Propagation Properties Of A Gaussian Schell-model (GSM) Beam Under And Beyond The Paraxial Approximation

Partially coherent beams have important applications in free-space opticalcommunication, optical imaging, laser radar system, materical thermal processing, laserscanning, particle trapping, and particle scattering. Gaussian Schell-model (GSM) beam istypical and commonly encountered partially coherent beam. Recently, more and moreattention is being paid to the propagation properties of scalar and vector GSM beam. Mostof previous literatures on GSM beam were confined to its paraxial propagation properties.In some practial applications, some novel laser beams such as the beam emitted fromsemiconductor laser and the tighlty focused beam are widely used. Such beams have smallspot size or large far-field divergence angle, and the paraxial theory for treating itspropagation is no longer applicable. On the other hand, the actual output beams usually arenot completely coherent. Thus, it is of scientific and practical importance to study thenonparaxial propergation of partial coherent beams. In this paper, we mainly study theparaxial and nonparaxial propagation properties of a GSM beam in free space and crystal.The main novel results are as follows.1. We extend the concept of the degree of paraxiality from monochromatic fields tostochastic electromagnetic fields. As an application example, explicit expression for thedegree of paraxiality of an vector GSM beam is derived. The dependence of the degree ofparaxiality of an vector GSM beam on the degree of polarization, r.m.s. widths of thespectral densities and of the correlation functions is illustrated numerically.2. With the help of the tensor method, we study the nonparaxial propagation of aanisotropic twisted GSM beam in free space. Analytical nonparaxial propergation formulaeare derived. The nonparaxial porpagation properties of a anisotropic twisted GSM beamare explored in detail.3. We investigate the paraxial propagation properties of a twisted GSM beam in auniaxial crystal. Analytical formula for the CSD of a twisted GSM beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. Evolution properties of a twistedGSM beam in a uniaxial crystal are illustrated numerically.4. We extend the nonparaxial propagation theory of coherent beams in a uniaxialcrystal to the partially coherent case. Analytical propagation formula for a nonparaxialGSM is derived. The statistical properties of a nonparaxial GSM beam propagating in auniaxial crystal orthogonal to the optical axis are explored in detail.