Slow light, open-cavity formation, and large longitudinal electric field on a slab waveguide made of indefinite permittivity metamaterials

Abstract

The optical properties of slab waveguides made of indefinite permittivity ($\ensuremath{\varepsilon}$) materials (IEMs) are considered. In this medium, the real part of the transverse permittivity is negative while that of the longitudinal permittivity is positive. At any given frequency, the IEM waveguide supports an infinite number of transverse magnetic (TM) eigenmodes. For a slab waveguide with a fixed thickness, at most only one TM mode is forward wave. The remainder are backward waves which can have a very large phase index. At a critical thickness, the waveguide supports degenerate forward- and backward-wave modes with zero group velocity if loss is absent. Above the critical thickness, the waveguide supports complex-conjugate decay modes instead of propagating modes. The presence of loss in IEMs will lift the TM mode degeneracy, resulting in modes with finite group velocity. A feasible realization is proposed. The performance of the IEM waveguide is analyzed and possible applications are discussed, which are supported by numerical calculations. These slab waveguides can be used to make optical delay lines in optical buffers to slow down and trap light, to form open cavities, to generate strong longitudinal electric fields, and as phase shifters in optical integrated circuits. Although the presence of loss will hinder these applications, gain can be introduced to compensate the loss and enhance the performance.