Merge branch 'main' of cau-git.rz.uni-kiel.de:nt/mitarbeiter/silas/imdd_simulation
This commit is contained in:
Silas Oettinghaus
@@ -9,31 +9,35 @@
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% S0 - dispersion slope at ZDW [ps/(nm^2·km)]
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% ------------------------------------------------------------
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lambda0_nm = 1310;
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S0 = [0.07,0.09]';
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%% ZDW 1
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lambda0_nm = [1310];
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S0 = [0.075,0.095]';
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% wavelength axis around ZDW
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lambda_nm = linspace(lambda0_nm-60, lambda0_nm+60, 400);
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lambda_nm = linspace(1240, 1360, 400);
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% exact dispersion model
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D_exact = (S0./4) .* ( ...
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D_exact_1 = (S0./4) .* ( ...
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lambda_nm - (lambda0_nm^4)./(lambda_nm.^3) );
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% linearized model around ZDW
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D_lin = S0 .* (lambda_nm - lambda0_nm);
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%% ZDW 2
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lambda0_nm = [1320];
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% exact dispersion model
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D_exact_2 = (S0./4) .* ( ...
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lambda_nm - (lambda0_nm^4)./(lambda_nm.^3) );
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% plot
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%% plot
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figure('Color','w'); hold on;
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cols = [0.6510 0.8078 0.8902;...
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0.1216 0.4706 0.7059;...
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0.6980 0.8745 0.5412;...
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0.2000 0.6275 0.1725];
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% plot(lambda_nm, D_lin(1,:), '-', 'LineWidth',2, 'DisplayName','Linearized model','Color',[cols(1,:)]);
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plot(lambda_nm, D_exact(1,:), 'LineWidth',2, 'DisplayName',sprintf('S_0 = 0.07'),'Color',[cols(2,:)]);
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% plot(lambda_nm, D_lin(2,:), '-', 'LineWidth',2, 'HandleVisibility','off','Color',[cols(3,:)]);
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plot(lambda_nm, D_exact(2,:), 'LineWidth',2, 'HandleVisibility','on', 'DisplayName',sprintf('S_0 = 0.09'),'Color',[cols(4,:)]);
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plot(lambda_nm, D_exact_1(1,:), 'LineWidth',2, 'DisplayName',sprintf('$S_0=\SI{0.09}{\Dslope}$'),'Color',[0,0,0]);
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plot(lambda_nm, D_exact_1(2,:), 'LineWidth',2, 'DisplayName',sprintf('$S_0=\SI{0.09}{\Dslope}$'),'Color',[0,0,0]);
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% plot(lambda_nm, D_exact_2(1,:), 'LineWidth',2, 'HandleVisibility','on', 'DisplayName',sprintf('$S_0=\SI{0.09}{\Dslope}$'),'Color',[0,0,0]);
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% plot(lambda_nm, D_exact_2(2,:), 'LineWidth',2, 'HandleVisibility','on', 'DisplayName',sprintf('$S_0=\SI{0.09}{\Dslope}$'),'Color',[0,0,0]);
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xlabel('Wavelength $\lambda$ [nm]','Interpreter','latex');
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ylabel('D($\lambda$) [ps/(nm km)]','Interpreter','latex');
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@@ -44,3 +48,167 @@ xlim([min(lambda_nm) max(lambda_nm)])
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ylim([-5 5]);
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% mat2tikz_improved('C:\Users\Silas\Documents\6971e0b65b380ca6d71c837f\02_IMDD_System\tikz\dispersion\dispersion')
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%%
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%% plot_dispersion_dual_ZDW
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% Visualizes two ZDW fiber types, each with an S0 tolerance range.
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%% plot_dispersion_minimal_for_tikz
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% Minimal setup for clean TikZ tuning
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% 1. Parameters
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lambda_nm = linspace(1240, 1360, 400);
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S0_range = [0.075, 0.095];
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ZDW_range = [1300, 1325];
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% 2. Calculate Envelope and Nominal
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[S_mesh, Z_mesh] = meshgrid(S0_range, ZDW_range);
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D_all = zeros(length(lambda_nm), 4);
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for i = 1:4
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D_all(:,i) = (S_mesh(i)/4) .* (lambda_nm - (Z_mesh(i)^4)./(lambda_nm.^3));
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end
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D_env_min = min(D_all, [], 2);
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D_env_max = max(D_all, [], 2);
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D_nominal = (mean(S0_range)/4) .* (lambda_nm - (mean(ZDW_range)^4)./(lambda_nm.^3));
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% 3. Plotting
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figure('Color','w'); hold on;
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env_col = [0.1216, 0.4706, 0.7059];
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% Shaded area
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[hl, hp] = boundedline(lambda_nm, (D_env_min+D_env_max)/2, ...
