{HTML}{B27D12}
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\definecolor{ansi-blue}{HTML}{208FFB}
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\definecolor{ansi-blue-intense}{HTML}{0065CA}
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\definecolor{ansi-magenta}{HTML}{D160C4}
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\definecolor{ansi-magenta-intense}{HTML}{A03196}
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\definecolor{ansi-cyan}{HTML}{60C6C8}
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\definecolor{ansi-cyan-intense}{HTML}{258F8F}
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\definecolor{ansi-white}{HTML}{C5C1B4}
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\definecolor{ansi-white-intense}{HTML}{A1A6B2}
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% commands and environments needed by pandoc snippets
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||||
% extracted from the output of `pandoc -s`
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\providecommand{\tightlist}{%
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\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
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\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
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% Add ',fontsize=\small' for more characters per line
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\newenvironment{Shaded}{}{}
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\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
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\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
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\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
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\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
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\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
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\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
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\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
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\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
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\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
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\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
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\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
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\newcommand{\RegionMarkerTok}[1]{{#1}}
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\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
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\newcommand{\NormalTok}[1]{{#1}}
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% Additional commands for more recent versions of Pandoc
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\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
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\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
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\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
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\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
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\newcommand{\ImportTok}[1]{{#1}}
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\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
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\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
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\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
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\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
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\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
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\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
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\newcommand{\BuiltInTok}[1]{{#1}}
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\newcommand{\ExtensionTok}[1]{{#1}}
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\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
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\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
|
||||
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||||
|
||||
|
||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
|
||||
|
||||
|
||||
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|
||||
|
||||
|
||||
|
||||
\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}
|
||||
BIN
output_3_0.png
Normal file
BIN
output_3_0.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 13 KiB |
BIN
output_5_0.png
Normal file
BIN
output_5_0.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 13 KiB |
BIN
output_8_0.png
Normal file
BIN
output_8_0.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 13 KiB |
BIN
output_9_0.png
Normal file
BIN
output_9_0.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 14 KiB |
41
ref/simple_anim.py
Normal file
41
ref/simple_anim.py
Normal file
@ -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()
|
||||
62
ref/strip_chart.py
Normal file
62
ref/strip_chart.py
Normal file
@ -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()
|
||||
3
result_autocorr.csv
Normal file
3
result_autocorr.csv
Normal file
File diff suppressed because one or more lines are too long
3
result_autocorr.dat
Normal file
3
result_autocorr.dat
Normal file
File diff suppressed because one or more lines are too long
5
result_freq.csv
Normal file
5
result_freq.csv
Normal file
File diff suppressed because one or more lines are too long
5
result_freq.dat
Normal file
5
result_freq.dat
Normal file
File diff suppressed because one or more lines are too long
4
result_time.csv
Normal file
4
result_time.csv
Normal file
File diff suppressed because one or more lines are too long
4
result_time.dat
Normal file
4
result_time.dat
Normal file
File diff suppressed because one or more lines are too long
193
split_step_fourier_method.py
Normal file
193
split_step_fourier_method.py
Normal file
@ -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=",")
|
||||
177
split_step_fourier_method_v0.py
Normal file
177
split_step_fourier_method_v0.py
Normal file
@ -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];
|
||||
|
||||
Loading…
Reference in New Issue
Block a user