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Journal of the Physical Society of Japan

Coherent Multifrequency Optical Fields

Tiberiu S. Tudor

Published Jan 15, 2004• 1 citation
Publisher

Abstract

An analysis of the generalized coherence of multifrequency optical fields is given, both in terms of observable quantities (coherence functions) and in terms of field quantities (analytical signal and amplitude spectral density of the field). The spectral structure of the generalized coherence function for a widespread class of multifrequency optical fields is given. Experimental results obtained by interferometrical investigation of the generalized coherence of such fields are presented.

DOI
10.1143/jpsj.73.76

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An analysis of the generalized coherence of multifrequency optical fields is given, both in terms of observable quantities (coherence functions) and in terms of field quantities (analytical signal and amplitude spectral density of the field). The spectral structure of the generalized coherence function for a widespread class of multifrequency optical fields is given. Experimental results obtained by interferometrical investigation of the generalized coherence of such fields are presented.
Photoelectric correlation measurements of optical fields are now becoming commonplace and, as is well known, they require fourth order correlation functions of the field for a description. Nevertheless, the fourth order theory of optical coherence has not received a great deal of attention. This is the subject of the present paper. When interference effects are combined with intensity correlations, we encounter correlation functions of the general form Γ(2,2) ≡〈V* (r−1,t1)V* (r−2,t2)V (r−3,t 3)V (r−4,t4)〉, which are functions of four space‐time arguments. Some properties of such fourth order correlations, as they relate to interference and intensity correlation effects, are derived. The space arguments are generally suppressed in the calculation. The correlation functions are expressible as multiple Fourier transforms of certain fourth order spectral densities, which are functions of three frequencies in the stationary state. The superposition law for fourth order spectral densities is derived for independent light beams, and it is shown that the fourth order spectral densities exhibit the reproducing property under superposition only when the light obeys thermal statistics. Next the superposition law is found for the spectral densities of the photoelectric signals generated by light beams falling on photodetectors. Investigation of the photoelectric signal spectrum yields information on the spectrum of the light intensity fluctuations, and removes the measurement from the domain of optics to the domain of electronics. It is shown that the photoelectric spectral densities reproduce under superposition when the two light beams in question obey a certain factorization condition, that is analogous to the cross‐spectral purity condition for second order correlations. Finally, it is shown that, under certain circumstances, all the relevant fourth order correlation properties of the optical field are expressible in terms of simpler two‐frequency spectral functions.
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The work presented in this thesis deals with the coherence of optical pulse trains in time, frequency, and space domains.This thesis, based on the second-order coherence theory of nonstationary light, primarily consists of theoretical investigations which result in useful insights in the coherence characterization of pulsed optical sources.Analytical models that physically represent supercontinuum pulse trains, broadband axicon fields, and slightly disturbed mode-locked pulse trains are proposed.Numerically simulated realizations of supercontinuum pulse trains are also considered in this study.In addition, an experimental setup with corresponding analytical analysis is presented to illustrate the evaluation of the two-time coherence function of pulse trains and it is shown that for that one needs to perform time-resolved measurements of the interference fringes.Moreover, information conveyed by the timeintegrated measurements of the interference fringes produced by supercontinuum light and slightly perturbed mode-locked laser is explained through analytical and numerical investigations.An experimental demonstration of the time-integrated measurements is reported for an almost fully coherent femtosecond pulse train.
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