Propagation of optical beams in two transverse gradient index media

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 70; no. 5
• Main Authors: Martín-Ruiz, A., Martín-Heredia, J., Ruiz-Ochoa, L. A., Chan-López, E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2016
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Molecular; Optical and Plasma Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Regular Article; Spectroscopy/Spectrometry; Spintronics; Optical Phenomena and Photonics
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2016-60645-4

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. Graphical abstract