A laser pulse has envelope amplitude with

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

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

Problem

A laser pulse has envelope amplitude f(t)=e−t2/2τ02f(t) = e^{-t^2/2\tau_0^2} with τ0=2 ps\tau_0 = 2\,\mathrm{ps}, whose Fourier transform is f~(ω)=τ02π e−ω2τ02/2\tilde f(\omega) = \tau_0\sqrt{2\pi}\,e^{-\omega^2\tau_0^2/2}. A pulse compressor produces a new pulse h(t)=f(t/b)h(t) = f(t/b) with b=1/4b = 1/4. ((a)) Using the scaling theorem, find the effective time constant of the compressed pulse h(t)h(t). ((b)) Find the peak value h~(0)\tilde h(0) of its transform.

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