Bessel Beams: Unified and Extended Perspective

TL;DR

This paper offers a comprehensive unified theory of Bessel beams, extending their description to include noninteger orbital angular momentum and different mode types, enabling new applications and beam generation techniques.

Contribution

It introduces a unified integral superposition framework for all Bessel beams, including novel noninteger-OAM TE/TM modes, and proposes a method for their generation.

Findings

Existence of noninteger-OAM TE/TM Bessel beams demonstrated.

Mathematical relations established between LSE/LSM and TE/TM modes.

A technique for generating Bessel beams via superposition of sources proposed.

Abstract

We present a unified and extended perspective of Bessel beams, irrespective to their orbital angular momentum (OAM) -- zero, integer or noninteger -- and mode -- scalar or vectorial, and LSE/LSM or TE/TM in the latter case. The unification is based on the integral superposition of constituent waves along the angular-spectrum cone of the beam, and allows to describe, compute, relate, and implement all the Bessel beams, and even other types of beams, in a universal fashion. The paper first establishes the integral superposition theory. Then, it demonstrates the previously unreported existence of noninteger-OAM TE/TM Bessel beams, compares the LSE/LSM and TE/TM modes, and establishes useful mathematical relations between them. It also provides an original description of the position of the noninteger-OAM singularity in terms of the initial phase of the constituent waves. Finally, it introduces a general technique to generate Bessel beams by an adequate superposition of properly tuned sources. This global perspective and theoretical extension may open up new avenues in applications such as spectroscopy, microscopy, and optical/quantum force manipulations.