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(D_env_max-D_env_min)/2, 'alpha', 'cmap', env_col);
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set(hl, 'YData', D_nominal, 'Color', 'k', 'LineWidth', 1.5);
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% Generate the outline and capture the handle
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ho = outlinebounds(hl, hp);
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% Change properties
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set(ho, 'Color', 'k', ... % Make it black
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'LineStyle', '--', ... % Make it dashed
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'LineWidth', 0.5, ... % Make it thin
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'HandleVisibility', 'off'); % Hide from legend
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% 4. "Minimal" Measurement Lines (Tweak these in TikZ later)
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% Vertical measurement at 1290nm
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lambda_v = 1290;
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[~, idx] = min(abs(lambda_nm - lambda_v));
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y_bot = D_env_min(idx);
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y_top = D_env_max(idx);
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% Simple line - in TikZ this will be a single \draw command
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line([lambda_v, lambda_v], [y_bot, y_top], 'Color', 'r', 'LineWidth', 1.2, 'Tag', 'VertArrow');
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text(lambda_v + 2, (y_top+y_bot)/2, '$\Delta D$', 'Color', 'r', 'Interpreter', 'latex');
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% Horizontal measurement at D=0
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z1 = ZDW_range(1);
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z2 = ZDW_range(2);
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line([z1, z2], [0, 0], 'Color', [0.1 0.5 0.1], 'LineWidth', 1.2, 'Tag', 'HorizArrow');
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text(mean(ZDW_range), 0.5, '$\Delta \lambda_0$', 'Color', [0.1 0.5 0.1], ...
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'Interpreter', 'latex', 'HorizontalAlignment', 'center');
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% 5. Aesthetics
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xlabel('Wavelength $\lambda$ [nm]', 'Interpreter', 'latex');
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ylabel('$D(\lambda)$ [ps/(nm km)]', 'Interpreter', 'latex');
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grid on; box on;
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xlim([1240 1360]); ylim([-5 5]);
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line(xlim, [0 0], 'Color', [0.4 0.4 0.4], 'LineStyle', '--', 'HandleVisibility', 'off');
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% Legend using the handles we have
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legend([hp, hl], {'Worst-case Envelope', 'Nominal Realization'}, ...
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'Location', 'northwest', 'Interpreter', 'latex');
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% To export, run:
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% matlab2tikz('dispersion.tex', 'standalone', true);
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%% plot_dispersion_for_tikz
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% Optimized for matlab2tikz compatibility with manual arrows
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%% plot_dispersion_statistical_envelopes
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% Visualizes hard spec limits vs. 98% statistical distribution
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%% plot_dispersion_final_for_tikz
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lambda_nm = linspace(1240, 1360, 400);
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% 1. Statistical & Specification Parameters
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p01_L = norminv(0.01, 1317, 2);
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p99_L = norminv(0.99, 1317, 2);
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p01_S = norminv(0.01, 0.0872, 0.0012);
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p99_S = norminv(0.99, 0.0872, 0.0012);
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% Scenarios: [ZDW_min, ZDW_max], [S0_min, S0_max], [Color RGB]
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scenarios = { ...
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[1303, 1325], [0.075, 0.0925], [0.6510, 0.8078, 0.8902]; ... % 1. Wide Spec (Gray)
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[p01_L, p99_L], [p01_S, p99_S], [0.6, 0.6, 0.6] ... % 2. 98% Stats (Blue)
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};
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figure('Color','w'); hold on;
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hp_handles = [];
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% 2. Calculate and Plot Envelopes
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for k = 1:size(scenarios, 1)
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Zr = scenarios{k,1};
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Sr = scenarios{k,2};
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col = scenarios{k,3};
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[S_mesh, Z_mesh] = meshgrid(Sr, Zr);
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D_all = zeros(length(lambda_nm), 4);
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for i = 1:4
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D_all(:,i) = (S_mesh(i)/4) .* (lambda_nm - (Z_mesh(i)^4)./(lambda_nm.^3));
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end
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D_min_env = min(D_all, [], 2);
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D_max_env = max(D_all, [], 2);
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[hl, hp] = boundedline(lambda_nm, (D_min_env+D_max_env)/2, (D_max_env-D_min_env)/2, ...
