Half-integer order Bessel beams

TL;DR

This paper introduces a new class of optical beams based on half-integer order Bessel functions, providing analytical solutions, numerical methods, and experimental validation for their generation and analysis.

Contribution

It presents the first analytical solutions for half-integer order Bessel beams using the angular spectrum method, enabling better analysis and synthesis of complex optical fields.

Findings

Closed-form integral solutions for half-integer Bessel beams

Numerical simulation methods demonstrated

Experimental confirmation of theoretical predictions

Abstract

Optical beams are solutions to the paraxial wave equation (PWE). In this work we report a new, to our knowledge, optical beam. We solve the PWE by using the angular spectrum of plane waves theory in circular cylindrical coordinates. This lead us to solutions expressed in integral form that can be evaluated in closed-form for half-integer order Bessel functions. We show how to implement numerical simulation and how these results are confirmed by experiment. We believe this approach facilitates the analysis and synthesis of generic optical beams.