147 lines
4.7 KiB
Matlab
147 lines
4.7 KiB
Matlab
%% ------------------------------------------------------------
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% Contour plot: λ_null as function of bandwidth (f_target) and reach (L)
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% ------------------------------------------------------------
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% Parameters
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lambda0 = 1310e-9; % [m]
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S0 = 0.08; % [ps/(nm²·km)]
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c = physconst('lightspeed');
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% Sweep dimensions
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f_targets = linspace(50e9, 120e9, 100); % [Hz] (x-axis)
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L_values = linspace(0.5e3, 10e3, 100); % [m] (y-axis)
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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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% Outer loop over fiber length (since L must be scalar)
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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_vec = 2*abs(lambda0 - lambda_vec);
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if 0
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fprintf('\n- %d km ------------------------------------\n',L);
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fprintf(' f_null [GHz] lambda [nm] Dacc [ps/nm]\n');
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fprintf('----------------------------------------------\n');
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fprintf('%10.1f %8.2f %+8.3f\n',[f_targets(:)/1e9, lambda_vec(:)*1e9, Dacc_vec(:)].');
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fprintf('----------------------------------------------\n\n');
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end
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lambda_surface(iL, :) = lambda_vec; % λ for each f_target
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Dacc_surface(iL, :) = Dacc_vec; % corresponding accumulated dispersion
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end
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% Convert for plotting
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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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%% Contour plot
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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, 1300:2.5:1310];
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lambda_levels = [100:-20:50, 50:-10:30,30:-5:0];
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% Contour plot
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contour(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', '%.0f nm');
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% Colormap and colorbar
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colormap((cbrewer2('RdYlGn',100)));
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colorbar;
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clim([0 100]);
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% Axis formatting
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xlabel('Signal Bandwidth [GHz]');
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ylabel('Fiber length [km]');
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legend('$\Delta \lambda$')
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% X-axis ticks at 56 : 16 : 150 GHz
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xticks(56:8:150);
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grid on; box on;
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%% Optional: overlay accumulated-dispersion contours
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if 0
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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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end
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function [lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_target, L, lambda0, S0)
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% lambda_for_first_null_full (stable, single-branch + validity checks)
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% --------------------------------------------------------------------
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% Computes the wavelength(s) at which the first IM/DD fading null
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% occurs at frequency/ies f_target using the full dispersion model:
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%
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% D(lambda) = (S0/4)*(lambda - lambda0^4 / lambda^3)
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%
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% Restricted to the NORMAL-dispersion branch (λ < λ0),
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% and valid only in the O-band (1260–1360 nm).
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%
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% Inputs:
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% f_target - scalar or vector of target null frequencies [Hz]
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% L - fiber length [m]
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% lambda0 - zero-dispersion wavelength (ZDW) [m]
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% S0 - dispersion slope at ZDW [ps/(nm²·km)]
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%
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% Outputs:
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% lambda_vec - wavelength(s) [m] where first null occurs (clamped to O-band)
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% Dacc_vec - accumulated dispersion(s) [ps/nm] (NaN if out of valid range)
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% --------------------------------------------------------------------
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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 = 1255e-9;
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lambda_max = 1361e-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 = NaN(N,1);
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Dacc_vec = NaN(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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% Limit the search to [λ_min, λ0)
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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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% If the zero is not within bounds, skip this point
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lambda_sol = NaN;
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end
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% Validate solution
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if isnan(lambda_sol) || lambda_sol < lambda_min || lambda_sol > lambda_max
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lambda_vec(k) = NaN;
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Dacc_vec(k) = NaN;
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continue
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end
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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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% Sanity bound on dispersion (avoid unphysical > ±100 ps/nm)
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if abs(Dacc_val) > 100
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lambda_vec(k) = NaN;
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Dacc_vec(k) = NaN;
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else
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lambda_vec(k) = lambda_sol;
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Dacc_vec(k) = Dacc_val;
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end
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end
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end
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