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'cmap','alpha', col);
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hp_handles(k) = hp;
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set(hl, 'Visible', 'off');
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if k == 1
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D_wide_min = D_min_env;
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D_wide_max = D_max_env;
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% ho = outlinebounds(hl, hp);
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% % Change properties
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% set(ho, 'Color', 'k', ... % Make it black
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% 'LineStyle', '--', ... % Make it dashed
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% 'LineWidth', 1, ... % Make it thin
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% 'HandleVisibility', 'off'); % Hide from legend
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% Capture Wide Spec (k=1) bounds for the TikZ measurement lines
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hp.FaceAlpha = 0.5;
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else
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hp.FaceAlpha = 0.8;
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end
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end
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% 3. Nominal Line
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D_nom = (0.0872/4) .* (lambda_nm - (1317^4)./(lambda_nm.^3));
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h_nom = plot(lambda_nm, D_nom, 'k', 'LineWidth', 1,'LineStyle','-');
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% 4. Minimal Lines for TikZ (Measuring Wide Spec)
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lambda_v = 1290;
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[~, idx_v] = min(abs(lambda_nm - lambda_v));
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% Vertical line showing full Wide Spec dispersion range at 1290nm
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line([lambda_v, lambda_v], [D_wide_min(idx_v), D_wide_max(idx_v)], 'Color', 'k', 'Tag', 'VertArrow','LineWidth', 1);
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% Horizontal line showing Wide Spec ZDW range at D=0
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% line([1303, 1325], [0, 0], 'Color', 'k', 'Tag', 'HorizArrow','LineWidth', 1);
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% 5. Aesthetics & Legend
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xlabel('Wavelength $\lambda$ [nm]', 'Interpreter', 'latex');
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ylabel('$D(\lambda)$ [ps/(nm km)]', 'Interpreter', 'latex');
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grid on; box on;
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xlim([1240 1360]); ylim([-5 5]);
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leg_labels = { ...
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'$\lambda_0 \in [1303, 1325], S_0 \in [0.075, 0.0925]$', ...
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'$\lambda_0 \in [1312, 1322], S_0 \in [0.084, 0.090]$', ...
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'$\lambda_0 = 1317, S_0 = 0.0872$'};
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legend([hp_handles, h_nom], leg_labels, 'Location', 'northwest', 'Interpreter', 'latex', 'FontSize', 8);
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% Export command (uncomment to use)
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% mat2tikz_improved('C:\Users\Silas\Documents\6971e0b65b380ca6d71c837f\02_IMDD_System\tikz\dispersion\dispersion_slope.tikz')
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@@ -0,0 +1,183 @@
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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] = contour(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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|
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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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||||
|
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c = physconst('lightspeed');
|
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S0_si = S0 * 1e3; % ps/(nm²·km) -> s/(m³)
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|
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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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|
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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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|
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lambda_vec = NaN(N,1);
|
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Dacc_vec = NaN(N,1);
|
||||
|
||||
|
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|
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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)
|
||||
fun = @(lambda) -(S0_si/4).*(lambda - (lambda0^4)./(lambda.^3)).*lambda.^2 - RHS;
|
||||
|
||||
% 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
|
||||
% If the zero is not within bounds, skip this point
|
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lambda_sol = NaN;
|
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end
|
||||
|
||||
% Validate solution
|
||||
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
|
||||
|
||||
% 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
|
||||
142
Functions/Theory/Dissertation/dispersion_contour_bivariate.m
Normal file
142
Functions/Theory/Dissertation/dispersion_contour_bivariate.m
Normal file
@@ -0,0 +1,142 @@
|
||||
% Festen Betriebsparameter
|
||||
lambda = 1290; % nm
|
||||
L = 1; % km
|
||||
mu_zwd = 1317; % nm
|
||||
sigma_zwd = 2; % nm
|
||||
mu_s0 = 0.0872; % ps / nm2 km
|
||||
sigma_s0 = 0.0012; % ps / nm2 km
|
||||
rho = -0.5; % Korrelation
|
||||
|
||||
% Gitter für lambda0 und S0
|
||||
lambda0_vec = linspace(mu_zwd-10, mu_zwd+10, 100);
|
||||
S0_vec = linspace(mu_s0-0.01, mu_s0+0.01, 100);
|
||||
|
||||
% Korrigierte meshgrid Reihenfolge
|
||||
[S0, Lambda0] = meshgrid(S0_vec, lambda0_vec);
|
||||
|
||||
% Dispersion berechnen
|
||||
D = (S0./4) .* ( lambda - (Lambda0.^4)./(lambda^3) ) * L;
|
||||
|
||||
% 2D Verteilung (Bivariate Gauss) berechnen
|
||||
Z_x = (S0 - mu_s0) / sigma_s0;
|
||||
Z_y = (Lambda0 - mu_zwd) / sigma_zwd;
|
||||
PDF_2D = exp(-1 / (2 * (1 - rho^2)) * (Z_x.^2 - 2 * rho .* Z_x .* Z_y + Z_y.^2));
|
||||
|
||||
%% Plot zusammenbauen
|
||||
figure('Color','w');
|
||||
hold on % EINZIGES hold on für den gesamten Plot!
