Coherence properties of one-dimensional pulses in dispersive media

Abstract

In recent years longitudinal coherence of electron and neutron wave packets has been investigated,1,2 and it was shown that their coherence length remains unchanged even though the length of the wave packet increases on propagation.3,4 As pointed out in Ref. 3, one may expect that a similar result will hold for light that propagates in a dispersive medium. We present some new general theorems relating to an ensemble of identical 1-D optical pulses which propagate in a linear homogeneous medium of any given dispersive properties. In particular we derive a general expression for the mutual coherence function and for the cross-spectral density function of the pulse field in the medium in terms of the Fourier spectrum of a single pulse shape. The analysis brings out clearly the distinction (already noted in Ref. 4) between the coherence length and the coherence time of fields in dispersive media. We also show that the pulse field is spatially completely coherent at each frequency, even though the shape of each pulse changes on propagation. The results have potential application to interferometry with optical pulses and with de Broglie wave packets of elementary particles.