Optical Bloch waves in periodic planar waveguides

Abstract

The elementary solutions of the wave equation in a periodic waveguide (Fig. 1) are waves of the Floquet-Bloch type.^1,2 They are formed by the superposition of a set of plane waves, called space harmonics (SHs). An equivalent description is possible³ by the coupled mode formalism, considering plane waves (the SHs) as the elementary excitations which are coupled by the structure of the guide. For a discussion of wave propagation over extended areas of periodic guides we adopt here the Bloch viewpoint. Below, we summarize briefly the properties of optical Bloch waves of general direction s → of propagation. We show their direct excitation by a prism coupler, permitting a measurement of the complete dispersion characteristic ω β → of the guide. We then discuss transitions between periodic and nonperiodic guides, showing the unusual optical effect of negative refraction.