  We consider transmission band edge resonance in periodic layered structures
involving birefringent layers. Previously we have shown that the presence of
birefringent layers with misaligned in-plane anisotropy can dramatically
enhance the performance of the photonic-crystal Fabry-Perot resonator. It
allows to reduce its size by an order of magnitude without compromising on its
performance. The key characteristic of the enhanced photonic-crystal cavity is
that its Bloch dispersion relation displays a degenerate photonic band edge,
rather than only regular ones. This can be realized in specially arranged
stacks of misaligned anisotropic layers. On the down side, the presence of
birefringent layers results in the Fabry-Perot resonance being coupled only
with one (elliptic) polarization component of the incident wave, while the
other polarization component is reflected back to space. In this paper we show
how a small modification of the periodic layered array can solve the above
fundamental problem and provide a perfect impedance match regardless of the
incident wave polarization, while preserving the giant transmission resonance,
characteristic of a degenerate photonic band edge. Both features are of
critical importance for a variety of practical applications, including
antennas, light amplification, optical and microwave filters, etc.
