Twisted Electromagnetic Multi-Gaussian Schell-Model Pulsed Source and Its Propagation

Abstract

Here, a novel family of random electromagnetic sources (twisted electromagnetic multi-Gaussian Schell-model pulsed beams) exhibiting transverse orbital angular momentum is proposed. The physically realizable conditions for these sources are established, and the analytical formulas of the cross-spectral density matrix elements of the beam propagating through an ABCD optical system are derived within the framework of the extended Collins formula. The behaviors of the spectral density, and the spectral degree of coherence of the beam during transmission are investigated numerically. This work enriches the classical theory of stochastic electromagnetic beams propagation, and may benefit applications requiring a specified degree of beam coherence with transverse orbital angular momentum. Index Terms-multi-Gaussian function, optical propagation, optical pulse, transverse orbital angular momentum. I. INTRODUCTION OR nearly 30 years, vortex beams exhibiting orbital angular momentum (OAM) have attracted enormous attention owing to their various potential applications in free-space optical communications (FSOC), optical tweezers, astronomy [1-5], etc. In a 1993 paper, Simon and Mukunda introduced the twisted Gaussian Shell-model (GSM) beam [6] exhibiting OAM. This phase, which can only exist in the partially coherent field, can twist the beam around its axis during propagation [6, 7]. Ever since, twisted partially coherent field has generated significant interest. For example, Borghi et al. presented a twisted Schell-model beam exhibiting axial symmetry [8]. Mei and Korotkova constructed two different random sources bearing the twisted phase via the modal representation technique [9]. Gori and Santarsiero presented a mathematical method for generating genuine twisted sources [10]. Moreover, unique twisted partially coherent sources, such as twisted electromagnetic beams with structured correlations [11], twisted Laguerre-GSM beams [12], twisted GSM array beams