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American Journal of Physics

Measurement of the second-order coherence of pseudothermal light

Tom Kuusela

Published Mar 21, 2017• 21 citations
Publisher

Abstract

We describe photon statistics experiments using pseudothermal light that can be performed in an undergraduate physics laboratory. We examine the light properties in terms of a second-order coherence function, as determined either by measuring the light intensity as a function of time or via coincidence analysis of a pair of photon detectors. We determine the coherence time and intensity distribution of the pseudothermal light source that exhibits either Gaussian or non-Gaussian statistics as a function of their optical parameters, and then compare the results with theoretical predictions. The simple photodiode method can be used for the qualitative analysis of the coherence time, but more accurate measurements are achieved using the coincidence method.

DOI
10.1119/1.4975212

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We describe photon statistics experiments using pseudothermal light that can be performed in an undergraduate physics laboratory. We examine the light properties in terms of a second-order coherence function, as determined either by measuring the light intensity as a function of time or via coincidence analysis of a pair of photon detectors. We determine the coherence time and intensity distribution of the pseudothermal light source that exhibits either Gaussian or non-Gaussian statistics as a function of their optical parameters, and then compare the results with theoretical predictions. The simple photodiode method can be used for the qualitative analysis of the coherence time, but more accurate measurements are achieved using the coincidence method.
Superbunching pseudothermal light has important applications in studying the second- and higher-order interference of light in quantum optics. Unlike the photon statistics of thermal or pseudothermal light is well understood, the photon statistics of superbunching pseudothermal light has not been studied yet. In this paper, we will employ single-photon detectors to measure the photon statistics of superbunching pseudothermal light and calculate the degree of second-order coherence. It is found that the larger the value of the degree of second-order coherence of superbunching pseudothermal light is, the more the measured photon distribution deviates from the one of thermal or pseudothermal light in the tail part. The results are helpful to understand the physics of two-photon superbunching with classical light. It is suggested that superbunching pseudothermal light can be employed to generate non-Rayleigh temporal speckles.
We present a simple technique for measuring coherence times for stationary light fields using a single detector with tunable time resolution. By measuring the equal-time second-order correlation function at varying instrument response functions it is possible to determine the coherence time and also the shape of the temporal decay without the need to record time-resolved data. The technique is demonstrated for pseudothermal light. Possible applications for dynamic light scattering and photon statistics measurements are discussed.
We present a photon counting experiment designed for an undergraduate physics laboratory. The statistics of the number of photons of a pseudo thermal light source is studied in two limiting cases: well above and well below the coherence time, giving Poisson and Bose-Einstein distributions, respectively. We show that using a digital oscilloscope the experiment can be done in a reasonable time, without need of counting boards. The use of the oscilloscope has the additional advantage of allowing the storage of the data for further processing. Hence, using the same set of data, the analysis of the statistics of the occurrence of n photons as a function of the time windows adds important evidence to determine accurately the nature of the light source. The stochastic nature of the detection phenomena adds an additional value to this type of experiments, since the student is forced to a thorough visit through data processing and statistics.
We describe a simple and compact electrical version of a pseudothermal light source. The source is based on electrical white noise whose spectral properties are tailored by analog filters. This signal is used to drive a light-emitting diode. The type of second-order coherence of the output light can be either Gaussian or Lorentzian, and the intensity distribution can be either Gaussian or non-Gaussian. The output light field is similar in all viewing angles, and thus, there is no need for a small aperture or optical fiber in temporal coherence analysis.
It is well known that the photocount distribution associated with the photoelectric detection of fluctuating light beams carries information about the probability density of the light intensity. In this paper, we present an exact solution to a problem of particular interest which arises in connection with the photoelectric detection of narrow-band Gaussian (thermal or pseudothermal) light, namely, the problem of determining the photocount distribution when the counting-time interval is not necessarily short compared to the coherence time of the light. The method developed in this paper is applied to the case where the spectral profile of the light is Lorentzian; it leads to an exact expression for the photocount generating function and it provides simple recurrence relations for the photocount distribution and for its factorial moments.