Dispersion theory scripts

Functions/Theory/dispersion_10km.m

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+%% ============================================================
+%  IM/DD Fading Notch – λ_null vs. Bandwidth (Fixed 10 km)
+% ============================================================
+
+
+
+%% Fiber and dispersion parameters
+lambda0 = 1315e-9;   % Zero-dispersion wavelength [m]
+S0      = 0.08;      % Dispersion slope at ZDW [ps/(nm²·km)]
+L       = 10e3;      % Fiber length [m]
+c       = physconst('lightspeed');
+
+%% Frequency sweep (defines the desired first-fading notch)
+f_targets = linspace(40e9, 150e9, 200);   % [Hz]
+f_GHz = f_targets / 1e9;
+
+%% Compute wavelength λ_null for each target f_null
+[lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_targets, L, lambda0, S0);
+lambda_nm = lambda_vec * 1e9;   % Convert to nm
+
+%% ------------------------------------------------------------
+% Plot λ_null vs. f_null for 10 km fiber
+% ------------------------------------------------------------
+% figure('Color','w');
+% plot(lambda_nm,f_GHz,  'LineWidth', 2);
+% grid on; box on;
+
+cols = cbrewer2('Paired',10);
+figure('Color','w');hold on
+
+plot(lambda_nm, f_GHz, 'LineWidth',2,'DisplayName',sprintf('%d km',L),'Color',cols(2,:));
+
+yticks([56,75,90,112])
+
+f_GHz = [56,75,90,112] * 1e9;
+[lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_GHz, L, lambda0, S0);
+lambda_nm = lambda_vec * 1e9;   % Convert to nm
+
+xticks(round(lambda_nm))
+
+xlabel('$\Delta \lambda$ from ZDW [nm]');
+ylabel('$F_{null}$  [GHz]');
+grid on; box on;
+lim=(lambda0.*1e9)-[8,40];
+xlim([lim(2) lim(1)]);
+% ylim([40,130])
+
+%% ------------------------------------------------------------
+% 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 [m]
+lambda_min = 1260e-9;
+lambda_max = 1360e-9;
+
+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 normal-dispersion range
+    try
+        lambda_sol = fzero(fun, [lambda_min, lambda0 * 0.999]);
+    catch
+        lambda_sol = lambda_min;
+    end
+
+    % Clamp to O-band
+    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
+    Dacc_val = min(max(Dacc_val, -100), 100);
+
+    Dacc_vec(k) = Dacc_val;
+end
+end