|
||||
|
||||
% --- 1. ZUERST: 2D Verteilung (Bivariate Gauss) "ganz unten" ---
|
||||
numLevels_2D = 6;
|
||||
colors_2D = cbrewer2('Greys', numLevels_2D+0);
|
||||
colors_2D = colors_2D(1:numLevels_2D,:);
|
||||
% Nur die Anzahl der Level übergeben!
|
||||
[C2, h2] = contourf(S0, Lambda0, PDF_2D, numLevels_2D);
|
||||
h2.HandleVisibility='off';
|
||||
% Colormap für die rote Fläche setzen
|
||||
|
||||
colormap(gcf, colors_2D(1:end,:));
|
||||
try
|
||||
clim([min(PDF_2D(:)), max(PDF_2D(:))]);
|
||||
catch
|
||||
caxis([min(PDF_2D(:)), max(PDF_2D(:))]);
|
||||
end
|
||||
|
||||
h2.EdgeColor = 'none'; % Keine schwarzen Ränder
|
||||
|
||||
% --- 2. DARÜBER: Dispersions-Konturlinien ---
|
||||
numLevels_D = 9;
|
||||
% Erzeuge glatte, auf 1 Nachkommastelle gerundete Werte
|
||||
levels_D = round(linspace(min(D(:)), max(D(:)), numLevels_D), 1);
|
||||
levels_D = unique(levels_D);
|
||||
cmap_bg = flip(cbrewer2('Blues', length(levels_D)+3));
|
||||
|
||||
for i = 1:length(levels_D)
|
||||
% Konturlinien zeichnen (explizit Schwarz)
|
||||
[C,h] = contour(S0, Lambda0, D, [levels_D(i), levels_D(i)], ...
|
||||
'Color', cmap_bg(i,:),...
|
||||
'LineWidth', 1, ...
|
||||
'ShowText', 'off','handlevisibility','off');
|
||||
if i == 1
|
||||
h.HandleVisibility='on';
|
||||
h.DisplayName='$D(\lambda=1290)$';
|
||||
end
|
||||
end
|
||||
|
||||
% --- 3. MANUELLE TEXTBOXEN AUF DEN LINIEN ---
|
||||
% Wähle eine feste S0-Position für alle Beschriftungen (z.B. bei 0.082)
|
||||
S0_label = 0.095;
|
||||
|
||||
for i = 1:length(levels_D)
|
||||
% Berechne exakte ZDW (Y-Koordinate) durch Umstellen der D-Formel:
|
||||
% Lambda0 = (lambda^3 * (lambda - 4*D / (S0 * L)))^(1/4)
|
||||
zdw_label = (lambda^3 * (lambda - 4*levels_D(i) / (S0_label * L)))^0.25;
|
||||
|
||||
% Nur zeichnen, wenn der Punkt auch im sichtbaren Plot-Bereich liegt
|
||||
if zdw_label >= min(lambda0_vec) && zdw_label <= max(lambda0_vec)
|
||||
text(S0_label, zdw_label, sprintf('%0.1f', levels_D(i)), ...
|
||||
'Color', 'k', ...
|
||||
'BackgroundColor', 'w', ... % Weiße Box überdeckt die schwarze Linie!
|
||||
'Margin', 2, ... % Abstand der Box zum Text
|
||||
'HorizontalAlignment', 'center', ...
|
||||
'VerticalAlignment', 'middle', ...
|
||||
'FontSize', 10);
|
||||
end
|
||||
end
|
||||
|
||||
% --- 3. GANZ OBEN: Randverteilungen (1D Gauss) an den Achsen ---
|
||||
% S0 Verteilung (unten)
|
||||
s0_vals = linspace(min(S0_vec), max(S0_vec), 500);
|
||||
gauss_s0 = exp(-0.5*((s0_vals - mu_s0)/sigma_s0).^2);
|
||||
scale_s0 = 4;
|
||||
y_s0_base = min(lambda0_vec);
|
||||
plot(s0_vals, y_s0_base + gauss_s0 * scale_s0, 'LineWidth', 1,'LineStyle','--','DisplayName','$S_0$','Color',[0,0,0],'HandleVisibility','off');
|
||||
% ANNOTATION S0: Automatisch platziert leicht über dem Peak
|
||||
str_s0 = sprintf('\\mu_{S0} = %.4f\n\\sigma_{S0} = %.4f', mu_s0, sigma_s0);
|
||||
text(0.0915,1308, str_s0, ...
|
||||
'Interpreter', 'tex', ...
|
||||
'HorizontalAlignment', 'left', ... % Entspricht 'right' in TikZ
|
||||
'VerticalAlignment', 'middle', ...
