Teaching temporal coherence and the Wiener Khintchin theorem at a senior/graduate level

Abstract

One important issue in teaching interferences is that two separate wavelengths usually do not interfere: any interference pattern is the spectral integral of all interference patterns of all monochromatic components. Although optical detectors are quadratic in nature, crossed terms involving two different frequencies in the expression of an interference pattern vanish. More precisely, while in non stationary signals such as ultrashort pulses two wavelengths can give rise to beating phenomena, this does not happen with the usual thermal light beams. The phenomenon is directly connected with the Wiener Khintchin theorem, and therefore with the principle of Fourier transform spectroscopy.In an introductory course, oversimplification leading to frustrating physical and mathematical deficiencies is hardly avoidable. In this communication, we suggest an introduction of this question at a senior/graduate level. Numerical simulations are used to provide an intuitive understanding of the phenomena. If the Wiener Khintchin theorem is introduced by defining the power spectrum from the infinite time limit of the ordinary Fourier transform of a gaussian windowed version of the signal, the mathematics are simple and the method offers a clear connection with the operation of real (i.e. finite time) detectors analysing interference fringes.