Fresnel's laws in discrete optical media

Alexander Szameit,Ulf Peschel,Andreas Tünnermann,Falk Lederer,Stefan Nolte,Matthias Heinrich,Thomas Pertsch,Felix Dreisow,Henrike Trompeter

doi:10.1088/1367-2630/10/10/103020

Abstract

We present the discrete analog of Snell's refraction law at the interface between two dissimilar waveguide arrays. Additionally, reflection and transmission coefficients for the Bloch waves are derived analytically. The theoretical findings were confirmed by analyzing the evolution of light in femtosecond laser written waveguide arrays.

Highlights

When light crosses the interface between two dissimilar media, it experiences refraction as well as partial reflection
For the experimental verification of these results we used planar waveguide arrays fabricated by the fs laser writing technique (Szameit et al 2005, 2006)
Since the induced change of the refractive index is a function of the writing velocity (Blomer et al 2006), the fs writing technique is in particular well suited to induce defects and interfaces in waveguide arrays

Summary

Introduction

When light crosses the interface between two dissimilar media, it experiences refraction as well as partial reflection. The research on discrete propagation in waveguide arrays gained further stimulus, when the existence of localized nonlinear modes at surfaces (Kartashov et al 2006, Kominis et al 2007, Makris et al 2005, Molina et al 2006, 2007) and interfaces (Makris et al 2006, Molina and Kivshar 2007) in waveguide arrays was predicted. These phenomena were experimentally demonstrated in 1D (Iwanow et al 2004, Rosberg et al 2006, Smirnov et al 2006, Suntsov et al 2006, 2007) and only recently in 2D (Szameit et al 2007, 2008, Wang et al 2007). This is somewhat surprising since one can expect that interfaces have a strong impact on the refraction, reflection and transmission properties of light, culminating in modifications of the laws of Snell and Fresnel with respect to the continuous case

Results

Discussion

Conclusion