|
||||
'BackgroundColor', 'w', ... % Entspricht 'fill=white'
|
||||
'EdgeColor', 'k', ... % Entspricht 'draw=black'
|
||||
'Margin', 1, ... % Entspricht 'inner sep=1pt'
|
||||
'FontSize', 10);
|
||||
|
||||
% ZDW Verteilung (links)
|
||||
% ZDW Verteilung (links)
|
||||
zwd_vals = linspace(min(lambda0_vec), max(lambda0_vec), 500);
|
||||
gauss_zwd = exp(-0.5*((zwd_vals - mu_zwd)/sigma_zwd).^2);
|
||||
scale_zwd = 0.005;
|
||||
x_zwd_base = min(S0_vec);
|
||||
plot(x_zwd_base + gauss_zwd * scale_zwd, zwd_vals, 'LineWidth', 1,'LineStyle','--','DisplayName','ZDW','Color',[0,0,0],'HandleVisibility','off');
|
||||
|
||||
% ANNOTATION ZDW: Automatisch platziert leicht rechts neben dem Peak
|
||||
str_zwd = sprintf('\\mu_{ZDW} = %.1f\n\\sigma_{ZDW} = %.1f', mu_zwd, sigma_zwd);
|
||||
text(0.079,1312, str_zwd, ...
|
||||
'Interpreter', 'tex', ...
|
||||
'HorizontalAlignment', 'left', ... % Entspricht 'right' in TikZ
|
||||
'VerticalAlignment', 'middle', ...
|
||||
'BackgroundColor', 'w', ... % Entspricht 'fill=white'
|
||||
'EdgeColor', 'k', ... % Entspricht 'draw=black'
|
||||
'Margin', 1, ... % Entspricht 'inner sep=1pt'
|
||||
'FontSize', 10);
|
||||
|
||||
% Hilfslinien für die Mittelwerte
|
||||
% xline(mu_s0,'LineWidth',0.5,'HandleVisibility','off','LineStyle',':');
|
||||
% yline(mu_zwd,'LineWidth',0.5,'HandleVisibility','off','LineStyle',':');
|
||||
|
||||
% --- Achsenbeschriftung, Titel & Formatierung ---
|
||||
xlabel('$S_0$ [$\nicefrac{\text{ps}}{(\text{nm}^2\text{ km})}$]', 'FontSize', 12);
|
||||
ylabel('ZDW [nm]', 'FontSize', 12);
|
||||
% title(sprintf('Dispersion: %d km; %d nm', L, lambda), 'FontSize', 14);
|
||||
|
||||
grid on
|
||||
% Exakte Begrenzung, damit die Randverteilungen bündig anliegen
|
||||
axis([min(S0_vec) max(S0_vec) min(lambda0_vec) max(lambda0_vec)]);
|
||||
|
||||
% legend;
|
||||
hold off % EINZIGES hold off ganz am Ende!
|
||||
|
||||
%% Export
|
||||
% Hier erzwingen wir die rote Colormap für pgfplots, damit mat2tikz es nicht blau exportiert!
|
||||
mat2tikz_improved("C:/Users/Silas/Documents/6971e0b65b380ca6d71c837f/02_IMDD_System/tikz/dispersion/dispersion_contour_bi2.tikz");
|
||||
@@ -1,124 +0,0 @@
|
||||
%% ============================================================
|
||||
% SNR vs Optical Input Power (dBm) — Shot vs Thermal vs Combined
|
||||
% - Generate optical field as sine with target RMS power (verified)
|
||||
% - Magnitude-square detection -> optical power
|
||||
% - Photocurrent = Rd * P
|
||||
% - Add shot noise + thermal noise (white, PSD-based)
|
||||
% - Compute SNR for: shot-only, thermal-only, combined
|
||||
% ============================================================
|
||||
|
||||
|
||||
% Constants
|
||||
k = Constant.Boltzmann;
|
||||
q = Constant.ElementaryCharge;
|
||||
|
||||
% Receiver / PD parameters
|
||||
T = 20 + 273.15; % K
|
||||
R = 50; % Ohm (front-end/load)
|
||||
Rd = 0.7; % A/W (responsivity)
|
||||
Be = 100e9; % Hz (electrical noise bandwidth)
|
||||
Id = 0; % A (dark current, optional)
|
||||
|
||||
% Sampling for time-domain demo (needs to be >> Be)
|
||||
fs = 1e12; % Hz
|
||||
N = 2^14; % samples
|
||||
t = (0:N-1).'/fs;
|
||||
|
||||
% Choose an electrical tone within bandwidth (arbitrary for demo)
|
||||
f0 = 10e9; % Hz
|
||||
|
||||
% Thermal current PSD (two-sided) and variance in Be
|
||||
Si_th = 4*k*T/R; % A^2/Hz (two-sided)
|
||||
sigma2_th = Si_th * Be; % A^2
|
||||
sigma_th = sqrt(sigma2_th); % A_rms
|
||||
|
||||
% Optical input power sweep (in dBm)
|
||||
P_dBm = linspace(-40, 10, 300);
|
||||
P_W = 10.^((P_dBm - 30)/10); % W
|
||||
|
||||
% Pre-allocate results
|
||||
SNR_shot_dB = zeros(size(P_dBm));
|
||||
SNR_th_dB = zeros(size(P_dBm));
|
||||
SNR_tot_dB = zeros(size(P_dBm));
|
||||
|
||||
% --- Main loop over optical input power
|
||||
for ii = 1:numel(P_W)
|
||||
Pavg = P_W(ii);
|
||||
|
||||
% Optical field with RMS power = Pavg:
|
||||
% Let x(t) be the optical field amplitude such that |x|^2 has mean Pavg.
