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Journal of Applied Physics

Enhancement of Photon-Bunching Effects

Melvin D. Aldridge

Published Mar 15, 1969• 5 citations
Publisher

Abstract

An analysis is presented which shows that photon-bunching effects in a spatially coherent noise field can be enhanced by the superposition of a monochromatic coherent ``signal'' and/or by shaping the spectrum of the incident noise. For a Lorentz spectral shape, the addition of ``signal'' to noise is shown to increase bunching effects by a factor no greater than 4. By changing the noise spectrum from a Lorentz to a rectangular shape, bunching effects are shown to increase by a factor of 2 despite the fact that total incident noise power decreases. In all cases, the ratio of bunching noise to shot noise is proportional to the average number of detected noise photons per cycle of noise bandwidth. For the specific problem analyzed, the maximum value of the ratio of bunching noise to shot noise is determined. In the absence of ``signal,'' the results are found to agree with the exact distribution of Bèdard.

DOI
10.1063/1.1657838

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arXiv:1602.02335•The Astrophysical Journal•Jul 20, 2018•3 citations
An analysis is presented which shows that photon-bunching effects in a spatially coherent noise field can be enhanced by the superposition of a monochromatic coherent signal'' and/or by shaping the spectrum of the incident noise. For a Lorentz spectral shape, the addition of signal'' to noise is shown to increase bunching effects by a factor no greater than 4. By changing the noise spectrum from a Lorentz to a rectangular shape, bunching effects are shown to increase by a factor of 2 despite the fact that total incident noise power decreases. In all cases, the ratio of bunching noise to shot noise is proportional to the average number of detected noise photons per cycle of noise bandwidth. For the specific problem analyzed, the maximum value of the ratio of bunching noise to shot noise is determined. In the absence of ``signal,'' the results are found to agree with the exact distribution of Bèdard.
The shot noise which occurs in photoelectric detection is calculated utilizing fully quantum mechanical procedures. The results which are obtained in this paper include the effects of photon bunching and they differ considerably from classical results which are obtained on the assumption of Poisson statistics. In some cases the Poisson-based classical results lead to shot-noise powers that are in error by as much as an order of magnitude. The results reveal the existence of a relative minimum in the plot of shot noise vs input signal to noise ratio. This suggests the possibility of optimum input signal to noise ratios within certain restricted ranges of the input signal to noise ratio. A plot of the shot noise which is in excess of that predicted by Poisson-based statistics vs input signal to noise ratio reveals a maximum at an input signal to noise ratio of approximately 1.5. This suggests that the enhancement of the Hanbury-Brown and Twiss effect that is obtained when coherent radiation is superposed upon chaotic radiation will be maximized at a coherent-to-chaotic ratio of approximately 1.5.
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 recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor [Formula: see text] (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium. This is the optical analogue of Büttiker's formula for electronic shot noise. Scattering by itself has no effect on the Fano factor, which remains equal to 1 (as for a Poisson process). Absorption and amplification both increase the Fano factor above the Poisson value. For strong absorption [Formula: see text] has the universal limit [Formula: see text], with f the Bose–Einstein function at the frequency of the incident radiation. This is the optical analogue of the one-third reduction factor of electronic shot noise in diffusive conductors. In the amplifying case the Fano factor diverges at the laser threshold, while the signal-to-noise ratio [Formula: see text] reaches a finite, universal limit.
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.
A review is given of recent theoretical studies devoted to the problem of generating radiation fields that exhibit the opposite of the well-known bunching of photons observed in light from thermal sources, the so-called antibunching effect. It is made clear that this phenomenon reflects the corpuscular nature of light and, hence, cannot be interpreted in terms of classical electrodynamics, needing, instead, the quantum-mechanical formalism for its description. It is shown in some detail that nonlinear interaction mechanisms like multiphoton absorption and parametric three-wave interaction are suited to change the photon statistical properties of incident (in most cases coherent) light such that the output field will be endowed with antibunching properties. Special emphasis is given to the problem of correctly specifying the dimensions of the mode volume occurring in the usual single-mode treatment of the field, which is, in fact, of great practical interest, since the magnitude of the antibunching effect is determined by the inverse average number of photons contained in that volume. In a later section it is pointed out that destructive interference with a coherent reference beam provides a means of (a) effectively enhancing photon antibunching that is already present in a high-intensity field, through reduction of the intensity, and (b) transforming phase fluctuations produced in a Kerr medium into antibunching-type intensity fluctuations. On the other hand, there exists a way of directly generating light with antibunching properties, the physical mechanism being resonance fluorescence from a single atom. The main features of this technique, both theoretical and experimental, are outlined, including a discussion of the first experimental results obtained a few years ago.
Abstract We report the experimental observation of photon-bunching noise through shot noise measurements made on a pseudo-thermal state of light using balanced detection. A full theory describing the measurement is developed, and, in agreement with the theory, it is found that the shot noise variance in the balanced signal reproduces the time series of the flux of the primary incoherent beam. Moreover, when the average power of the pseudo-thermal light is varied, the balanced detection is seen to track this change. A comparison of direct detection and balanced detection of the thermal field shows that the balanced detection performs at least as well as the direct detection and under some conditions appears to outperform the direct detection. There is not necessarily a contradiction with quantum field theory, which predicts that at best the performance of the balanced detection should be equal to the direct detection because the direct detection process is subject to nonlinearity that has not been excluded by measurements (even though any tests we performed suggest that such effects are small). This is the first time that the bunching noise effect of high occupation number chaotic light via the shot noise of the field has successfully been measured, to the point of using it to infer the flux of the field. The findings may be relevant to radio receiver design, specifically from the viewpoint of sensitivity improvement.