Exact elegant Laguerre-Gaussian vector wave packets

TL;DR

This paper derives an exact closed-form expression for vector elegant Laguerre-Gaussian wave packets, revealing their orthogonal components and polarization properties, with implications for their behavior at planar interfaces.

Contribution

It introduces a novel exact representation of vector elegant Laguerre-Gaussian wave packets, detailing their orthogonal components and polarization characteristics.

Findings

Wave packets have three orthogonal components distinguished by radial indices.

Transverse components exhibit tm-radial and te-azimuthal polarization.

Wave packets act as eigenmodes of planar structures with specific eigenvalues.

Abstract

An exact closed-form representation is derived of a vector elegant Laguerre-Gaussian wave packet. Its space-time representation consists of three mutually orthogonal field components - of a common azimuthal index and different radial indices - uniquely distinguished by first three powers of the paraxial parameter. The transverse components are of tm-radial and te-azimuthal polarization and appear, under their normal incidence, to be eigenmodes of any horizontally planar, homogeneous and isotropic structure, with eigenvalues given by the reflection and transmission coefficients. In this context, the interrelations between the cross-polarization symmetries of wave packets in free space and at medium planar interfaces are discussed.