  We study the local density of states (LDOS) in a finite photonic crystal, in
particular in the frequency range of the band gap. We propose a new point of
view on the band gap, which we consider to be the result of vacuum fluctuations
in free space that tunnel in the forbidden range in the crystal. As a result,
we arrive at a model for the LDOS that is in two major items modified compared
to the well-known expression for infinite crystals. Firstly, we modify the
Dirac delta functions to become Lorentzians with a width set by the crystal
size. Secondly, building on characterization of the fields versus frequency and
position we calculated the fields in the band gap. We start from the fields at
the band edges, interpolated in space and position, and incorporating the
exponential damping in the band gap. We compare our proposed model to exact
calculations in one dimension using the transfer matrix method and find very
good agreement. Notably, we find that in finite crystals, the LDOS depends on
frequency, on position, and on crystal size, in stark contrast to the
well-known results for infinite crystals.
