Compensation of loss to approach –1 effective index by gain in metal-dielectric stacks

¹ Institut Fresnel, CNRS, Aix-Marseille Université, Domaine Universitaire de Saint-Jérôme, Service 161, 13397 Marseille Cedex 20, France
² State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, P.R. China
³ Pohl Institute of Solid State Physics, Tongji University, Shanghai 200092, P.R. China

Corresponding author: stefan.enoch@fresnel.fr

Received: 30 January 2008
Revised: 26 March 2008
Accepted: 2 April 2008
Published online: 25 July 2008

Abstract

We propose a theoretical study of optimization of metal-dielectric multilayer in order to approach -1 effective refractive index for transverse magnetic waves and a wavelength in the visible. The absorption losses of metal appear to be a crucial factor that affects the effective properties of the multilayer. Taking advantage of the dispersion relation of Bloch modes, we show that the losses not only decrease the transmission of the stack, but also change the negatively refracted angle. Then, we propose that using a gain-providing semiconductor (GaN) may allow compensating for the losses in metal layers. In theory, the performances of the structure can be improved greatly when gain is involved. When considering finite thickness structures, and with appropriate thickness for the terminating layers, it is possible to obtain a high transmission of the structure. A near -1 effective index metal-dielectric stack with high transmission may pave the way to the realization of negative quasi-isotropic refraction in the visible or ultraviolet wavelength range.