Planar GRIN Media with Hyperbolic Secant Refractive Index Profile

Abstract

Light propagation in GRIN media with a wide variety of gradient profiles has been analyzed with emphasis on focusing and collimation properties of importance for integrated optics, fiber optics, micro-optics, and optical sensing [6.1]. In designing GRIN structures, one goal is to select an index profile that provides focusing and collimation. The simplest GRIN medium with this capability is the parabolic one, where the equation governing light propagation can be solved analytically in the paraxial region [6.2], as discussed in Chap. 1. There is another GRIN medium with focusing and collimation properties. It is characterized by a hyperbolic secant profile (hereafter referred to as HS) that presents the following advantages in comparison with the parabolic one [6.2–6.5]. First, it is a more general profile, because the parabolic function can be considered as the first-order approximation of the Taylor expansion series of the hyperbolic secant function. Second, the equation governing light propagation can be solved analytically without carrying out any type of approximation. Third, the medium is free of aberrations for meridional rays (rays propagating in planes such that they include the optical axis). Fabrication of GRIN media with HS profiles has already been demonstrated by a microcontrolled dip-coating procedure from colloidal solutions [6.6]. Other methods include field-assisted ion exchange [6.7] and vapor deposition techniques [6.8].