Interactions of Electromagnetic Waves With 3-D Opal-Based Magnetophotonic Crystals at Microwave Frequencies

The propagation of electromagnetic waves at microwave frequencies was investigated numerically in SiO₂ opal based magnetic nanostructures, using rigorous mathematical models solving Maxwell´s equations with electrodynamic boundary conditions, complemented by the Landau-Lifshitz equation. The numerical approach is based on the Galerkin´s projection method using the decomposition algorithm on autonomous blocks with Floquet channels. The opal structure consists of 250 nm SiO₂ nanospheres, with inter-sphere voids infiltrated with octagonal nanoparticles of either Ni_0.7Zn_0.3Fe₂O₄ with 4πM_s=5 kG, or NiFe₂O₄ with 4πM_s=3.12 kG . Both the opal matrix and the ferrite are assumed to be lossy through complex dielectric constants. The field dependence of the complex wave number of the fundamental extraordinary mode of the propagating EMWs in the 3-D opal-based magnetophotonic crystals was determined for transverse orientation of the bias magnetic field at a frequency of 9.375 GHz. The numerical technique shows an excellent agreement when applied to model recent experimental data of waveguide measurements on similar ferrite opals.