Interaction of surface polaritons with periodic surface structures; Rayleigh waves and gratings

Abstract

We describe the interaction of surface polaritons with Rayleigh surface waves for the case of arbitrary angle between the surface-polariton propagation direction and that of the Rayleigh wave. We presume the surface polariton couples to the Rayleigh wave through the periodic displacement of the surface produced by it, and also through the modulation of the dielectric constant of the substrate by the elasto-optic effect. We take the unstressed substrate to be an isotropic dielectric, and no special assumption about its elastic constants is required. The results here may be applied also to the interaction of surface polaritons with periodic gratings, provided the depth of the grooves is small. We obtain expressions for the amplitude of the diffracted electromagnetic waves produced by interaction of the surface polariton with a grating or Rayleigh wave. The diffracted beams may describe either fields localized near the surface or radiation induced by interaction with the periodic disturbance, depending on the kinematics of the interaction process. A small modification of these formulas may be used to compute the amplitude of a surface-polariton wave generated by interaction of incoming electromagnetic radiation with a periodic structure. Finally, we obtain a remarkably simple analytic expression for the surface-polariton dispersion relation in the near vicinity of gaps opened up by interaction with the periodic surface structure. This expression includes the effect of elasto-optic coupling and may be applied to propagation at an arbitrary angle to a set of grating lines, or to the propagation direction of a Rayleigh wave. The experimental study of these gaps offers the possibility of measuring the magnitude and frequency variation of the elements of the photoelastic tensor of the substrate in situations where these quantities are difficult to measure by conventional methods; i.e., for metals at infrared frequencies.