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Optics Letters

Reply to comment on “Complete electromagnetic coherence in the space–frequency domain”

Tero Setälä, Jani Tervo, Ari T. Friberg

Published Aug 1, 2004• 26 citations
Publisher

Abstract

We emphasize that the visibility of interference fringes is not an appropriate characteristic for the electromagnetic degree of coherence. Our definition is consistent with the notions of complete coherence. All points put forward in the Comment were already noted in our previous publication [Opt. Express11, 1137 (2003)].
DOI
10.1364/ol.29.001713

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The changes in the interference pattern in Young's interference experiment, produced by placing two identical narrow-band filters in front of the pinholes, are analyzed. It is shown theoretically that, in general, the fringes will not become sharp (i.e., their maximum visibility will not tend to unity) even when the filters have arbitrarily narrow passbands. The analysis brings out a relationship between the complex degree of coherence in the space-time and the space-frequency domains. When the passbands of the filters are narrow enough, the filtered light is found to be cross-spectrally pure.
The first-order coherence condition is derived in terms of correlations between different field modes. Fluctuations of the electromagnetic field are shown to play an important role in the concept of coherence. The coherent states are shown to be the only ones which reduce these fluctuations to their minimum value. For the case of a field in which the different field modes are independent, the degree of first-order coherence and the visibility of interference fringes are shown to be specified completely by these fluctuations. Measurements of this visibility yield information on the statistical properties of radiation fields. For squeezed states, this visibility is expressed as a function of squeezed parameters. Moreover, the difference between generalized coherent states becomes manifest in measurements of this visibility.