%% ============================================================
%  IM/DD Fading Notch Design Map
%  Shows λ_null vs. bandwidth (f_target) and fiber length (L)
% ============================================================

clear; close all; clc;

%% Parameters
lambda0 = 1310e-9;   % Zero-dispersion wavelength [m]
S0      = 0.08;      % Dispersion slope at ZDW [ps/(nm²·km)]
c       = physconst('lightspeed');

% Frequency and length sweep
f_targets = linspace(20e9, 140e9, 80);   % [Hz]  → x-axis
L_values  = linspace(0.5e3, 12e3, 80);   % [m]   → y-axis

% Preallocate result matrices
lambda_surface = zeros(numel(L_values), numel(f_targets));
Dacc_surface   = zeros(numel(L_values), numel(f_targets));

%% Compute λ_null and Dacc for each (f_target, L)
for iL = 1:numel(L_values)
    L = L_values(iL);
    [lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_targets, L, lambda0, S0);
    lambda_surface(iL, :) = lambda_vec;   % [m]
    Dacc_surface(iL, :)   = Dacc_vec;     % [ps/nm]
end

%% Convert to display units
lambda_surface_nm = lambda_surface * 1e9;  % [nm]
L_km              = L_values / 1000;       % [km]
f_GHz             = f_targets / 1e9;       % [GHz]

%% ------------------------------------------------------------
% Contour plot (λ_null as function of f_null and L)
% ------------------------------------------------------------
figure('Color','w');

% Define wavelength contour levels [nm]
lambda_levels = [1260:10:1290, 1290:5:1300, 1300:2:1310];

contourf(f_GHz, L_km, lambda_surface_nm, lambda_levels, ...
    'LineWidth', 1.5, ...
    'ShowText', 'on', ...
    'LabelFormat', '%1.1d nm');

% Colormap and colorbar
colormap(flip(cbrewer2('RdYlGn',100)));
clim([1260 1310]);
% c = colorbar;
% ylabel(c, 'λ_{null} [nm]', 'Rotation', 90);

% Axis formatting
xlabel('Signal Bandwidth [GHz]');
ylabel('Fiber length  L [km]');
% X-axis ticks (every 16 GHz starting at 56 GHz)
xticks(56:8:120);
xlim([56,120])
grid on; box on;

%% Optional overlay: accumulated dispersion contours
hold on;
[CS, h] = contour(f_GHz, L_km, Dacc_surface, 10, 'k--', 'LineWidth', 0.8);
clabel(CS, h, 'Color','k', 'FontSize',8);
legend('λ_{null} contours','|D_{acc}| [ps/nm]','Location','best');

%% ============================================================
% Helper function: lambda_for_first_null_full
% Stable, single-branch, clamped to O-band
% ============================================================
function [lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_target, L, lambda0, S0)
    c = physconst('lightspeed');
    S0_si = S0 * 1e3;   % ps/(nm²·km) -> s/(m³)

    % Define O-band boundaries (in meters)
    lambda_min = 1260e-9;
    lambda_max = 1360e-9;

    % Force column vector
    f_target = f_target(:);
    N = numel(f_target);

    lambda_vec = zeros(N,1);
    Dacc_vec   = zeros(N,1);

    for k = 1:N
        RHS = c * 0.5 / (f_target(k)^2 * L);

        % Normal-dispersion branch (λ < λ0)
        fun = @(lambda) -(S0_si/4).*(lambda - (lambda0^4)./(lambda.^3)).*lambda.^2 - RHS;

        % Solve within the normal-dispersion range
        try
            lambda_sol = fzero(fun, [lambda_min, lambda0 * 0.999]);
        catch
            lambda_sol = lambda_min;
        end

        % Clamp to O-band range
        lambda_sol = min(max(lambda_sol, lambda_min), lambda_max);
        lambda_vec(k) = lambda_sol;

        % Compute D(lambda) and accumulated dispersion
        D_lambda = (S0_si/4) * (lambda_sol - (lambda0^4)/(lambda_sol^3)) / 1e-6; % ps/(nm·km)
        Dacc_val = D_lambda * (L/1000);  % ps/nm

        % Clamp to physical range
        Dacc_val = min(max(Dacc_val, -100), 100);
        Dacc_vec(k) = Dacc_val;
    end
end