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.