|
||||
% Use a sinusoid: x(t) = A*sin(2*pi*f0*t), then mean(|x|^2)=A^2/2.
|
||||
A = sqrt(2*Pavg); % -> mean(|x|^2) = Pavg
|
||||
|
||||
x = A * sin(2*pi*f0*t); % "optical field" (real for simplicity)
|
||||
|
||||
% Verify RMS/mean power numerically (optional)
|
||||
P_meas = mean(abs(x).^2); % should be ~ Pavg
|
||||
|
||||
a = P_meas - Pavg;
|
||||
assert(a<1);
|
||||
|
||||
% Magnitude-square detection -> optical power waveform
|
||||
Popt = abs(x).^2; % W (instantaneous)
|
||||
|
||||
% Photocurrent waveform (includes DC + 2f0 component for this demo)
|
||||
I_sig = Rd * Popt; % A
|
||||
|
||||
% Define "signal power" as the mean-squared photocurrent due to signal
|
||||
% (for this sine-squared waveform, it's OK for a demo SNR definition)
|
||||
P_sig = mean(I_sig.^2);
|
||||
|
||||
% -------- Shot noise (white) --------
|
||||
% Two-sided PSD: Si_shot = 2*q*(I_photo + I_dark)
|
||||
% For this demo, use average current to set the white-noise level:
|
||||
Ibar = mean(I_sig) + Id;
|
||||
Si_shot = 2*q*Ibar; % A^2/Hz
|
||||
sigma2_sh = Si_shot * Be; % A^2
|
||||
sigma_sh = sqrt(sigma2_sh); % A_rms
|
||||
|
||||
n_sh = sigma_sh * randn(N,1); % time-domain shot noise
|
||||
|
||||
% -------- Thermal noise (white Gaussian) --------
|
||||
n_th = sigma_th * randn(N,1); % time-domain thermal noise
|
||||
|
||||
% Noise powers (mean-square) in time domain
|
||||
Pn_sh = mean(n_sh.^2);
|
||||
Pn_th = mean(n_th.^2);
|
||||
Pn_tot = mean((n_sh + n_th).^2); % ~ Pn_sh + Pn_th (independent)
|
||||
|
||||
% SNRs
|
||||
SNR_shot = P_sig / Pn_sh;
|
||||
SNR_th = P_sig / Pn_th;
|
||||
SNR_tot = P_sig / Pn_tot;
|
||||
|
||||
SNR_shot_dB(ii) = 10*log10(SNR_shot);
|
||||
SNR_th_dB(ii) = 10*log10(SNR_th);
|
||||
SNR_tot_dB(ii) = 10*log10(SNR_tot);
|
||||
|
||||
% Optional sanity check (can comment out)
|
||||
% if ii == 1
|
||||
% fprintf('Check Pavg target/meas: %.3g W / %.3g W\n', Pavg, P_meas);
|
||||
% end
|
||||
end
|
||||
|
||||
% Plot comparison
|
||||
figure(1); clf; hold on;
|
||||
plot(P_dBm, SNR_shot_dB, 'LineWidth', 1.5);
|
||||
plot(P_dBm, SNR_th_dB, 'LineWidth', 1.5);
|
||||
plot(P_dBm, SNR_tot_dB, 'LineWidth', 1.5);
|
||||
grid on;
|
||||
xlabel('Optical input power [dBm]');
|
||||
ylabel('SNR [dB]');
|
||||
title('SNR vs Optical Input Power: Shot vs Thermal vs Combined');
|
||||
legend('Shot-noise only','Thermal-noise only','Shot + Thermal','Location','best');
|
||||
|
||||
% Print example at 0 dBm
|
||||
[~,idx0] = min(abs(P_dBm - 0));
|
||||
fprintf('At 0 dBm:\n');
|
||||
fprintf(' SNR (shot only) = %.2f dB\n', SNR_shot_dB(idx0));
|
||||
fprintf(' SNR (thermal only) = %.2f dB\n', SNR_th_dB(idx0));
|
||||
fprintf(' SNR (combined) = %.2f dB\n', SNR_tot_dB(idx0));
|
||||
|
||||
% Also print NEP based on thermal PSD (constant NEP_th)
|
||||
NEP_th = sqrt(Si_th)/Rd; % W/sqrt(Hz)
|
||||
fprintf('Thermal NEP = %.3g W/sqrt(Hz)\n', NEP_th);
|
||||
47
Functions/Theory/Dissertation/power_fading.m
Normal file
47
Functions/Theory/Dissertation/power_fading.m
Normal file
@@ -0,0 +1,47 @@
|
||||
%% ============================================================
|
||||
% Minimal IM/DD Power Fading Plot
|
||||
% ============================================================
