Near-field thermal emission from metamaterials

• Local density of electromagnetic states for media of arbitrary electric permittivity and magnetic permeability derived.
• Surface polariton dispersion relation that accounts for losses presented.
• Near-field phenomena of emitting metallic and dielectric based metamaterials analyzed.

A closed form expression for the local density of electromagnetic states (LDOS) due to a thermally emitting metamaterial bulk is derived from Maxwell's equations combined with fluctuational electrodynamics. The final form is the same as that for nonmagnetic materials, where the influence of the magnetic permeability is embedded in the Fresnel reflection coefficients. Spectral distributions of LDOS near metallic- and dielectric-based metamaterials are investigated. Results reveal that LDOS profiles are dominated by surface polaritons (SPs) in both TE and TM polarization states. A detailed discussion is provided on the necessary conditions for exciting TM- and TE-polarized SPs via a dispersion relation analysis that accounts for losses. Beyond the conventional conditions for excitation of SPs, the lossy dispersion relation analysis demonstrates mathematically that SPs exist when the imaginary parts of the permittivity or permeability, as well as n′n″, are close to zero, where n′ and n″ are the real and imaginary parts of the refractive index, respectively. An asymptotic expression for the extreme near field LDOS is derived, showing a Δ−3 power law relationship, as for nonmagnetic media, between LDOS and distance from the emitting bulk Δ. Results obtained from this study will assist in assessing material properties of arbitrarily electromagnetic materials in applications related to energy harvesting.