Effective and efficient method of calculating Bessel beam fields

Abstract

Bessel beams have gathered much interest of late due to their properties of near diffraction free propagation and self reconstruction after obstacles. Such laser beams have already found applications in fields such as optical tweezers and as pump beams for SRS applications. However, to model the self reconstruction property of Bessel beams, it is necessary to calculate the field at all points in space before and after the obstacle – a computationally intensive task give the large spatial distribution of Bessel beams. In this work we propose a computationally efficient method of calculating the arbitrary propagation of a Bessel beam, which is both fast and accurate. This method is based on transforming the problem to a new co-ordinate system more in line with the conical nature of the wavefronts, and shows excellent agreement with more traditional methods of calculation based on the Kirchoff-Fresnel diffraction theory in cylindrical co-ordinates. The success of the method is shown for the case of Bessel beams and Bessel-Gauss fields passing through non-transparent obstacles, as well as the case of these fields propagating through a scattering medium.