Eur. Phys. J. D (2016) 70: 110
https://doi.org/10.1140/epjd/e2016-60645-4

Regular Article

Propagation of optical beams in two transverse gradient index media

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 México, Distrito Federal, México
² Colegio de Bachilleres de Tabasco. Plantel No.6. Cunduacán, Tabasco, México
³ División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, 86690 Cunduacán, Tabasco, México

^a e-mail: alberto.martin@nucleares.unam.mx

Received: 14 November 2015
Received in final form: 17 February 2016
Published online: 12 May 2016

Abstract

We investigate the propagation of optical beams in two gradient index inhomogeneous media. The Green’s function for paraxial propagation in an inhomogeneous medium is derived as a Feynman path integral involving summation over real rays. We use a simple method based on discontinuous functions, which is similar to that used in General Relativity when studying metric discontinuities across an hypersurface, to study the propagation in two transverse refractive index gradients which are coupled in the propagation direction. We show that this method is consistent with the geometric-optics ray theory, and then with the definition of the coupled Green’s function. The propagation of Gaussian beams in two homogeneous media with different refractive indices is analyzed. We also study the propagation of Airy beams in two media with different linear transverse refractive index gradients. We demonstrate that by controlling the gradient strength of the media it is possible to reduce to zero their acceleration, yielding an Airy beam that propagates linearly.