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Merge branch 'main' of cau-git.rz.uni-kiel.de:nt/mitarbeiter/silas/imdd_simulation

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Silas Oettinghaus
2025-10-17 11:50:52 +02:00
parent 3ea6439947 b5387f78c6
commit c33264a515
5 changed files with 335 additions and 0 deletions
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90
Functions/Theory/dispersion_10km.m Normal file
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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

32
Functions/Theory/dispersion_wavelength_notch.m Normal file
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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])

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Functions/Theory/dispersion_wdm.m Normal file
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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

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Functions/Theory/power_fading.m Normal file
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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');