Modal description of paraxial structured light propagation: tutorial

Abstract

Here we outline a description of paraxial light propagation from a modal perspective. By decomposing the initial transverse field into a spatial basis whose elements have known and analytical propagation characteristics, we are able to analytically propagate any desired field, making the calculation fast and easy. By selecting a basis other than that of planes waves, we overcome the problem of numerical artefacts in the angular spectrum approach and at the same time are able to offer an intuitive understanding for why certain classes of fields propagate as they do. We outline the concept theoretically, compare it to the numerical angular spectrum approach, and confirm its veracity experimentally using a range of instructive examples. We believe that this modal approach to propagating light will be a useful addition to toolbox for propagating optical fields.

Revisiting the photonic orbital Hall effect with the vortex mode decomposition

“…The LG modes form a fully orthonormal basis, which can be characterized by two parameters, p and m, related to the radial and azimuthal profile of the beam [61], respectively. Any field pattern can be decomposed into a superposition of this basis [2,43,[45][46][47][48]. We now project the abnormal mode onto the LG mode, i.e.,…”

“…In recent years, these two kinds of spin-orbit interactions have been studied in many systems [32][33][34][35][36][37][38][39][40][41], and a topological transition from one kind of spin-orbit interaction to another may occur in a same system [42][43][44]. This topological phase transition process can be understood and explained by a vortex mode decomposition method [2,43,[45][46][47][48]. More interestingly, the interaction between IOAM and EOAM has also been reported, which is referred to as photonic orbit-orbit interaction or photonic orbital Hall effect (POHE) [49][50][51].…”

Eigenmodes of aberrated systems: the tilted lens

“…As such, the expansion in equation ( 1) represents a superposition of multiple scalar HG fields having corresponding normalised coefficients given by c k l . The dynamics of the optical field can be described using these coefficients [8] and this will become essential in expressing the action of the tilted lens on light beams. Similar to the Jones formalism, in the modal space, we can describe the action of one or more optical elements as an operator M which operates in any state vector |Ψ⟩ as in…”

“…Topical examples of mode families that inherit these characteristics, are the famous Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modes, forming solutions in cylindrical and Cartesian coordinates, respectively [3,4]. For this reason, the modal description of light can be a powerful tool, including forming a measurement basis [5], for control of beam sizes [6,7] to optical propagation description [8] and self-imaging selection rules [9]. Based on their constituting polynomials, it is possible to decompose some mode families into others and thus describe * Author to whom any correspondence should be addressed.…”

Transfer and evolution of structured polarization in a double-V atomic system

“…Since they were first conceived and demonstrated [21,22], OAM-laden beams have found many applications: in communications [23][24][25][26], field manipulation [27,28], trapping [29], beam shaping [30] and, lately, a new type of compass [31]. This latter work was based on the marriage of EIT and OAM effects demonstrated by Radwell et al [32]: where coherent interaction of optical OAM and atoms allowed for spatially dependent EIT.…”