Properties of "special'' hyperbolic Bessel-Gaussian optical beams

TL;DR

This paper introduces a new class of hyperbolic Bessel-Gaussian beams called 'special' SHBG beams, deriving their explicit formulas, analyzing their properties, and exploring their unique annular and vortex-like phase behaviors.

Contribution

The work provides the first explicit formula for SHBG beams, including a new parameter for shape modification, and analyzes their fundamental properties and phase characteristics.

Findings

Beams exhibit an annular structure with a single ring splitting into multiple rings along propagation.

The parameter γ influences the beam's shape and ring splitting behavior.

The phase exhibits vortex-like properties, indicating complex wavefront structures.

Abstract

An explicit formula for a new type of beams, which in this work are called the "special" hyperbolic Bessel-Gaussian (SHBG) beams, has been derived, using the method of the Hankel transform formulated in our previous work. The fundamental properties of these beams are analyzed. The parameters that define the beam shape have been identified and related to those of the fundamental Gaussian beam. The analytical expressions for the SHBG beams include an additional parameter $\gamma$, which allows the beam's shape to be modified to some extent. In the plane perpendicular to the propagation direction, these beams exhibit the annular nature. Interestingly, initially (i.e. near the beam's spot) a single ring splits into a number of rings as one is moving along the beam. This is especially apparent for $\gamma$ close to unity, as this effect then appears for values of $z$ relatively small compared to the Rayleigh length i.e., where the energy concentration in the beam is still high. The phase of the wave, whose behavior is in certain aspects typical of modes having the vortex character, is also studied in this paper.