Abstract
We show that dielectric waveguides formed by materials with strong optical anisotropy support electromagnetic waves that combine the properties of propagating and evanescent fields. These “ghost waves” are created in tangent bifurcations that “annihilate” pairs of positive- and negative-index modes and represent the optical analogue of the “ghost orbits” in the quantum theory of nonintegrable dynamical systems. Ghost waves can be resonantly coupled to the incident evanescent field, which then grows exponentially through the anisotropic media—as in the case of negative index materials. As ghost waves are supported by transparent dielectric media, the proposed approach to electromagnetic field enhancement is free from the “curse” of material loss that is inherent to conventional negative index composites.
Highlights
Recent development of negative index metamaterials, where the subwavelength structure of the composite unit cell allows simultaneously negative electric and magnetic responses,[1,2] gave rise to the experimental demonstration of such unusual phenomena as negative refraction and backwards wave propagation,[3] electromagnetic cloaking,[4] and subwavelength focusing.[5]
We demonstrate that strongly anisotropic dielectric waveguides support “ghost waves,” which differ from the “regular” propagating and evanescent fields
The strong local field enhancement at or near the condition of resonant coupling to the ghost waves can find many applications from optical sensing, e.g., in Kretschmann geometry, where a small variation of the refraction index of the isotropic medium surrounding the biaxial slab would lead to a dramatic change of the observed reflectivity, to nonlinear-optical phenomena
Summary
Recent development of negative index metamaterials, where the subwavelength structure of the composite unit cell allows simultaneously negative electric and magnetic responses,[1,2] gave rise to the experimental demonstration of such unusual phenomena as negative refraction and backwards wave propagation,[3] electromagnetic cloaking,[4] and subwavelength focusing.[5]. Do not rely on the magnetic response.[18,19,20] If the desired negative index performance can be limited to propagation in a waveguide, a number of such solutions are possible—using hyperbolic metamaterials,[19] Clarricoats–Waldron geometry,[18] or a waveguide with the core formed by biaxial anisotropic dielectric20 [see Fig. 1(a)]. The actual mode spectra below the tangent bifurcation threshold show the signatures of the so called “ghost orbits” formally defined as extensions of the system dynamics to a higher-dimensional phase space (e.g., extended to complex time and/or spatial coordinates).[16,23,24,25] We conclude that negative index systems, in a waveguide geometry that does not rely on magnetic response,[18,19,20] support optical equivalents of these “ghosts.” such optical ghost waves are essentially different from both positive- and negativeindex modes.
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