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

Functions/Theory/dispersion_wavelength_notch.m

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+%% Dependency f_null vs Delta_lambda
+lambda0 = 1310e-9;
+S0 = 0.09;       % ps/(nm²·km)
+L  = 10e3;       % m
+c  = physconst('lightspeed');
+
+% Convert slope to SI
+S0_si = S0 * 1e3;   % s/m³
+
+Delta_lambda = linspace(5e-9, 80e-9, 300); % [m] detuning
+f_null_2 = sqrt( c * 0.5 ./ (S0_si .* abs(Delta_lambda) .* lambda0.^2 .* L) );
+L  = 2e3;       % m
+f_null_10 = sqrt( c * 0.5 ./ (S0_si .* abs(Delta_lambda) .* lambda0.^2 .* L) );
+
+cols = cbrewer2('Paired',10);
+figure('Color','w');hold on
+cnt = 2;
+for L = 10%[2,5,10]
+    f_null_10 = sqrt( c * 0.5 ./ (S0_si .* abs(Delta_lambda) .* lambda0.^2 .* L*1e3) );
+    plot(1310-Delta_lambda*1e9, f_null_10/1e9, 'LineWidth',2,'DisplayName',sprintf('%d km',L),'Color',cols(cnt,:));
+    cnt = cnt+2;
+end
+yticks([56,75,90,112])
+tickse = 1310-[7.5, 12, 17, 31.5];
+xticks(flip(tickse));
+
+xlabel('$\Delta \lambda$ from ZDW [nm]');
+ylabel('$F_{null}$  [GHz]');
+grid on; box on;
+lim=1310-[5,35];
+xlim([lim(2) lim(1)]);
+ylim([40,130])

Functions/Theory/dispersion_wdm.m

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+%% ============================================================
+%  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

Functions/Theory/power_fading.m

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+%% ============================================================
+%  Minimal IM/DD Power Fading Plot
+% ============================================================
+
+
+%% Fiber and system parameters
+lambda0 = 1310e-9;       % zero-dispersion wavelength [m]
+lambda  = 1275e-9;       % operating wavelength [m]
+S0      = 0.08;          % dispersion slope [ps/(nm²·km)]
+L       = 10e3;          % fiber length [m]
+c       = physconst('lightspeed');
+
+%% Derived quantities
+S0_si = S0 * 1e3;                                    % → s/m³
+D_lambda = (S0/4) * (lambda*1e9 - (lambda0*1e9)^4/(lambda*1e9)^3); % ps/(nm·km)
+D_si = D_lambda * 1e-6;                              % → s/m²
+b2   = -D_si * lambda^2 / (2*pi*c);                  % s²/m
+
+%% Frequency grid
+f_max = 150e9;
+f = linspace(0, f_max, 4000);                        % [Hz]
+
+%% IM/DD transfer function (power fading)
+phi = 2*pi^2 * b2 * f.^2 * L;
+H = abs(cos(phi));
+
+%% Plot
+figure('Color','w');
+plot(f/1e9, 10*log10(H), 'LineWidth', 1.8);
+grid on; box on;
+xlabel('Frequency [GHz]');
+ylabel('Magnitude [dB]');
+title(sprintf('IM/DD Power Fading |H| for λ = %.1f nm, L = %.1f km', lambda*1e9, L/1000));
+ylim([-30 0]);
+
+%% Mark analytic first-null frequency
+f_null = sqrt(c*(0.5)/(abs(D_si)*lambda^2*L));
+xline(f_null/1e9, 'r--', 'LineWidth', 1.2, ...
+       'Label', sprintf('f_{null}=%.1f GHz', f_null/1e9), ...
+       'LabelOrientation', 'horizontal', 'LabelVerticalAlignment', 'bottom');

Functions/convert_freq_lambda.m

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+%% ============================================================
+%  Wavelength–Frequency Conversion Utilities
+% ============================================================
+
+% Example usage:
+%   f = lambda2freq(1310e-9);              % 1310 nm -> Hz
+%   lambda = freq2lambda(224e12);          % 224 THz -> m
+%   delta_lambda_nm = df2dlambda(224e12, 400e9); % 400 GHz @ 224 THz -> nm
+%   delta_freq_GHz  = dlambda2df(1310e-9, 3.45); % 3.45 nm @ 1310 nm -> GHz
+
+%% ---- Core conversion functions ----
+function f = lambda2freq(lambda)
+% lambda2freq Convert wavelength [m] → frequency [Hz]
+    c = physconst('lightspeed');
+    f = c ./ lambda;
+end
+
+function lambda = freq2lambda(f)
+% freq2lambda Convert frequency [Hz] → wavelength [m]
+    c = physconst('lightspeed');
+    lambda = c ./ f;
+end
+
+%% ---- Differential conversions ----
+function d_lambda = df2dlambda(f_center, d_f)
+% df2dlambda Convert frequency spacing Δf [Hz] → wavelength spacing Δλ [m]
+% around a given center frequency f_center [Hz].
+% Uses first-order differential: Δλ ≈ (c / f^2) * Δf
+
+    c = physconst('lightspeed');
+    d_lambda = (c ./ (f_center.^2)) .* d_f;
+end
+
+function d_f = dlambda2df(lambda_center, d_lambda)
+% dlambda2df Convert wavelength spacing Δλ [m] → frequency spacing Δf [Hz]
+% around a given center wavelength λ_center [m].
+% Uses first-order differential: Δf ≈ (c / λ^2) * Δλ
+
+    c = physconst('lightspeed');
+    d_f = (c ./ (lambda_center.^2)) .* d_lambda;
+end
+
+%% ============================================================
+%  Example section (can be commented out)
+% ============================================================
+
+if ~isdeployed
+    fprintf('--- Example conversions ---\n');
+
+    lambda_nm = 1310;                 % nm
+    lambda = lambda_nm * 1e-9;        % m
+    f = lambda2freq(lambda);          % Hz
+    fprintf('λ = %.1f nm  →  f = %.3f THz\n', lambda_nm, f/1e12);
+
+    d_f = 2000e9;                      % 400 GHz spacing
+    d_lambda = df2dlambda(f, d_f);    % [m]
+    fprintf('Δf = %.0f GHz @ %.1f nm  →  Δλ = %.3f nm\n', d_f/1e9, lambda_nm, d_lambda*1e9);
+
+    % Verify reverse direction
+    d_f_back = dlambda2df(lambda, d_lambda);
+    fprintf('Δλ = %.3f nm @ %.1f nm  →  Δf = %.0f GHz\n', d_lambda*1e9, lambda_nm, d_f_back/1e9);
+end