Dielectric waveguide model for guided surface polaritons

Abstract

Although surface polariton modes supported by finite-width interfaces can guide electromagnetic energy in three dimensions, we demonstrate for the first time to our knowledge that such modes can be modeled by the solutions of two-dimensional dielectric slab waveguides. An approximate model is derived by a ray-optics interpretation that is consistent with previous investigations of the Fresnel relations for surface polariton reflection. This model is compared with modal solutions for metal stripe waveguides obtained by full vectorial magnetic-field finite-difference methods. The field-symmetric modes of such waveguides are shown to be in agreement with the normalized dispersion relationship for analogous TE modes of dielectric slab waveguides. Lateral confinement is investigated by comparison of power-density profiles, and implications for the diffraction limit of guided polariton modes are discussed. © 2005 Optical Society of America OCIS codes: 130.2790, 160.3220, 160.3900, 240.5420, 240.6680, 240.6690. Surface plasmon polaritons and surface phonon polaritons have received much attention for their ability to guide electromagnetic energy. 1-3 Unlike dielectric waveguides, which confine volume electromagnetic waves to an optically dense core, these surface electromagnetic waves are localized at interfaces between dielectric materials and metals or ionic solids that support charge density oscillations. This surface localization has led researchers to explore the potential for transporting information via guided polariton modes with smaller spatial extents than can be achieved with diffraction-limited dielectric waveguides. 4The best-studied guided polariton modes involve surface plasmon polaritons supported by finite-width metal stripes.5 Although such modes have proved difficult to calculate, recent characterization by nearfield scanning optical microscopy has probed their localized light intensities.6 Based on published bound modal solutions, initial interpretation of these images led to conclusions that surface plasmon modes are inconsistent with dielectric waveguide theory. However, recent solutions for the experimentally relevant leaky modes may provide for an interpretation that is consistent with ray optics. 7 In this Letter we investigate the applicability of dielectric waveguide theory to surface polariton modes along finite-width interfaces. By combining previous research on the optics of surface polaritons 8 with a ray-optics model for guided waves, we demonstrate that an equivalent dielectric slab waveguide can be used to approximate the solutions of guided polariton modes.By definition, a guided mode is an eigenstate of the electromagnetic field that propagates in a specified direction (e.g., z) with a unique propagation constant (i.e., k z ϵ ␤ + i␣). For dielectric slab waveguides an exact analytical formulation for the modal solutions is possible. Nevertheless, to acquire a physical intuition for these waveguides, a ray-optics interpretation is often used. In this model the guided mode is define...

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