theory silas diss
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Silas Oettinghaus
191
Functions/Theory/Dissertation/mach_zehnder_nonlinearities.m
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191
Functions/Theory/Dissertation/mach_zehnder_nonlinearities.m
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%MZM demo -> sinus als eingang in MZM intensity TF: 2nd and 3rd roder
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%nonlinearities in PSD visible
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clear; close all; clc;
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set(groot,'defaultLegendInterpreter','tex');
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set(groot,'defaultAxesTickLabelInterpreter','tex');
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set(groot,'defaultTextInterpreter','tex');
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%% Fixed parameters
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Vpi = 5.2; % [V]
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f0 = 10e9; % [Hz]
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fs = 400e9; % [Hz]
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Nper = 500; % periods for PSD quality
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t = (0:1/fs:(Nper/f0 - 1/fs)).';
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w = 2*pi*f0;
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% PSD settings
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nfft = 2^(nextpow2(min(length(t), 2^18))-1);
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win = hann(2^12);
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ovl = round(0.5*numel(win));
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N_bessel = 10;
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%% UI defaults (normalized)
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vb0 = 1.0; % Vbias/Vpi
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vpp0 = 0.5; % Vpp/Vpi
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%% Figure + layout
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fig = figure('Color','w','Name','MZM Nonlinearity: Bias & Drive','NumberTitle','off');
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tl = tiledlayout(fig,1,2,'TileSpacing','compact','Padding','compact');
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axTF = nexttile(tl,1); hold(axTF,'on'); grid(axTF,'on');
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axPSD = nexttile(tl,2); hold(axPSD,'on'); grid(axPSD,'on');
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% Scatter placeholders
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hEx = scatter(axTF, nan, nan, 6, '.', 'DisplayName','Exact');
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hTa = scatter(axTF, nan, nan, 6, '.', 'DisplayName','Taylor (3rd order)');
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hJa = scatter(axTF, nan, nan, 6, '.', 'DisplayName',sprintf('Jacobi--Anger (N=%d)',N_bessel));
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hBias = plot(axTF, nan, nan, 'ko', 'MarkerFaceColor','k', 'DisplayName','Bias');
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xlabel(axTF,'v/V_\pi'); ylabel(axTF,'P_{out}/P_0'); % <-- TeX (no $...$)
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title(axTF,'Transfer characteristic (scatter)');
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ylim(axTF,[-0.1 1.1]);
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xlim(axTF,[0 2]);
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legend(axTF,'Location','best');
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% PSD placeholders
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hPex = plot(axPSD, nan, nan, 'LineWidth',2.0, 'DisplayName','Exact');
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hPta = plot(axPSD, nan, nan, '-', 'LineWidth',1.5, 'DisplayName','Taylor (3rd order)');
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hPja = plot(axPSD, nan, nan, '--', 'LineWidth',0.1, 'DisplayName',sprintf('Jacobi--Anger (N=%d)',N_bessel));
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xlabel(axPSD,'Frequency [GHz]'); ylabel(axPSD,'PSD [dB/Hz]');
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title(axPSD,'Output spectrum (PSD)');
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xlim(axPSD,[0 10*f0/1e9]);
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legend(axPSD,'Location','best');
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%% Sliders + labels
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sH = 0.05; mL = 0.08; wS = 0.38; y1 = 0.04; dy = 0.06;
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uicontrol(fig,'Style','text','Units','normalized', ...
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'Position',[mL, y1+dy, wS, 0.03], ...
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'String','v_{bias}/V_{\pi}','HorizontalAlignment','left');
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sBias = uicontrol(fig,'Style','slider','Units','normalized', ...
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'Position',[mL, y1+dy-0.02, wS, sH], ...
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'Min',0,'Max',2,'Value',vb0);
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tBiasVal = uicontrol(fig,'Style','text','Units','normalized', ...
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'Position',[mL+wS+0.01, y1+dy, 0.08, 0.03], ...
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'String',sprintf('%.3f',vb0),'HorizontalAlignment','left');
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uicontrol(fig,'Style','text','Units','normalized', ...
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'Position',[mL, y1, wS, 0.03], ...
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'String','v_{pp}/V_{\pi}','HorizontalAlignment','left');
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sVpp = uicontrol(fig,'Style','slider','Units','normalized', ...
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'Position',[mL, y1-0.02, wS, sH], ...
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'Min',0,'Max',2,'Value',vpp0);
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tVppVal = uicontrol(fig,'Style','text','Units','normalized', ...
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'Position',[mL+wS+0.01, y1, 0.08, 0.03], ...
