112 lines
3.6 KiB
Matlab
112 lines
3.6 KiB
Matlab
%% ============================================================
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% IM/DD Fading Notch Design Map
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% Shows λ_null vs. bandwidth (f_target) and fiber length (L)
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% ============================================================
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clear; close all; clc;
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%% Parameters
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lambda0 = 1310e-9; % Zero-dispersion wavelength [m]
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S0 = 0.08; % Dispersion slope at ZDW [ps/(nm²·km)]
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c = physconst('lightspeed');
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% Frequency and length sweep
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f_targets = linspace(20e9, 140e9, 80); % [Hz] → x-axis
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L_values = linspace(0.5e3, 12e3, 80); % [m] → y-axis
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% Preallocate result matrices
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lambda_surface = zeros(numel(L_values), numel(f_targets));
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Dacc_surface = zeros(numel(L_values), numel(f_targets));
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%% Compute λ_null and Dacc for each (f_target, L)
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for iL = 1:numel(L_values)
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L = L_values(iL);
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[lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_targets, L, lambda0, S0);
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lambda_surface(iL, :) = lambda_vec; % [m]
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Dacc_surface(iL, :) = Dacc_vec; % [ps/nm]
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end
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%% Convert to display units
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lambda_surface_nm = lambda_surface * 1e9; % [nm]
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L_km = L_values / 1000; % [km]
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f_GHz = f_targets / 1e9; % [GHz]
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%% ------------------------------------------------------------
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% Contour plot (λ_null as function of f_null and L)
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% ------------------------------------------------------------
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figure('Color','w');
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% Define wavelength contour levels [nm]
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lambda_levels = [1260:10:1290, 1290:5:1300, 1300:2:1310];
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contourf(f_GHz, L_km, lambda_surface_nm, lambda_levels, ...
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'LineWidth', 1.5, ...
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'ShowText', 'on', ...
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'LabelFormat', '%1.1d nm');
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% Colormap and colorbar
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colormap(flip(cbrewer2('RdYlGn',100)));
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clim([1260 1310]);
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% c = colorbar;
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% ylabel(c, 'λ_{null} [nm]', 'Rotation', 90);
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% Axis formatting
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xlabel('Signal Bandwidth [GHz]');
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ylabel('Fiber length L [km]');
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% X-axis ticks (every 16 GHz starting at 56 GHz)
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xticks(56:8:120);
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xlim([56,120])
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grid on; box on;
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%% Optional overlay: accumulated dispersion contours
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hold on;
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[CS, h] = contour(f_GHz, L_km, Dacc_surface, 10, 'k--', 'LineWidth', 0.8);
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clabel(CS, h, 'Color','k', 'FontSize',8);
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legend('λ_{null} contours','|D_{acc}| [ps/nm]','Location','best');
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%% ============================================================
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% Helper function: lambda_for_first_null_full
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% Stable, single-branch, clamped to O-band
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% ============================================================
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function [lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_target, L, lambda0, S0)
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c = physconst('lightspeed');
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S0_si = S0 * 1e3; % ps/(nm²·km) -> s/(m³)
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% Define O-band boundaries (in meters)
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lambda_min = 1260e-9;
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lambda_max = 1360e-9;
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% Force column vector
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f_target = f_target(:);
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N = numel(f_target);
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lambda_vec = zeros(N,1);
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Dacc_vec = zeros(N,1);
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for k = 1:N
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RHS = c * 0.5 / (f_target(k)^2 * L);
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% Normal-dispersion branch (λ < λ0)
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fun = @(lambda) -(S0_si/4).*(lambda - (lambda0^4)./(lambda.^3)).*lambda.^2 - RHS;
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% Solve within the normal-dispersion range
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try
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lambda_sol = fzero(fun, [lambda_min, lambda0 * 0.999]);
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catch
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lambda_sol = lambda_min;
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end
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% Clamp to O-band range
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lambda_sol = min(max(lambda_sol, lambda_min), lambda_max);
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lambda_vec(k) = lambda_sol;
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% Compute D(lambda) and accumulated dispersion
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D_lambda = (S0_si/4) * (lambda_sol - (lambda0^4)/(lambda_sol^3)) / 1e-6; % ps/(nm·km)
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Dacc_val = D_lambda * (L/1000); % ps/nm
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% Clamp to physical range
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Dacc_val = min(max(Dacc_val, -100), 100);
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Dacc_vec(k) = Dacc_val;
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end
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end
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