Long-range propagation of surface plasmons in a thin metallic film deposited on an anisotropic photonic crystal

We propose using a strongly anisotropic dielectric as a substrate for plasmonic devices. We show that the propagation range of surface plasmons is increased if the substrate is a birefringent dielectric crystal with a properly oriented optical axis. The increase of the propagation range depends on the degree of anisotropy, and, consequently, it turns out to be small for substrates of natural optical crystals, where anisotropy is weak. However, in specially designed photonic crystals, the anisotropy may be very strong, thus leading to appreciable increase of the propagation range. A photonic-crystal substrate, being a medium with nonlinear dispersion, also affects the dispersion law of the surface plasmon. All these effects may increase the efficiency of modern plasmonic and optoelectronic devices.

Figure 1

(Color online) Metal film of thickness $d$ on semi-infinite anisotropic substrate. A surface plasmon propagates along axis $x$. The coordinate axes are directed along the principal axes of the dielectric tensor.

Figure 2

(Color online) Two orientations, (a) parallel and (b) perpendicular, of the optical axis of the substrate with respect to the metal film. The substrate is a positive uniaxial crystal with ${ϵ}_{\Vert }>{ϵ}_{\perp }$.

Figure 3

(Color online) Dispersion curves for SP in a structure with anisotropic substrate. The plasmonic structure is $50\text{−}\mathrm{nm}$-thick silver film on an anisotropic substrate with ${ϵ}_z=7.5$ and ${ϵ}_x=2$. The solid (dotted) line is for the orientation of the optical axis perpendicular (parallel) to the metal film. The dashed curve is for the equivalent isotropic substrate with $ϵ=\sqrt{{ϵ}_x{ϵ}_z}=3.87$.

Figure 4

(Color online) Propagation range of the SP (a) in the optical region and (b) in the infrared region of frequencies.

Figure 5

(Color online) Penetration depth of the electromagnetic field of the SP into the dielectric substrate.