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Applied Optics

Computer simulation of superposed coherent and chaotic radiation

Giovanni Vannucci, Malvin Carl Teich

Published Feb 15, 1980• 30 citations
Publisher

Abstract

A computer simulation technique useful for generating superposed coherent and chaotic radiation of arbitrary spectral shape is described. Its advantages over other techniques include flexibility and ease of implementation, as well as the capability of incorporating spectral characteristics that cannot be generated by other methods. We discuss the implementation of the technique and present results to demonstrate its validity. The technique can be used to obtain numerical solutions to photon statistics problems through computer simulation. We furthermore argue that experiments involving photon statistics can be carried out using a wideband source in place of an amplitude-stabilized source whenever the spectral characteristics of the source are not important. Experimental results that corroborate the argument are presented.

DOI
10.1364/ao.19.000548

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A computer simulation technique useful for generating superposed coherent and chaotic radiation of arbitrary spectral shape is described. Its advantages over other techniques include flexibility and ease of implementation, as well as the capability of incorporating spectral characteristics that cannot be generated by other methods. We discuss the implementation of the technique and present results to demonstrate its validity. The technique can be used to obtain numerical solutions to photon statistics problems through computer simulation. We furthermore argue that experiments involving photon statistics can be carried out using a wideband source in place of an amplitude-stabilized source whenever the spectral characteristics of the source are not important. Experimental results that corroborate the argument are presented.
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There has been considerable interest in recent years in the statistical properties of optical frequency electromagnetic fields. Of particular interest is the study of photon bunching and the probability density for waiting time between adjacent photocounts. In this paper we derive an expression for the probability density of the time interval distribution as well as some other quantities of interest in photon bunching for the case where the incident radiation is comprised of superposed coherent and chaotic radiation of arbitrary spectral shapes. Calculations show that the key parameters are the average number of chaotic counts per coherence time and the ratio of the strengths of coherent and chaotic parts (signal-to-noise ratio).
A method for computing the approximate photocount statistics for Gaussian light is presented. This method may be used for the superposition of coherent radiation with chaotic radiation of arbitrary spectral shape. Data is presented for Gaussian-, triangular-, and square-shaped spectra as well as for Lorentzian-shaped spectra. The results show that the photocount statistics are significantly dependent upon spectral shape for intermediate time-bandwidth products. The results also show that the Bedard, Chang, and Mandel approximation gives a better fit to a Gaussian-shaped spectrum then to a Lorentzian-shaped spectrum. Significant differences between the photocount statistics for a time-bandwidth product of 10 and Poisson statistics were also obtained; even for a signal-to-noise ratio of 40:1.
Methods are developed for discussing the photon statistics of arbitrary fields in fully quantum-mechanical terms. In order to keep the classical limit of quantum electrodynamics plainly in view, extensive use is made of the coherent states of the field. These states, which reduce the field correlation functions to factorized forms, are shown to offer a convenient basis for the description of fields of all types. Although they are not orthogonal to one another, the coherent states form a complete set. It is shown that any quantum state of the field may be expanded in terms of them in a unique way. Expansions are also developed for arbitrary operators in terms of products of the coherent state vectors. These expansions are discussed as a general method of representing the density operator for the field. A particular form is exhibited for the density operator which makes it possible to carry out many quantum-mechanical calculations by methods resembling those of classical theory. This representation permits clear insights into the essential distinction between the quantum and classical descriptions of the field. It leads, in addition, to a simple formulation of a superposition law for photon fields. Detailed discussions are given of the incoherent fields which are generated by superposing the outputs of many stationary sources. These fields are all shown to have intimately related properties, some of which have been known for the particular case of blackbody radiation.
In recent years there has been considerable utilization of photocount statistics for studying theoretical and experimental properties of a quantized electromagnetic field. The electromagnetic field, which has been of greatest interest in these areas, is a superposition of coherent and chaotic radiation. In this paper closed-form recurrence equations are derived for the photocount distribution and the factorial moments for this case. The photocount distribution is then obtained by using a well-known solution for p(0, T), and the factorial moments are generated by using the fact that the zeroth factorial moment is unity.
Definitions of the coherence time, coherence area and coherence volume are proposed for superposed coherent and chaotic radiation, such as laser radiation above the threshold, on the basis of the photon statistics of the radiation. Such definitions may contribute to a unified judgment of the coherence properties of the radiation in any order, while the definitions usually used are connected with interferometric measurements of the second-order coherence properties. A close relationship to the definitions proposed earlier in the literature for chaotic radiation is shown.