Definition and measurement of the local density of electromagnetic states close to an interface

We propose in this article an unambiguous definition of the local density of electromagnetic states (LDOS) in a vacuum near an interface in equilibrium at temperature T. We show that the LDOS depends only on the electric-field Green function of the system but does not reduce in general to the trace of its imaginary part, as often is used in the literature. We illustrate this result by a study of the LDOS variations with the distance to an interface and point out deviations from the standard definition. We show nevertheless that this definition remains correct at frequencies close to the material resonances such as surface polaritons. We also study the feasibility of detecting such a LDOS with apertureless scanning near-field optical microscope (SNOM) techniques. We first show that a thermal near-field emission spectrum above a sample should be detectable and that this measurement could give access to the electromagnetic LDOS. It is further shown that the apertureless SNOM is the optical analog of the scanning tunneling microscope, which is known to detect the electronic LDOS. We also discuss some recent SNOM experiments aimed at detecting the electromagnetic LDOS.