% MZM bias sweep (physical coefficients) + field & power transfer functions
% Uses your notation:
%   Pout/Pin = cos^2( (pi/2)*(v/Vpi) ),  v = Vbias + Δv
% Taylor around Vbias:
%   Pout/Pin ≈ a0 + a1 Δv + a2 Δv^2 + a3 Δv^3
%
% Coefficients (physical units):
%   a0 [-], a1 [1/V], a2 [1/V^2], a3 [1/V^3]
%
% Also plots:
%   Field TF amplitude:  Eout/Ein = cos( (pi/2)*(Vbias/Vpi) )
%   Power TF:            Pout/Pin = cos^2( (pi/2)*(Vbias/Vpi) )

clear; close all; clc;

set(groot,'defaultLegendInterpreter','tex');
set(groot,'defaultAxesTickLabelInterpreter','tex');
set(groot,'defaultTextInterpreter','tex');

%% Parameters
Vpi = 3;                       % [V] device half-wave voltage
xb  = linspace(0, 2, 2001);    % x_b = Vbias/Vpi
Vbias = xb * Vpi;              % [V]

%% Static transfer functions (at Vbias)
H_field = cos((pi/2)*xb);        % field amplitude TF (balanced MZM)
T_power = H_field.^2;            % intensity TF

%% Taylor coefficients (physical units)
a0 = T_power;
a1 = -(pi/(2*Vpi))      .* sin(pi*xb);     % [1/V]
a2 = -(pi^2/(4*Vpi^2))  .* cos(pi*xb);     % [1/V^2]
a3 = +(pi^3/(12*Vpi^3)) .* sin(pi*xb);     % [1/V^3]
A0 = a0;
A1 = a1 * Vpi;
A2 = a2 * Vpi^2;
A3 = a3 * Vpi^3;

%% Plot
figure('Color','w'); clf;
% --- (1) Field + power TF vs bias ---
hold on; grid on;
plot(xb, H_field, 'LineWidth', 1.4, 'DisplayName','Field','Color','black','LineStyle','--');
% plot(xb, T_power, 'LineWidth', 1.4, 'DisplayName','Intensity','Color','black','LineStyle','-');


% --- (2) Physical Taylor coefficients vs bias ---
% nexttile; hold on; grid on;
plot(xb, a0, 'LineWidth', 1.4, 'DisplayName','Intensity','Color','black','LineStyle','-');
plot(xb, a1, 'LineWidth', 1.4, 'DisplayName','Linear');
plot(xb, a2, 'LineWidth', 1.4, 'DisplayName','Even');
plot(xb, a3, 'LineWidth', 1.4, 'DisplayName','Odd');

xlabel('$V/V_\pi$','Interpreter','latex');
ylabel('Transfer');
title('Static transfer functions vs bias');
xlim([min(xb) max(xb)]);
ylim([-1.05 1.05]);
legend('Location','best');

% Optional: tighten y-limits to avoid a0 dominating the view
% Comment out if you prefer auto-scaling.
yl = ylim;
ylim([min(yl(1), -max(abs([a1 a2 a3]))*1.1), max(yl(2), max(abs([a1 a2 a3]))*1.1)]);

xticks([0:0.5:2]);