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'String',sprintf('%.3f',vpp0),'HorizontalAlignment','left');
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%% Store handles in fig.UserData (so callback can always access them)
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S = struct();
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S.Vpi = Vpi; S.f0 = f0; S.fs = fs; S.w = w; S.t = t;
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S.win = win; S.ovl = ovl; S.nfft = nfft;
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S.N_bessel = N_bessel;
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S.axTF = axTF; S.axPSD = axPSD;
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S.hEx = hEx; S.hTa = hTa; S.hJa = hJa; S.hBias = hBias;
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S.hPex = hPex; S.hPta = hPta; S.hPja = hPja;
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S.sBias = sBias; S.sVpp = sVpp;
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S.tBiasVal = tBiasVal; S.tVppVal = tVppVal;
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fig.UserData = S;
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%% Continuous update while dragging
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addlistener(sBias,'Value','PostSet',@(~,~)updatePlots(fig));
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addlistener(sVpp ,'Value','PostSet',@(~,~)updatePlots(fig));
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% Initial draw
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updatePlots(fig);
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%% ===== Callback (separate function at end of script) =====
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function updatePlots(fig)
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S = fig.UserData;
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% Read slider values (normalized)
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vb_n = S.sBias.Value; % Vbias/Vpi
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vpp_n = S.sVpp.Value; % Vpp/Vpi
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% Update value labels
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S.tBiasVal.String = sprintf('%.3f', vb_n);
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S.tVppVal.String = sprintf('%.3f', vpp_n);
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% Convert to volts / amplitude
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Vpi = S.Vpi;
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Vbias = vb_n * Vpi;
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Vpp = vpp_n * Vpi;
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Vm = Vpp/2;
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t = S.t; w = S.w;
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% Drive
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v = Vbias + Vm*cos(w*t);
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x = v./Vpi;
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% Exact intensity
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P_exact = cos((pi/2)*x).^2;
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% Taylor 3rd order around Vbias
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k = (pi/2)/Vpi;
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vb = Vbias;
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g0 = cos(k*vb)^2;
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g1 = -k*sin(2*k*vb);
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g2 = -2*k^2*cos(2*k*vb);
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g3 = 4*k^3*sin(2*k*vb);
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dv = v - vb;
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P_taylor = g0 + g1*dv + 0.5*g2*dv.^2 + (1/6)*g3*dv.^3;
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% Jacobi–Anger / Bessel series (truncated)
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a = pi*(Vbias/Vpi);
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b = pi*(Vm/Vpi);
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N = S.N_bessel;
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P_ja = 0.5*ones(size(t));
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P_ja = P_ja + 0.5*cos(a)*besselj(0,b);
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for m = 0:floor((N-1)/2)
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n = 2*m + 1;
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P_ja = P_ja - (0.5*2)*sin(a)*besselj(n,b).*cos(n*w*t);
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end
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for m = 1:floor(N/2)
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n = 2*m;
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P_ja = P_ja - (0.5*2)*cos(a)*besselj(n,b).*cos(n*w*t);
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end
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% Update TF scatter
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S.hEx.XData = x; S.hEx.YData = P_exact;
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S.hTa.XData = x; S.hTa.YData = P_taylor;
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S.hJa.XData = x; S.hJa.YData = P_ja;
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xb = Vbias/Vpi;
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pb = cos((pi/2)*xb)^2;
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S.hBias.XData = xb; S.hBias.YData = pb;
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xpad = 0.05*(max(x)-min(x) + eps);
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% xlim(S.axTF,[min(x)-xpad, max(x)+xpad]);
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ylim(S.axTF,[-0.1 1.1]);
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% PSDs
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fs = S.fs;
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[Se,f] = pwelch(P_exact-mean(P_exact), S.win, S.ovl, S.nfft, fs, 'onesided');
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[St,~] = pwelch(P_taylor-mean(P_taylor), S.win, S.ovl, S.nfft, fs, 'onesided');
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[Sj,~] = pwelch(P_ja-mean(P_ja), S.win, S.ovl, S.nfft, fs, 'onesided');
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S.hPex.XData = f/1e9; S.hPex.YData = 10*log10(Se + realmin);
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S.hPta.XData = f/1e9; S.hPta.YData = 10*log10(St + realmin);
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S.hPja.XData = f/1e9; S.hPja.YData = 10*log10(Sj + realmin);
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xlim(S.axPSD,[0 10*(S.f0)/1e9]);
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ylim(S.axPSD,[-180 -80]);
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drawnow limitrate;
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end
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