Abstract. We consider a Fabry-Perot resonance (a transmission band edge resonance) in periodic layered structures involving birefringent layers. In our previous publication [2] we have shown that the presence of birefringent layers with misaligned in-plane anisotropy can dramatically enhance the performance of the photonic-crystal resonator. It allows to reduce its size by an order of magnitude without compromising on its performance. The key characteristic of the enhanced slow-wave resonator is that the Bloch dispersion relation ω (k) of the periodic structure displays a degenerate photonic band edge, in the vicinity of which the dispersion curve can be approximated as ∆ω ∼ (∆k) 4 , rather than ∆ω ∼ (∆k) 2 . Such a situation can be realized in specially arranged stacks of misaligned anisotropic layers. On the down side, the presence of birefringent layers results in the slow wave 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 slow-wave resonance characteristic of a degenerate photonic band edge. Both features are of critical importance for many practical applications, such as the enhancement of various light-matter interactions, light amplification and lasing, optical and microwave filters, antennas, etc.