|
||||
|
||||
|
||||
%% Fiber and system parameters
|
||||
lambda0 = 1310e-9; % zero-dispersion wavelength [m]
|
||||
lambda = 1290e-9; % operating wavelength [m]
|
||||
S0 = 0.09; % 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 = 200e9;
|
||||
f = linspace(0, f_max, 5000); % [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,'Color','black');
|
||||
grid on; box on;
|
||||
xlabel('Frequency [GHz]');
|
||||
ylabel('Magnitude [dB]');
|
||||
% title(sprintf('IM/DD Power Fading: 10 km; 1275nm', lambda*1e9, L/1000),"Interpreter","latex");
|
||||
ylim([-20 0]);
|
||||
|
||||
%% Mark analytic null frequencies up to order 5
|
||||
max_order = 3;
|
||||
for n = 0:max_order
|
||||
f_null_n = sqrt( c*(2*n + 1)/(2*abs(D_si)*lambda^2*L) );
|
||||
xline(f_null_n/1e9, '--', 'LineWidth', 1.2, ...
|
||||
'Color', [0.1216, 0.4706, 0.7059]);
|
||||
text(f_null_n/1e9, -15, sprintf('$f_{\\mathrm{null}, %d}=%.1f$ GHz', n, f_null_n/1e9), ...
|
||||
'BackgroundColor', 'w', 'EdgeColor', 'k', 'Interpreter', 'latex', ...
|
||||
'HorizontalAlignment', 'center', 'VerticalAlignment', 'middle');
|
||||
end
|
||||
|
||||
% mat2tikz_improved('C:\Users\Silas\Documents\6971e0b65b380ca6d71c837f\02_IMDD_System\tikz\dispersion\power_fading.tikz')
|
||||
@@ -1,68 +0,0 @@
|
||||
%% ============================================================
|
||||
% IM/DD Power Fading Evolution GIF (1 km -> 20 km)
|
||||
% Uses the provided GifWriter (serial mode)
|
||||
% ============================================================
|
||||
|
||||
clear; close all; clc;
|
||||
|
||||
%% Fiber and system parameters
|
||||
lambda0 = 1310e-9; % zero-dispersion wavelength [m]
|
||||
lambda = 1275e-9; % operating wavelength [m]
|
||||
S0 = 0.09; % dispersion slope [ps/(nm^2·km)]
|
||||
c = physconst('lightspeed');
|
||||
|
||||
%% Derived quantities (length-independent)
|
||||
D_lambda = (S0/4) * (lambda*1e9 - (lambda0*1e9)^4/(lambda*1e9)^3); % ps/(nm·km)
|
||||
D_si = D_lambda * 1e-6; % s/m^2
|
||||
b2 = -D_si * lambda^2 / (2*pi*c); % s^2/m
|
||||
|
||||
%% Frequency grid
|
||||
f_max = 150e9;
|
||||
f = linspace(0, f_max, 4000); % [Hz]
|
||||
|
||||
%% Figure setup (keep it stable for nicer GIFs)
|
||||
fig = figure('Color','w');
|
||||
ax = axes(fig); %#ok<LAXES>
|
||||
hold(ax,'on'); grid(ax,'on'); box(ax,'on');
|
||||
xlabel(ax,'Frequency [GHz]');
|
||||
ylabel(ax,'Magnitude [dB]');
|
||||
ylim(ax,[-30 0]);
|
||||
xlim(ax,[0 f_max/1e9]);
|
||||
|
||||
%% GIF writer (serial mode; simplest)
|
||||
g = GifWriter('Name','power_fading_evolution', 'DelayTime',0.12, 'Parallel',false);
|
||||
|
||||
%% Loop: 1 km to 20 km
|
||||
L = [1:20,19:-1:1];
|
||||
for L_km = L
|
||||
L_meter = L_km * 1e3; % [m]
|
||||
|
||||
% IM/DD transfer function (power fading)
|
||||
phi = 2*pi^2 * b2 * f.^2 * L_meter;
|
||||
H = abs(cos(phi));
|
||||
HdB = 10*log10(max(H, 1e-12)); % avoid -Inf for deep notches
|
||||
|
||||
% Clear and redraw (stable axes)
|
||||
cla(ax);
|
||||
|
||||
plot(ax, f/1e9, HdB, 'LineWidth', 1.8, 'Color','black');
|
||||
|
||||
% Analytic first-null frequency marker
|
||||
f_null = sqrt(c*(0.5)/(abs(D_si)*lambda^2*L_meter));
|
||||
xline(ax, f_null/1e9, 'r--', 'LineWidth', 1.2, ...
