An ultrafast laser used in spectroscopy produces pulses whose electric-field envelope…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Optics & Photonics · Lasers and laser physics

Mathematical Methods for Physics, Ch Fourier transforms, spectra and convolution

Problem

An ultrafast laser used in spectroscopy produces pulses whose electric-field envelope

|f(t)|

is Gaussian, with a half-width at half maximum of

30\,\mathrm{fs}

. The carrier wavelength is

800\,\mathrm{nm}

. ((a)) Estimate the full spread in frequency,

2\Delta f

, between the two points where

|\tilde f(\omega)|

falls to half its peak. ((b)) Express this spread as a fraction of the carrier frequency

f_0 = c/\lambda