Fourth-order spatial correlation functions of a laser field

V. V. Rakhvalov

Sergei A. Akhmanov

Feng Wen, Xinxin Xue, Xun Zhang +4 more

In a near-field four-photon correlation measurement, ghost imaging with classical incoherent light is investigated. By applying the Klyshko advanced-wave picture, we consider the properties of four-photon spatial correlation and find that the fourth-order spatial correlation function can be decomposed into multiple lower-order correlation functions. On the basis of the spatial correlation properties, a proof-of-principle four-photon ghost imaging is proposed, and the effect of each part in a fourth-order correlation function on imaging is also analyzed. In addition, the similarities and differences among ghost imaging by fourth-, second-, and third-order correlations are also discussed. It is shown that the contrast and visibility of fourth-order correlated imaging are improved significantly, while the resolution is unchanged. Such studies can be very useful in better understanding multi photon interference and multi-channel correlation imaging.

Mario Corti, Vittorio Degiorgio

Etienne Boileau, B. Picinbono

The higher-order coherence functions of optical fields involving phase fluctuations have not yet been studied extensively. We discuss here an experiment which can in principle yield the fourth-order coherence function. This experiment is a study of the correlation function of the irradiance fluctuations obtained in some interference experiments. Two kinds of delay are then used: optical delays in the interferometer and electrical delays with suitable variations in the correlator.The results of the experiment are calculated theoretically with a particular statistical model of laser light. The possibility of using a spectrum analyzer instead of a correlator is discussed.

Feng Wen, Xun Zhang, Xinxin Xue +3 more

We investigate the fourth-order spatial correlation properties of pseudo-thermal light in the photon counting regime, and apply the Klyshko advanced-wave picture to describe the process of four-photon coincidence counting measurement. We deduce the theory of a proof-of-principle four-photon coincidence counting configuration, and find that if the four randomly radiated photons come from the same radiation area and are indistinguishable in principle, the fourth-order correlation of them is 24 times larger than that when four photons come from different radiation areas. In addition, we also show that the higher-order spatial correlation function can be decomposed into multiple lower-order correlation functions, and the contrast and visibility of low-order correlation peaks are less than those of higher orders, while the resolutions all are identical. This study may be useful for better understanding the four-photon interference and multi-channel correlation imaging.