Photonic density of states in hyperbolic metamaterials with finite feature sizes

We investigate the photonic density of states (PDOS) in indefinite dielectric media metamaterials and specifically in hyperbolic metamaterials (HMMs) taking into account the finite feature sizes of the subwavelength pattern or meta-atoms in those metamaterials. While the PDOS for an ideal and homogeneous HMM diverges, the finite feature sizes imposed by practical constraints limits the highest k vector length k_max, which in turn makes the PDOS finite. We derive expressions for the finite PDOS in relation to the smallest feature sizes of the metamaterials. We also discuss the modification to black body radiation in an indefinite medium, which is remarkably different from that in free space since it is largely polarized.