A stationary light source has a flat (rectangular) power spectral density of full…

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Coherence and statistical optics · Coherence and statistical optics

What an Instrument Can See, Ch Temporal coherence: correlation, spectrum and the interferometer

Problem

A stationary light source has a flat (rectangular) power spectral density S^(ν)\hat S(\nu) of full width Δν=15\Delta\nu = 15 GHz, centred on an optical frequency ν0\nu_0 in the visible, and zero outside this band. (a) State, in one sentence, which frequencies are kept in forming the analytic signal V(t)V(t) of the real field, and why Γ11(τ)=⟨V(t+τ)V∗(t)⟩\Gamma_{11}(\tau) = \langle V(t+\tau)V^*(t)\rangle must be built from VV rather than from the real field itself. (b) Apply the Wiener-Khinchin theorem to translate this frequency-domain description into the time-domain self-coherence function Γ11(τ)\Gamma_{11}(\tau), up to the overall normalisation Γ11(0)\Gamma_{11}(0), writing your result in terms of a sinc\mathrm{sinc} function, sinc(x)≡sin⁡(πx)/(πx)\mathrm{sinc}(x) \equiv \sin(\pi x)/(\pi x). (c) Using the integral definition of coherence time applied to this rectangular spectrum, give the numerical value of τc\tau_c.

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