CLEANUP - changes to folder structure
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Silas Oettinghaus
183
Theory/Dissertation/dispersion_contour_bandwidth_lambda.m
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183
Theory/Dissertation/dispersion_contour_bandwidth_lambda.m
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%% ------------------------------------------------------------
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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 = 0.09; % [ps/(nm²·km)]
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c = physconst('lightspeed');
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% Sweep dimensions
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f_targets = linspace(50e9, 130e9, 200); % [Hz] (x-axis)
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L_values = linspace(0.5e3, 15e3, 200); % [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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% Store the 1x absolute offset |lambda - lambda0|
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lambda_surface(iL, :) = abs(lambda0 - lambda_vec);
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Dacc_surface(iL, :) = Dacc_vec;
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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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hold on;
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% Define wavelength contour levels [nm]
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% Focus on a clean range of 1x offset values
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lambda_levels = unique([50:-10:30, 30:-5:5]);
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% Contour plot
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[C,h] = contourf(f_GHz, L_km, lambda_surface_nm, lambda_levels, ...
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'LineWidth', 1.2, ...
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'ShowText', 'off');
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% Colormap: Modern Blue palette with light colors removed for visibility
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cmap_full = cbrewer2('Blues', 40);
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colormap(cmap_full(10:end, :));
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clim([min(lambda_levels) max(lambda_levels)]);
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cb = colorbar;
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ylabel(cb, '$\Delta \lambda$ [nm]', 'Interpreter', 'latex');
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% --- MANUAL TEXTBOX ANNOTATIONS ---
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% Find placement along the first-null curve for each level
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for i = 1:length(lambda_levels)
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lvl = lambda_levels(i);
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% Re-calculate the specific (f, L) curve for this delta-lambda
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lambda_target = lambda0 - (lvl * 1e-9);
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LHS = -( (S0*1e3) / 4 ) * (lambda_target - (lambda0^4)/(lambda_target^3)) * lambda_target^2;
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const_val = (c*0.5) / LHS;
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f_curve_GHz = linspace(min(f_GHz), max(f_GHz), 500);
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L_curve_km = const_val ./ (f_curve_GHz * 1e9).^2 / 1000;
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% Filter for points within the plot axes
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in_bounds = find(L_curve_km >= min(L_km)*1.1 & L_curve_km <= max(L_km)*0.9 & ...
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f_curve_GHz >= min(f_GHz)*1.1 & f_curve_GHz <= max(f_GHz)*0.9);
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if ~isempty(in_bounds)
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% Specific alternating pattern for weight to minimize overlapping
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if i < 9
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weight = 0.05;
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else
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weight = 0.05 + 0.1 * mod(i, 2);
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end
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idx = in_bounds(max(1, min(length(in_bounds), round(length(in_bounds) * weight))));
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text(f_curve_GHz(idx), L_curve_km(idx), sprintf('%g nm', lvl), ...
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'Color', 'k', 'BackgroundColor', 'w', 'Margin', 1.5, ...
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'HorizontalAlignment', 'center', 'VerticalAlignment', 'middle', ...
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'EdgeColor', 'k', 'FontSize', 9);
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end
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end
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% Axis formatting
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xlabel('Signal Bandwidth [GHz]', 'FontSize', 11);
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ylabel('Fiber length [km]', 'FontSize', 11);
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xticks(min(f_GHz):10:max(f_GHz));
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yticks(min(L_km):2.5:max(L_km));
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grid on; box on;
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axis([min(f_GHz) max(f_GHz) min(L_km) max(L_km)]);
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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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min_D = min(Dacc_surface(:), [], 'omitnan');
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max_D = max(Dacc_surface(:), [], 'omitnan');
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% Calculate 3 integer levels well within the data range
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D_levels = unique(round(linspace(min_D*0.8, max_D*0.8, 3)));
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[CS, h] = contour(f_GHz, L_km, Dacc_surface, D_levels, 'k--', 'LineWidth', 0.8);
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clabel(CS, h, 'Color','k', 'FontSize',8);
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end
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%% Export
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% Hier erzwingen wir die rote Colormap für pgfplots, damit mat2tikz es nicht blau exportiert!
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% mat2tikz_improved("C:/Users/Silas/Documents/6971e0b65b380ca6d71c837f/02_IMDD_System/tikz/dispersion/dispersion_power_fading_contour2.tikz");
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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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