Added presentation; DE-QPSK; CD with FFT; split-step Fourier

[4yp.git] / agrawalAppendixB.m

diff --git a/agrawalAppendixB.m b/agrawalAppendixB.m
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+distance = input('Enter fiber length in L_D ');
+beta2 = input('dispersion: 1 for normal, -1 for anomalous ');
+N = input('Nonlinear parameter N = '); % Soliton order
+mshape = input('m = 0 for sech, m > 0 for super-Gaussian ');
+chirp0 = 0;
+
+% set simulation parameters
+nt = 1024; Tmax = 32; % FFT points and window size
+step_num = round(20 * distance * N^2); % No. of z steps
+deltaz = distance/step_num; % step size in z
+dtau = (2*Tmax) / nt; % step size in tau
+
+%% tau and omega arrays
+tau = (-nt/2 : nt/2-1) * dtau; % temporal grid
+omega = (pi/Tmax) * [(0:nt/2-1) (-nt/2:-1)]; % freq grid
+
+if mshape == 0
+  uu = sech(tau) .* exp(-0.5j * chirp0 * tau.^2);
+else
+  uu = exp(-0.5 * (1 + 1j * chirp0) .* tau.^(2 * mshape));
+end
+
+%% plot input pulse shape and spectrum
+temp = fftshift(ifft(uu)) .* (nt * dtau) / sqrt(2 * pi); % spectrum
+figure(1); clf; subplot(2,1,1);
+plot(tau, abs(uu).^2, '--k'); hold on;
+axis([-5 5 0 inf]);
+xlabel('Normalized Time');
+ylabel('Normalized Power');
+title('Input and Output pulse shape and spectrum');
+
+subplot(2, 1, 2);
+plot(fftshift(omega)/(2*pi), abs(temp) .^ 2, '--k'); hold on;
+axis([-.5 .5 0 inf]);
+xlabel('Normaized freq');
+ylabel('spectral power');
+
+%% store dispersive phase shifts to speed up code
+dispersion = exp(0.5j * beta2 * omega.^2 * deltaz); % [hase factor
+hhz = 1j * N^2 * deltaz;
+
+%% begin main loop
+%% N/2 -> D -> N/2 first half step nonlinear
+temp = uu .* exp(abs(uu) .^ 2 .* hhz / 2);
+for n = 1 : step_num
+  f_temp = ifft(temp) .* dispersion;
+  uu = fft(f_temp);
+  temp = uu .* exp(abs(uu) .^ 2 .* hhz);
+end
+uu = temp .* exp(-abs(uu) .^ 2 .* hhz); % final field
+temp = fftshift(ifft(uu)) .* (nt*dtau) / sqrt(2 * pi); % final spectrum
+%% end of main loop
+
+%% plot output pulse shape and spectrum
+subplot(2,1,1);
+plot(tau, abs(uu).^2, '-k');
+subplot(2,1,2);
+plot(fftshift(omega) / (2*pi), abs(temp).^2, '-k');