halfway merged and pulled?!

Functions/Theory/dispersion_wdm.m

@@ -0,0 +1,111 @@
+%% ============================================================
+%  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