Local Density of States (LDOS) of an HMM. (a) Isofrequency surfaces at slightly different energies for an isotropic dielectric and a Type I HMM. The enclosed volume between the two isofrequency surfaces is a measure of the photonic density of states of the system. It is clear that the HMM has a diverging enclosed volume and thus, in the ideal limit, can support an infinite photonic density of states. (b) Lifetime of a dipole, normalized to the free space lifetime, versus distance above the HMM surface (“d”). An Ag-TiO2 system with 35% fill fraction is considered in the Type I (λ = 350 nm) and Type II (λ = 645 nm) regions. A thick film of silver (λ=372 nm) is also shown for comparison. Local density of states (LDOS) versus wavevector for a 200 nm Ag-TiO2 slab (35% fill fraction) and 200 nm silver film for an emitter placed (c) 20 nm and (d) 3 nm above the structure. Note that high-k modes exist in both (c) and (d) however a clear broad quenching peak is seen in (d).