  Omnidirectional light propagation in two-dimensional (2D) photonic crystals
(PCs) has been investigated by extending the formerly developed 2D finite
element analysis (FEA) of in-plane light propagation in which the corresponding
band structure (BS) and photon density of states (PDOS) of 2D PCs with complex
geometry configurations had been calculated more accurately by using an
adaptive FEA in real space for both the transverse electric (TE) and transverse
magnetic (TM) modes. In this work, by adopting a waveguiding theory under the
consideration of translational symmetry, the omnidirectional PDOS corresponding
to both the radiative and evanescent waves can be calculated accurately and
efficiently based on the in-plane dispersion relations of both TE and TM modes
within the irreducible Brillouin zone. We demonstrate that the complete band
gaps shown by previous work considering only the radiative modes will be closed
by including the contributions of the evanescent modes. These results are of
general importance and relevance to the spontaneous emission by an atom or to
dipole radiation in 2D periodic structures. In addition, it may serve as an
efficient approach to identifying the existence of a complete photonic band gap
in a 2D PC instead of using time-consuming 3D BS calculations.
