Multimode theory of plasmon excitation at a metal–photonic crystal interface

Surface plasmon excitation at a photonic crystal–metal interface is studied taking into account multiple scattering of an initial light wave on a periodical crystal structure. The analysis is focused on calculating characteristics of the eigenwaves in a onedimensional crystal, which comprise a set of harmonics with the wavevectors separated from each other by the value of the crystal lattice wavevector. Reflection from the crystal–metal interface binds the amplitudes of propagating and evanescent modes. Calculations show that for the dielectric characteristics of a synthetic opal and a substrate made of a real metal with a ruby laser radiation used as the initial wave, the fulfilment of plasmon resonance conditions leads to a local increase in the surface plasmon amplitude by a factor of 6.4–9 as compared to the average amplitude of the initial wave. As a rule, the effect can only be obtained for a single surface wave, all other waves being substantially weaker than the main plasmon. There is a specific case where the resonance condition holds for two modes simultaneously. In this case, two oppositely directed fluxes of equal intensity are generated at the interface. The resonance condition breaks at a small deviation of the incident angle of the initial wave θ from the normal direction (|θ| ≥ 10^-4 rad). In the latter case, the picture is asymmetric: at angles |θ| ≥ 5 × 10^-3 rad, only one plasmon remains intensive. The local density of electromagnetic energy at the photonic crystal–metal interface may exceed the corresponding value of the initial wave by a factor of 40–80.