CLEANUP - changes to folder structure

Theory/Dissertation/pmd_vs_length.m

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+
+% pmd_vs_length.m
+% ------------------------------------------------------------
+% Plots the Foschini-Poole (1991) analytical variance formula for PMD:
+%
+%   sigma_T^2(z) = 2*(Delta_beta1)^2 * lc^2
+%                  * [ exp(-z/lc) + z/lc - 1 ]
+%
+% and overlays the two asymptotic regimes:
+%   - Short-reach  (z << lc) : sigma_T(z) ~ (Delta_beta1) * z
+%   - Long-haul    (z >> lc) : sigma_T(z) ~ Dp * sqrt(z)
+%
+% Parameters follow typical SMF values from the literature.
+% ------------------------------------------------------------
+
+clear; clc;
+
+%% ── Parameters ──────────────────────────────────────────────────────────────
+% Intrinsic local birefringence  [ps/km]
+Delta_beta1 = 1e-1;           % typical value, adjust as needed
+
+% Correlation length [km]
+lc          = 0.01;           % ~50 m, typical for G.652 SMF
+
+% PMD parameter  [ps / sqrt(km)]  —  derived from the two above
+Dp          = Delta_beta1 * sqrt(2 * lc);
+
+% Distance axis [km]
+z_max       = 10;            % maximum distance
+z           = linspace(0.001, z_max, 10000);   % avoid z = 0 in log plot
+
+%% ── Exact Foschini-Poole formula (sigma_T in ps) ────────────────────────────
+sigma_T_sq  = 2 .* Delta_beta1.^2 .* lc.^2 ...
+    .* (exp(-z ./ lc) + z ./ lc - 1);
+sigma_T     = sqrt(sigma_T_sq);          % RMS DGD  [ps]
+
+%% ── Asymptotic regimes ───────────────────────────────────────────────────────
+% Short-reach: linear growth  (z << lc)
+sigma_T_short = Delta_beta1 .* z;        % [ps]
+
+% Long-haul: square-root growth  (z >> lc)
+sigma_T_long  = Dp .* sqrt(z);          % [ps]
+
+%% ── Plot ─────────────────────────────────────────────────────────────────────
+figure('Color','w','Position',[100 100 760 480]);
+hold on;
+
+% Color palette (matching dissertation style)
+c_exact = [0.1216, 0.4706, 0.7059];      % blue  – exact
+c_short = [0.8392, 0.1529, 0.1569];      % red   – short-reach asymptote
+c_long  = [0.1961, 0.6314, 0.1725];      % green – long-haul asymptote
+
+% Exact solution
+h_exact = plot(z, sigma_T, ...
+    'Color', c_exact, 'LineWidth', 2.0, ...
+    'DisplayName', 'Exact (Foschini \& Poole)');
+
+% Short-reach asymptote  σ_T ≈ Δβ₁ · z
+h_short = plot(z, sigma_T_short, ...
+    'Color', c_short, 'LineWidth', 1.4, 'LineStyle', '--', ...
+    'DisplayName', '$\sigma_T \approx \Delta\beta_1 \cdot z$  \quad ($z \ll l_c$)');
+
+% Long-haul asymptote  σ_T ≈ D_p √z
+h_long  = plot(z, sigma_T_long, ...
+    'Color', c_long,  'LineWidth', 1.4, 'LineStyle', ':', ...
+    'DisplayName', '$\sigma_T \approx D_p \sqrt{z}$  \quad ($z \gg l_c$)');
+
+%% ── Axes & decoration ────────────────────────────────────────────────────────
+ax = gca;
+set(ax, 'XScale', 'log', 'YScale', 'log');
+
+% ── X-axis: linear-style tick labels on log scale ────────────────────────
+x_ticks = [1e-3, 1e-2, 1e-1, 1, 10];
+ax.XTick = x_ticks;
+ax.XTickLabel = arrayfun(@(v) sprintf('%g km', v), x_ticks, 'UniformOutput', false);
+
+% ── Y-axis: linear-style tick labels on log scale ────────────────────────
+y_ticks = [1e-3, 1e-2, 1e-1, 1, 10];
+ax.YTick = y_ticks;
+ax.YTickLabel = arrayfun(@(v) sprintf('%g ps', v), y_ticks, 'UniformOutput', false);
+
+xlabel('Fiber length $z$ [km]',              'Interpreter', 'latex');
+ylabel('RMS DGD $\sigma_T$ [ps]',            'Interpreter', 'latex');
+
+grid on; box on;
+xlim([min(z) z_max]);
+
+legend([h_exact, h_short, h_long], ...
+    'Location', 'northwest', 'Interpreter', 'latex', 'FontSize', 9);
+
+% Parameter annotation
+anno_str = sprintf( ...
+    ['$\\Delta\\beta_1 = %.3g$ ps/km\n' ...
+    '$l_c = %.0f$ m\n' ...
+    '$D_p = \\Delta\\beta_1\\sqrt{2l_c} = %.4g$ ps/$\\sqrt{\\mathrm{km}}$'], ...
+    Delta_beta1, lc*1e3, Dp);
+
+annotation('textbox', [0.57 0.14 0.38 0.22], ...
+    'String',        anno_str, ...
+    'Interpreter',   'latex', ...
+    'FontSize',      8.5, ...
+    'BackgroundColor','w', ...
+    'EdgeColor',     [0.5 0.5 0.5], ...
+    'LineWidth',     0.8, ...
+    'FitBoxToText',  'on');
+
+%% ── Regime transition marker ─────────────────────────────────────────────────
+% Mark the crossover region around z = lc
+xline(lc, '--', ...
+    'Color', [0.5 0.5 0.5], 'LineWidth', 0.8, ...
+    'HandleVisibility', 'off');
+text(lc * 1.15, min(sigma_T)*3, '$l_c$', ...
+    'Interpreter', 'latex', 'Color', [0.4 0.4 0.4], 'FontSize', 9);
+
+%% ── Export (uncomment to use) ────────────────────────────────────────────────
+% mat2tikz_improved('C:\...\tikz\pmd\pmd_vs_length.tikz')