  The light emission rate from a scanning tunneling microscope (STM) scanning a
noble metal surface is calculated taking retardation effects into account. As
in our previous, non-retarded theory [Johansson, Monreal, and Apell, Phys. Rev.
B 42, 9210 (1990)], the STM tip is modeled by a sphere, and the dielectric
properties of tip and sample are described by experimentally measured
dielectric functions. The calculations are based on exact diffraction theory
through the vector equivalent of the Kirchoff integral. The present results are
qualitatively similar to those of the non-retarded calculations. The light
emission spectra have pronounced resonance peaks due to the formation of a
tip-induced plasmon mode localized to the cavity between the tip and the
sample. At a quantitative level, the effects of retardation are rather small as
long as the sample material is Au or Cu, and the tip consists of W or Ir.
However, for Ag samples, in which the resistive losses are smaller, the
inclusion of retardation effects in the calculation leads to larger changes:
the resonance energy decreases by 0.2-0.3 eV, and the resonance broadens. These
changes improve the agreement with experiment. For a Ag sample and an Ir tip,
the quantum efficiency is $\approx$ 10$^{-4}$ emitted photons in the visible
frequency range per tunneling electron. A study of the energy dissipation into
the tip and sample shows that in total about 1 % of the electrons undergo
inelastic processes while tunneling.
