A photodetector's response to a single photon has the symmetric pulse shape 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 photodetector's response to a single photon has the symmetric pulse shape f(t)=e−∣t∣/τf(t) = e^{-|t|/\tau} with τ=5.0 ns\tau = 5.0\,\mathrm{ns}. ((a)) Compute the Fourier transform f~(ω)=∫−∞∞f(t)eiωt dt\tilde f(\omega) = \int_{-\infty}^{\infty}f(t)e^{i\omega t}\,\mathrm{d}t, the time convention of the text, by splitting the integral at t=0t = 0. ((b)) Evaluate f~(ω)\tilde f(\omega) at ω=2.0×108 rad s−1\omega = 2.0\times10^{8}\,\mathrm{rad\,s^{-1}}.

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