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Frontiers of Physics

Simulation of temporal second-order correlation function based on Monte Carlo algorithm

Yongsheng Hu, Tengfei Ma, Danqun Mao, Zhenyu Wang, Weihang Zhou, Hongxing Xu, Hongxing Dong, Wei Xie

Published Jan 1, 2025• 0 citations
Publisher

Abstract

The second-order correlation function of photons is the primary means to quantitatively describe the second-order coherence of a light field. In contrast to the stationary second-order correlation function, the temporal second-order correlation function can be used to study the second-order coherence of a transient light field. Based on the Monte Carlo algorithm, we carried out theoretical simulation on the temporal second-order correlation function from the perspective of photon statistics. By introducing experimental factors into the simulation, such as intensity jitter of the light field and time resolution of the instruments, the effects of imperfect experimental conditions on the measurement of second-order correlation function have also been elucidated. Our results provide theoretical guidance and analysis methods for experimental measurements on the second-order coherence of light fields.

DOI
10.15302/frontphys.2025.034204

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The second-order correlation function of photons is the primary means to quantitatively describe the second-order coherence of a light field. In contrast to the stationary second-order correlation function, the temporal second-order correlation function can be used to study the second-order coherence of a transient light field. Based on the Monte Carlo algorithm, we carried out theoretical simulation on the temporal second-order correlation function from the perspective of photon statistics. By introducing experimental factors into the simulation, such as intensity jitter of the light field and time resolution of the instruments, the effects of imperfect experimental conditions on the measurement of second-order correlation function have also been elucidated. Our results provide theoretical guidance and analysis methods for experimental measurements on the second-order coherence of light fields.
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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.
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A new approach to measure the second order correlation function g(2) and the coherence time was investigated. The g(2) was calculated from the photon pair time interval distribution by direct numerical self-convolution with the high order correction. The accuracy of this method was examined using an optical fiber based Hanbury-Brown-Twiss interferometer with a pseudo-thermal light source. We found that the significance of the high order correction is related to the factor Īτc, which is the overlapping of the photon wave packets. A novel technique was also demonstrated to measure the coherence time τc of a light source using the random phase modulation. This method is more suitable for a weak light source with a long coherence time using a simple experimental setup.