Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit

We present an effective medium theory that simultaneously determines the effective permittivity and effective permeability of a magnetodielectric composite beyond the long-wavelength limit. In the long-wavelength limit, our theory reproduces previous results obtained in two and three dimensions. To verify our theory, we performed band-structure calculations on a periodic composite in two dimensions for a specific configuration with complicated Mie resonances in the microstructure. Our results show that our theory can be valid even when the wavelength in the background medium, λ0, is as small as 1.3 times the lattice constant, a, whereas the long-wavelength theory breaks down when λ0 <3.5a.