Question on Mode locked laser pulse train

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Homework Statement



I have a question to calculate the spectrum of an infinite pulse train from a mode locked laser with each pulse having I(t) proportional to exp(t^2 / tau^2) where tau is the pulse width. tau is 50 fs, repetition rate is 100Mhz, wavelength of operation is 800nm.

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Homework Equations





The Attempt at a Solution


I was thinking of calculating the fourier transform of the intensity function I(t) and multiply it with the FT of the dirac comb of pulses. But I do not quite understand what spectrum means? Do I calculate the bandwidth ? or just the function in the frequency domain?

I calculated bandwidth of the output as :

L = c/2*Δν
L = 1.66m = q λ/2
q = 4.167E5 modes
Bandwidth = repetition rate * q = 33.3THz
 

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