Asked by Joe
on 28 Jun 2013

% speed of light m/s c = 299792458;

% pulse duration (T=tau) FWHM = 30e-15; T = FWHM/(2*(sqrt(log(2))));

% central wavelngth and central angular frequency lambda0 = 800e-9; w0 = (2*pi*c)/lambda0;

% chirp eta = 2;

% time interval t = -55e-15:.1e-15:55e-15;

% spectral phase phi_t = 0;

% length of FFT # of sampling points nfft = 200;

% This is an evenly spaced frequency vector f = [0:nfft - 1]/nfft;

% wavelength interval and angular frequency conversion lambda = (740e-9:20e-9:860e-9); w = (2.*pi.*c)./lambda;

% electric field E_t = exp((-t.^2/(2*T.^2)) + (-i*w0*t-(1/2)*i*eta*t.^2)); %*phi_t));

% Take fft, padding with zeros so that length(E_w) is equal to nfft E_w = abs(fftshift(fft(E_t,nfft))); I_w = ((abs(E_w)).^2); I_lambda = I_w.'*((2.*pi.*c)./lambda); (This is where I'm trying to convert to wavelength)

% Plot subplot(2, 1, 1); plot(t, real(E_t)); title('Gaussian Pulse Signal'); xlabel('time (s)'); ylabel('E_t');

subplot(2, 1, 2); plot(lambda, E_w); xlabel('\lambda'); ylabel('E_\omega');

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Answer by Wayne King
on 29 Jun 2013

Edited by Wayne King
on 29 Jun 2013

Accepted Answer

This runs perfectly for me:

c = 299792458; % pulse duration (T=tau) FWHM = 30e-15; T = FWHM/(2*(sqrt(log(2)))); % central wavelngth and central angular frequency lambda0 = 800e-9; w0 = (2*pi*c)/lambda0; % chirp eta = 2; % time interval t = -55e-15:.1e-15:55e-15; % spectral phase phi_t = 0; % wavelength interval and angular frequency conversion lambda = (740e-9:20e-9:860e-9); w = (2.*pi.*c)./lambda; % electric field E_t = exp((-t.^2/(2*T.^2)) + (i*w0*t-(1/2)*i*eta*t.^2)); %*phi_t));

Edft = fftshift(fft(E_t)); dt = t(2)-t(1); Fs = 1/dt; df = Fs/length(E_t); freq = -Fs/2+df:df:Fs/2; lambda = c./freq; plot(lambda,abs(Edft).^2); set(gca,'xlim',[0 10e-7])

And it shows the correct wavelength.

Answer by Wayne King
on 28 Jun 2013

Edited by Wayne King
on 29 Jun 2013

E_t = exp((-t.^2/(2*T.^2)) + (i*w0*t-(1/2)*i*eta*t.^2)); Edft = fftshift(fft(E_t)); dt = t(2)-t(1); Fs = 1/dt; df = Fs/length(E_t); freq = -Fs/2+df:df:Fs/2; lambda = c./freq; plot(lambda,abs(Edft).^2);

Now the wavelength you expect is

c/(w0/(2*pi))

so zoom in on that

set(gca,'xlim',[0 10e-7])

You see the peak at 8x10^{-7} as you expect

Joe
on 29 Jun 2013

What is "df" that you have for the "freq"?

Wayne King
on 29 Jun 2013

That is the frequency separation between the DFT bins. Sorry I forgot that line of code:

df = 1/(dt*length(E_t));

or equivalently

df = Fs/length(E_t);

I've added it above.

Joe
on 5 Jul 2013

Just to clarify... What is t(2) and t(1)? I know that dt is the time separation, but I'm not sure why you used t(2) and t(1). Also, is there another way of getting dt?

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