halfway merged and pulled?!
This commit is contained in:
Silas Labor Zizou
146
Functions/Theory/dispersion_contour_bandwidth_lambda.m
Normal file
146
Functions/Theory/dispersion_contour_bandwidth_lambda.m
Normal file
@@ -0,0 +1,146 @@
|
||||
%% ------------------------------------------------------------
|
||||
% Contour plot: λ_null as function of bandwidth (f_target) and reach (L)
|
||||
% ------------------------------------------------------------
|
||||
|
||||
% Parameters
|
||||
lambda0 = 1310e-9; % [m]
|
||||
S0 = 0.08; % [ps/(nm²·km)]
|
||||
c = physconst('lightspeed');
|
||||
|
||||
% Sweep dimensions
|
||||
f_targets = linspace(50e9, 120e9, 100); % [Hz] (x-axis)
|
||||
L_values = linspace(0.5e3, 10e3, 100); % [m] (y-axis)
|
||||
|
||||
lambda_surface = zeros(numel(L_values), numel(f_targets));
|
||||
Dacc_surface = zeros(numel(L_values), numel(f_targets));
|
||||
|
||||
% Outer loop over fiber length (since L must be scalar)
|
||||
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_vec = 2*abs(lambda0 - lambda_vec);
|
||||
|
||||
if 0
|
||||
fprintf('\n- %d km ------------------------------------\n',L);
|
||||
fprintf(' f_null [GHz] lambda [nm] Dacc [ps/nm]\n');
|
||||
fprintf('----------------------------------------------\n');
|
||||
fprintf('%10.1f %8.2f %+8.3f\n',[f_targets(:)/1e9, lambda_vec(:)*1e9, Dacc_vec(:)].');
|
||||
fprintf('----------------------------------------------\n\n');
|
||||
end
|
||||
|
||||
lambda_surface(iL, :) = lambda_vec; % λ for each f_target
|
||||
Dacc_surface(iL, :) = Dacc_vec; % corresponding accumulated dispersion
|
||||
end
|
||||
|
||||
% Convert for plotting
|
||||
lambda_surface_nm = lambda_surface * 1e9; % [nm]
|
||||
L_km = L_values / 1000; % [km]
|
||||
f_GHz = f_targets / 1e9; % [GHz]
|
||||
|
||||
%% Contour plot
|
||||
figure('Color','w');
|
||||
|
||||
% Define wavelength contour levels [nm]
|
||||
lambda_levels = [1260:10:1290, 1290:5:1300, 1300:2.5:1310];
|
||||
lambda_levels = [100:-20:50, 50:-10:30,30:-5:0];
|
||||
|
||||
% Contour plot
|
||||
contour(f_GHz, L_km, lambda_surface_nm, lambda_levels, ...
|
||||
'LineWidth', 1.5, ...
|
||||
'ShowText', 'on', ...
|
||||
'LabelFormat', '%.0f nm');
|
||||
|
||||
% Colormap and colorbar
|
||||
colormap((cbrewer2('RdYlGn',100)));
|
||||
colorbar;
|
||||
clim([0 100]);
|
||||
|
||||
% Axis formatting
|
||||
xlabel('Signal Bandwidth [GHz]');
|
||||
ylabel('Fiber length [km]');
|
||||
legend('$\Delta \lambda$')
|
||||
|
||||
% X-axis ticks at 56 : 16 : 150 GHz
|
||||
xticks(56:8:150);
|
||||
|
||||
grid on; box on;
|
||||
|
||||
|
||||
%% Optional: overlay accumulated-dispersion contours
|
||||
if 0
|
||||
hold on;
|
||||
[CS, h] = contour(f_GHz, L_km, Dacc_surface, 10, 'k--', 'LineWidth', 0.8);
|
||||
clabel(CS, h, 'Color','k', 'FontSize',8);
|
||||
end
|
||||
|
||||
function [lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_target, L, lambda0, S0)
|
||||
% lambda_for_first_null_full (stable, single-branch + validity checks)
|
||||
% --------------------------------------------------------------------
|
||||
% Computes the wavelength(s) at which the first IM/DD fading null
|
||||
% occurs at frequency/ies f_target using the full dispersion model:
|
||||
%
|
||||
% D(lambda) = (S0/4)*(lambda - lambda0^4 / lambda^3)
|
||||
%
|
||||
% Restricted to the NORMAL-dispersion branch (λ < λ0),
|
||||
% and valid only in the O-band (1260–1360 nm).
|
||||
%
|
||||
% Inputs:
|
||||
% f_target - scalar or vector of target null frequencies [Hz]
|
||||
% L - fiber length [m]
|
||||
% lambda0 - zero-dispersion wavelength (ZDW) [m]
|
||||
% S0 - dispersion slope at ZDW [ps/(nm²·km)]
|
||||
%
|
||||
% Outputs:
|
||||
% lambda_vec - wavelength(s) [m] where first null occurs (clamped to O-band)
|
||||
% Dacc_vec - accumulated dispersion(s) [ps/nm] (NaN if out of valid range)
|
||||
% --------------------------------------------------------------------
|
||||
|
||||
c = physconst('lightspeed');
|
||||
S0_si = S0 * 1e3; % ps/(nm²·km) -> s/(m³)
|
||||
|
||||
% Define O-band boundaries (in meters)
|
||||
lambda_min = 1255e-9;
|
||||
lambda_max = 1361e-9;
|
||||
|
||||
% Force column vector
|
||||
f_target = f_target(:);
|
||||
N = numel(f_target);
|
||||
|
||||
lambda_vec = NaN(N,1);
|
||||
Dacc_vec = NaN(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;
|
||||
|
||||
% Limit the search to [λ_min, λ0)
|
||||
try
|
||||
lambda_sol = fzero(fun, [lambda_min, lambda0 * 0.999]);
|
||||
catch
|
||||
% If the zero is not within bounds, skip this point
|
||||
lambda_sol = NaN;
|
||||
end
|
||||
|
||||
% Validate solution
|
||||
if isnan(lambda_sol) || lambda_sol < lambda_min || lambda_sol > lambda_max
|
||||
lambda_vec(k) = NaN;
|
||||
Dacc_vec(k) = NaN;
|
||||
continue
|
||||
end
|
||||
|
||||
% 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
|
||||
|
||||
% Sanity bound on dispersion (avoid unphysical > ±100 ps/nm)
|
||||
if abs(Dacc_val) > 100
|
||||
lambda_vec(k) = NaN;
|
||||
Dacc_vec(k) = NaN;
|
||||
else
|
||||
lambda_vec(k) = lambda_sol;
|
||||
Dacc_vec(k) = Dacc_val;
|
||||
end
|
||||
end
|
||||
end
|
||||
Reference in New Issue
Block a user