A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures

The magneto-optical (MO) Faraday effect of Bi-substituted yttrium iron garnet (Bi:YIG) films with random multilayer structures is analyzed using the random matrix approach, and the Faraday rotation angles (θF) are examined in comparison with those of periodic multilayer films. The films consist of Bi:YIG films and SiO2 dielectric films, which are stacked randomly (periodically) so as to form the random (periodic) multilayer structures. Similarly to the case of MO Kerr effect, a considerable enhancement in θF takes place when the film structure meets the nonreflection condition of light. In particular, θF of the film reaches a maximum of 1.4°/μm at λ=1.15 μm, with the fraction of Bi:YIG layers in the random multilayer film is 41%. This value is about seven times larger than that of a single Bi:YIG film (θF=0.2°/μm), and cannot be attained with periodic multilayer films.