Eigenmodes in a negative-refractive-index planar waveguide for high-sensitivity evanescent sensing and spectroscopic applications

Abstract

Characteristic equations for eigenmodes in a planar waveguide which utilizes negative refractive index (NRI) material as a guiding layer and positive refractive index (PRI) materials as cladding layers have been deduced from the first principles in this work. Although the deduced characteristic equations for a NRI planar waveguide are just slightly modified compared with those of a PRI planar waveguide, they change the eigenmodes in the waveguide considerably. Firstly, the fundamental modes for both TE and TM polarization are excluded in a NRI planar waveguide; secondly, the first order modes in a NRI planar waveguide exhibit antisymmetric mode profiles (with their maxima and minima at the interfaces of guiding and cladding layers); finally, the modes of higher orders are trivial and of little interest. Although NRI materials that operate at optical frequencies are not available yet, evolvement of the metamaterial technique may provide us with such materials in the future and a NRI optical planar waveguide can be fabricated. With its unique features predicted by the characteristic equations (such as the maximal field strength at the interfaces of guiding and cladding layers for the first order modes), the NRI optical planar waveguide is of great potential to be used as highly sensitive sensing elements or non-plasmonic enhancement substrates for waveguide spectroscopy.