Added technical milestone report and changes to 1st presentation

[4yp.git] / agrawalAppendixB.m

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');