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
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.
Key words: Optical Phenomena and Photonics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2016