141 lines
4.6 KiB
Matlab
141 lines
4.6 KiB
Matlab
% Minimal MZM transfer-function demo (sinusoidal drive) — aligned with your notation
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%
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% Implements exactly:
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% E_out(t) = E0 * exp(j*w0*t) * exp(-j*w0*L*n_eff/c0) * 1/2 * [ exp(-j*phi1(t)) + rho*exp(-j*phi2(t)) ]
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% with phi_{1,2}(t) = pi * v_{1,2}(t)/Vpi
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%
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% Push-pull:
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% v1(t) = +v_drive(t)/2 , v2(t) = -v_drive(t)/2 => phi1 = +pi/2 * v_drive/Vpi, phi2 = -pi/2 * v_drive/Vpi
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%
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% And the ideal TF (rho=1):
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% E_out/E_in = exp(-j*w0*L*n_eff/c0) * cos( (pi/2) * v_drive/Vpi )
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%
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% Note: E_in(t) = E0 * exp(j*w0*t) in this script.
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% Parameters
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c0 = physconst('lightspeed'); % [m/s]
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lambda0 = 1310e-9; % [m]
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omega0 = 2*pi*c0/lambda0;
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L = 5e-3; % [m] effective phase section length (set as needed)
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n_eff = 2.2; % [-] effective index (set as needed)
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E0 = 1; % field amplitude (arbitrary)
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Vpi = 3.2; % [V] half-wave voltage (your V_pi)
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% Drive
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f0 = 1e9; % [Hz]
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fs = 100e9; % [Hz]
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Nper = 1; % number of periods
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Vpp = 0.5*Vpi; % [V] peak-to-peak of v_drive(t)
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biasV = 2; % [V] differential bias added to v_drive
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% Analytic
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v_ = linspace(-1,2, 2001);
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% Field transfer function (amplitude)
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Field_mzm_analytic = cos((pi/2)*v_);
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% Power transfer function (intensity)
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P_mzm_analytic = Field_mzm_analytic.^2;
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% Imbalance factor in YOUR notation:
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rho = 1; % rho=1 -> ideal balanced MZM (collapses to ideal TF)
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% Time axis + differential drive voltage v_drive(t)
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T = Nper/f0;
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t = (0:1/fs:T-1/fs).';
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v_drive = biasV + (Vpp/2)*sin(2*pi*f0*t); % v_drive(t) (peak = Vpp/2)
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% Push-pull branch voltages (consistent with v_drive = v1 - v2)
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v1 = +0.5*v_drive; % arm 1
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v2 = -0.5*v_drive; % arm 2
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% Phases phi1, phi2
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phi1 = pi * v1 / Vpi;
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phi2 = pi * v2 / Vpi;
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% Fields: E_in and E_out (exactly your Eq. (mzm_e_field))
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E_in = E0 .* exp(1i*omega0*t);
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common_phase = exp(-1i * (omega0*L*n_eff/c0)); % exp(-j*omega0*L*n_eff/c0)
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E_out = E0 .* exp(1i*omega0*t) .* common_phase .* 0.5 .* ...
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( exp(-1i*phi1) + rho .* exp(-1i*phi2) );
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% Transfer function (numerical): E_out/E_in
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H_num = E_out ./ E_in;
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% Power (normalized)
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Pnorm_num = abs(H_num).^2; % since |E_out/E_in|^2
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% Ideal TF (analytic) for comparison (rho=1, push-pull)
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H_ideal = common_phase .* cos( (pi/2) * (v_drive./Vpi) );
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Pnorm_ideal = abs(H_ideal).^2;
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Pnorm_math = cos( (pi/2) * (v_drive./Vpi) ).^2;
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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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% Normalized voltage axis (multiples of Vpi)
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v_norm = v_drive./Vpi;
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colfield = [0,0,0]; %is black
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colpow = linspecer(2);
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colpow = colpow(1,:);
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colvdrive = linspecer(2);
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colvdrive = colvdrive(2,:);
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%% SIGNAL IN
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figure(1); clf
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plot(v_norm,t*1e9, 'LineWidth', 1.0,'Color',colvdrive); grid on;
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ylabel('t [ns]'); xlabel('v_{drive}(t)/V_\pi');
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title('Drive voltage (normalized)');
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xlim([min(v_) max(v_)]);
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%% IN/OUT (static transfer) — normalized x-axis + analytic curve
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figure(2); clf
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plot(v_, Field_mzm_analytic, 'LineWidth', 1.2,'LineStyle','--','Color',colfield); hold on;% analytic power TF
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plot(v_, P_mzm_analytic, 'LineWidth', 1.2, 'Color',colpow); hold on;% analytic power TF
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% show input time signal
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plot(v_norm,-1+t*1e9, 'LineWidth', 1.0,'Color',colvdrive); grid on;
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% show output time signal
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plot(2+t*1e9, Pnorm_num, 'LineWidth', 1.0,'DisplayName','Intensity', 'Color',colvdrive); hold on;
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plot(2+t*1e9, real(H_ideal), '--', 'LineWidth', 1.0,'DisplayName','Field','Color',colfield); hold on;
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scatter(v_norm, Pnorm_num, 12, '.', 'LineWidth', 1,'MarkerEdgeColor',colvdrive);
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scatter(biasV./Vpi,(cos((pi/2)*biasV./Vpi)^2),10,'Marker','o');
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line([min(v_drive), min(v_drive)]./Vpi,[(cos((pi/2)*min(v_drive)./Vpi)^2), -2],'linewidth',0.5,'color','black','linestyle','--');
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line([max(v_drive) max(v_drive)]./Vpi,[(cos((pi/2)*max(v_drive)./Vpi)^2), -2],'linewidth',0.5,'color','black','linestyle','--');
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xline([min(v_norm) max(v_norm)])
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grid on;
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xlabel('v_{drive}(t)/V_\pi'); ylabel('|E_{out}/E_{in}|^2');
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% legend
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xlim([min(v_) max(v_)+1]);
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ylim([-1 1]);
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% mat2tikz_improved('C:\Users\Silas\Documents\6971e0b65b380ca6d71c837f\02_IMDD_System\tikz\mzm.tex');
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%%
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% % FIELD TF (only field here; do not mix power into this figure)
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figure(3); clf
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% plot(t*1e9, real(H_num), 'LineWidth', 1.0); hold on;
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% plot(t*1e9, real(H_ideal), '--', 'LineWidth', 1.0,'DisplayName','Field','Color',colfield); hold on;
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plot(t*1e9, Pnorm_num, 'LineWidth', 1.0,'DisplayName','Intensity', 'Color',colpow); hold on;
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grid on;
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xlabel('t [ns]'); ylabel('Re\{E_{out}/E_{in}\}');
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legend
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mat2tikz_improved('C:\Users\Silas\Documents\6971e0b65b380ca6d71c837f\02_IMDD_System\tikz\mzm_out.tex');
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