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By Ewold Verhagen

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For all propagating 43 3 Negative index of refraction in surface plasmon polariton waveguides plane waves (with Re {k x } = 0), the phase velocity is defined by v p = ω/Re {k x }. In the absence of losses and high dispersion, the energy velocity v E is equal to the group velocity v g = dω/dk x . Therefore, for lossless materials, negative indices will manifest themselves by a region of negative slope on a plot of ω versus |k x |. 1 plots the dispersion relationships ω versus |Re {k x }| for lossless MIM, IIM, and IMI geometries with Ag as the metallic layer and GaP as the dielectric.

As Figs. 4 reveal, both IIM and IMI geometries can support negative index modes. However, these negative index modes are generally found in a frequency regime where additional positive index modes also exist. Such characteristics prohibit assignment of a single, unique index to the IIM and IMI geometries above the plasmon resonance, even including realistic material losses. Therefore, unlike the MIM geometry, planar IIM and IMI waveguides may not be regarded as single-mode, negative index materials.

Bloch boundary conditions are used to simulate an incident plane wave that is infinite in extent. 6(b) shows the simulated H y field in a plane through the waveguide core at a distance of 5 nm from the top Ag/GaP interface. The field is not evaluated in the middle of the waveguide, since the H y component of the antisymmetric mode is zero there. To the left, the incident wave makes an angle of 30◦ with respect to the xz plane, as shown by the arrow indicating the calculated Poynting vector. Inside the MIM waveguide, a wave can be seen to propagate over a distance of the order of a micron.

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