Faraday magneto-optical rotation in compositionally graded films

Abstract

We present a two-step homogenization method for studying the Faraday magneto-optical effect in graded metal-dielectric composite films of width W, in which the volume fraction of metal particles in a slice varies along the direction perpendicular to the film surface. First, we adopt the effective-medium theory to formulate the equivalent (local) dielectric permittivity tensor for a z slice. Second, the graded composite films are homogenized with an effective (overall) dielectric permittivity tensor including the diagonal and off-diagonal elements. Faraday rotation is studied as a function of the graded profile p(z) with the same total volume fraction. For a power-law form p(z)=a(z/W)m with different m, it is found that with increasing m, the magnitude of Faraday rotation becomes weak near the surface plasmon resonant band, accompanied with the redshift of the resonant center. Interestingly, it is possible to achieve strongly enhanced Faraday rotation in the high-frequency region, and to change the direction of rotation in the low-frequency one. Moreover, the magnitude can be further enhanced for needle-like particles. In the dilute limit, we show that Faraday rotation is indeed independent of m within Maxwell-Garnett theory.