Calculation of the local optical density of states in absorbing and gain media

The local optical density of states plays a key role in a wide range of phenomena. Near to structures displaying optical absorption or gain, the definition of the photonic local density of states needs to be revised. In this case two operative different definitions can be adopted to characterize photonic structures. The first (ρ(A)(r, ω)) describes the light intensity at a point r when the material system is illuminated isotropically and corresponds to what can be measured by a near-field microscope. The second (ρ(B)(r, ω)) gives a measure of vacuum fluctuations and coincides with ρ(A)(r, ω) in systems with real susceptibility. Scattering calculations in the presence of dielectric and metallic nanostructures show that these two definitions can give rather different results, the difference being proportional to the thermal emission power of the photonic structure. We present a detailed derivation of this result and numerical calculations for nanostructures displaying optical gain. In the presence of amplifying media, ρ(B)(r, ω) displays regions with negative photon densities, thus failing in describing a power signal. In contrast, ρ(A)(r, ω), positive definite, properly describes the near-field optical properties of these structures.