We study the local density of states (LDOS) in a finite photoniccrystal, in particular in the frequency range of the band gap. Wepropose an original point of view on the band gap, which we consider tobe the result of vacuum fluctuations in free space that tunnel in theforbidden range in the crystal. As a result, we arrive at a model forthe LDOS that is in two major items modified compared to the well-knownexpression for infinite crystals. First, we modify the Dirac δ functionsto become Lorentzian with a width set by the crystal size. Second,building on characterization of the fields versus frequency and positionwe calculated the fields in the band gap. We start from the fields atthe band edges, interpolated in space and position, and incorporatingthe exponential damping in the band gap. We compare our proposed modelto exact calculations in one dimension using the transfer matrix methodand find very good agreement. Notably, we find that in finite crystals,the LDOS inside the band gap depends on frequency, on position, and oncrystal size, in contrast to the well-known results for infinitecrystals where the LDOS is zero, independent of frequency and position.

http://prb.aps.org/abstract/PRB/v89/i4/e045123

E. Yeganegi, A. Lagendijk, A. P. Mosk, and W. L. Vos

2014

01/2014

Phys. Rev. B

89

045123: 1-10

finite size, Local density of optical states, photonic band gap