Coincidence Fractional Fourier Transform (FRT) With A Stochastic Electromagnetic Gaussian Schell-model (EGSM) Beam

Polarization and coherence are two important properties of light waves, and have beenstudied separately in the past decades. A few years ago it was found that the polarizationand coherence of a stochastic electromagnetic beam (vectorial partially coherent beam) areinterrelated. The degree of polarization of a stochastic electromagnetic beam may changeon propagation, and such changes depend on the coherence properties of the light source.The concept of the fractional Fourier transform (FRT) was firstly proposed in1980as ageneralization of the conventional Fourier transform. Since then, the properties and opticalimplementation of the FRT have been investigated widely, and the FRT has found wideapplications in signal processing, optical image encryption, beam shaping, and beamanalysis. Based on classical theory of optical coherence and polarization, coincidencefractional Fourier transform (FRT) with a stochastic electromagnetic Gaussian Schell-model (EGSM) beam is investigated. In all previous literatures on coincidence FRT withclassical light, the polarization properties of the light source wasn’t taken into consideration,in other words, the light source was assumed to be scalar source. Dependences of thequality and visibility of the coincidence FRT pattern of an object on the degree ofpolarization and correlation coefficients of the EGSM beam are studied numerically. westudy the dependence of the coincidence FRT pattern of the object on the degree ofpolarization and coherence of the EGSM beam numerically.The paper is organized as follows: In the first chapter, we make a summary and introduce its research purpose and main contents. In the second Chapter, we introducesome knowledge about FRT and the stochastic EGSM beam. The third、the fourth and thefifth are the main work we do. In the third chapter, we carry out experimental measurementof the beam parameters of an electromagnetic Gaussian Schell-model source. In the fourthchapter, we study the coincidence FRT implemented with a stochastic EGSM beam. In thefifth chapter, we study coincidence fractional Fourier transform (FRT) with a stochasticelectromagnetic Gaussian Schell-model (EGSM) beam numerically. And in the last chapter,we make some conclusion and foreground.