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.