Nonparaxial Propagation Properties of Specially Correlated Radially Polarized Beams in Free Space

Lina Guo,Yiming Dong,Li Chen,Yangjian Cai,Rong Lin,Yahong Chen,Minghui Zhang

doi:10.3390/app9050997

Abstract

A specially correlated radially polarized (SCRP) beam with unusual physical properties on propagation in the paraxial regime was introduced and generated recently. In this paper, we extend the paraxial propagation of an SCRP beam to the nonparaxial regime. The closed-form 3 × 3 cross-spectral density matrix of a nonparaxial SCRP beam propagating in free space is derived with the aid of the generalized Rayleigh–Sommerfeld diffraction integral. The statistical properties, such as average intensity, degree of polarization, and spectral degree of coherence, are studied comparatively for the nonparaxial SCRP beam and the partially coherent radially polarized (PCRP) beam with a conventional Gaussian–Schell-model correlation function. It is found that the nonparaxial properties of an SCRP beam are strikingly different from those of a PCRP beam. These nonparaxial properties are closely related to the correlation functions and the beam waist width. Our results may find potential applications in beam shaping and optical trapping in nonparaxial systems.

Highlights

Polarized beams have been investigated extensively in the past several decades because of their extraordinary properties and wide applications, such as in super-resolution imaging, optical tweezers, material processing, optical data storage, plasmon excitation, and nanofocusing [1,2,3,4,5,6,7].As a natural extension of a spatially coherent radially polarized beam, the partially coherent radially polarized (PCRP) beam with a conventional Gaussian–Schell-model correlation function was introduced and studied in detail [8]
Our experimental results indicated that a PCRP beam is more effective than a linearly polarized partially coherent beam for the mitigation of turbulence-induced degradation [10]
We extend the paraxial propagation of the specially correlated radially polarized (SCRP) beam to the nonparaxial region and explore the average intensity, the degree of polarization, and the spectral degree of coherence (SDOC) of a nonparaxial SCRP beam in free space

Summary

Introduction

Polarized beams have been investigated extensively in the past several decades because of their extraordinary properties and wide applications, such as in super-resolution imaging, optical tweezers, material processing, optical data storage, plasmon excitation, and nanofocusing [1,2,3,4,5,6,7]. Such partially coherent beams with engineered correlation functions exhibit many unusual properties during propagation They can find rich potential applications in laser beam shaping, optical imaging, optical trapping, and free-space optical communications [27,28,29,30,31,32,33,34,35,36]. It was demonstrated that by tailoring the spatial correlation function, the paraxial propagation properties of an SCRP beam in free space and turbulent atmosphere can be modulated [21,37]. The nonparaxial propagation of a PCRP beam is studied for comparison

Nonparaxial Propagation Theory of an SCRP Beam

Statistical Properties of a Nonparaxial SCRP Beam

Intensity distributions theSCRP

Intensity

Normalized

Conclusions