|
||||
'Label', sprintf('f_{null}=%.1f GHz', f_null/1e9), ...
|
||||
'LabelOrientation','horizontal', ...
|
||||
'LabelVerticalAlignment','bottom');
|
||||
|
||||
title(ax, sprintf('Power Fading for: %.0f km @ 1275 nm', L_km));
|
||||
|
||||
drawnow;
|
||||
|
||||
% Add frame to GIF
|
||||
g.addFrame(fig);
|
||||
end
|
||||
|
||||
%% Done
|
||||
g.compile(fig.Number);
|
||||
|
||||
disp(fullfile(g.OutputDir, sprintf('%s_fig_%d.gif', g.Name, fig.Number)));
|
||||
@@ -1,69 +0,0 @@
|
||||
%% ============================================================
|
||||
% IM/DD Power Fading Evolution vs Wavelength (L = 10 km)
|
||||
% ============================================================
|
||||
|
||||
clear; close all; clc;
|
||||
|
||||
%% Fixed fiber parameters
|
||||
lambda0 = 1310e-9; % zero-dispersion wavelength [m]
|
||||
S0 = 0.09; % dispersion slope [ps/(nm^2·km)]
|
||||
L = 10e3; % fiber length FIXED [m]
|
||||
c = physconst('lightspeed');
|
||||
|
||||
%% Frequency grid
|
||||
f_max = 150e9;
|
||||
f = linspace(0, f_max, 4000); % [Hz]
|
||||
|
||||
%% Figure setup (stable axes for clean GIF)
|
||||
fig = figure('Color','w');
|
||||
ax = axes(fig);
|
||||
hold(ax,'on'); grid(ax,'on'); box(ax,'on');
|
||||
xlabel(ax,'Frequency [GHz]');
|
||||
ylabel(ax,'Magnitude [dB]');
|
||||
ylim(ax,[-30 0]);
|
||||
xlim(ax,[0 f_max/1e9]);
|
||||
|
||||
%% GIF writer
|
||||
g = GifWriter('Name','power_fading_vs_wavelength', ...
|
||||
'DelayTime',0.12, ...
|
||||
'Parallel',false);
|
||||
|
||||
%% Wavelength sweep (around ZDW)
|
||||
lambda_vec = linspace(1260e-9, 1360e-9, 25); % 1260–1360 nm
|
||||
|
||||
for k = 1:length(lambda_vec)
|
||||
|
||||
lambda = lambda_vec(k);
|
||||
|
||||
%% Dispersion for current wavelength
|
||||
D_lambda = (S0/4) * (lambda*1e9 - (lambda0*1e9)^4/(lambda*1e9)^3); % ps/(nm·km)
|
||||
D_si = D_lambda * 1e-6; % s/m^2
|
||||
b2 = -D_si * lambda^2 / (2*pi*c); % s^2/m
|
||||
|
||||
%% Power fading transfer function
|
||||
phi = 2*pi^2 * b2 * f.^2 * L;
|
||||
H = abs(cos(phi));
|
||||
HdB = 10*log10(max(H, 1e-12));
|
||||
|
||||
cla(ax)
|
||||
plot(ax, f/1e9, HdB, 'LineWidth',1.8,'Color','black');
|
||||
|
||||
%% First-null frequency
|
||||
if abs(D_si) > 0
|
||||
f_null = sqrt(c*(0.5)/(abs(D_si)*lambda^2*L));
|
||||
xline(ax, f_null/1e9, 'r--', 'LineWidth',1.2, ...
|
||||
'Label', sprintf('f_{null}=%.1f GHz', f_null/1e9), ...
|
||||
'LabelOrientation','horizontal', ...
|
||||
'LabelVerticalAlignment','bottom');
|
||||
end
|
||||
|
||||
title(ax, sprintf('Power Fading for: 10 km @ %.0f nm', lambda*1e9));
|
||||
|
||||
drawnow;
|
||||
g.addFrame(fig);
|
||||
end
|
||||
|
||||
%% Compile GIF
|
||||
g.compile(fig.Number);
|
||||
|
||||
disp(fullfile(g.OutputDir, sprintf('%s_fig_%d.gif', g.Name, fig.Number)));
|
||||
Reference in New Issue
Block a user