Analyzing And Measuring Second Order Correlation And Phase Space Reconstruction Of Chaotic Light Field

Semiconductor lasers have a wide range of applications because of their advantages of compactness,lightness,long service life,wide wavelength range,low fabrication cost,easy integration,and convenience for direct current modulation.At the same time,with the development of manufacturing technology,people designed more than one hundred kinds of semiconductor lasers,and the application of semiconductor lasers has been extended to the entire field of optoelectronics.Compared with traditional lasers,chaotic laser formed by semiconductor lasers with optical feedback has the characteristics of being noise-like,sensitivity to initial values,inherent randomness,having short correlation time,and large complexity.Those characteristics have been applied to the fields of chaotic secure communication,chaotic key distribution,physical random number generation,chaotic laser sensing,and biological excitation information processing.The research on the characteristics of the chaotic laser generated by semiconductor lasers has drawn increasing attention.On quality evaluation of chaotic light sources,people generally use the Lyapunov index,entropy measurement and autocorrelation functions to characterize the strength of chaos.However,these methods mainly use the macroscopic intensity fluctuations to study the dynamic characteristics of chaotic light fields.So,it is becoming increasingly important for us to explore the physical mechanism of nonlinear system,such as chaotic laser source,based on its statistical characteristics of photons.The autocorrelation equations of intensity statistics and time series can be used to determine the chaos process,but it has a significant difference from actual experimental results,while,the photon number distribution and photonic coherence are more sensitive to the controlled parameters of the chaotic laser,which provides a new way to study and apply the chaotic laser.The study of second order correlation of the chaotic light allows us to understand the random fluctuations of the intensity and statistical characteristics of the chaotic laser radiation from the perspective of photon statistics,and to explore the application of chaotic laser due to the photon bunching effect and higher order coherence.Therefore,this paper,based on the statistical properties of chaotic light,study the statistical and coherent properties of the photon of the chaotic light field on theoretical and experimental,and analyze how it changes with applied current and feedback intensity.Then we propose a time correlation analysis method to measure the second order coherence of the chaotic light field,we explored the method of improving the measurement accuracy of the second order correlation,the theoretical error can be ignored with the increase of the convolution.Under the condition of the experimental parameters,the relative error of our result in theory within 40 ns delay time,the error is less than 0.25%.The above accuracy indicates that the method can reduce the dependence on short dead time and high efficiency of detector.Wigner function is an extremely important quasi-probability distribution function of light phase space,which describes the distribution of the light field.It contains all the information of the quantum state through the evolution process in the entire phase space.The study on Wigner function of the chaotic light field is helpful for us to intuitively understand the evolution and the characteristics of the chaotic light field in phase space.It can also provide an important basis for the use of multi-dimensional chaotic light field for key distribution and identification.The main work of this article is as follows:Based on the HBT experiments,different parameters from the theoretical Lang-Kobayashi(LK)equation controlling chaotic laser are changed,so that we obtained the variation of the second order correlation of the light field at zero delay time.We also obtain the changing rules of statistical distribution of photons in chaotic light field with the change of the state of the light,and the results meet the theory in the experiment.The zero delayed of second order correlation of the chaotic light field obtained by photon counting did not fully reflect the rule of the variation of the chaotic light field with delay time.Therefore,how to measure the variation of the second order correlation in the delay time and explore its underlying physical mechanism,has become a problem to be solved.Based on the theory,we propose time correlation counting method to obtain a high order form of the second order correlation of the light field as a function of delay time.This method can improve the accuracy of detection measurement of the second order correlation of a chaotic light field with delay time.And the results of the above theoretical analysis are verified in experiment.In this paper,according to the evolution of the phase space of chaotic light field and realization of the reconstruction of the phase field function of the light field,the preliminary theoretical analysis is performed and the theoretical analysis results of experimental conditions is given.