  An electromagnetic (EM) Bloch wave propagating in a photonic crystal (PC) is
characterized by the immittance (impedance and admittance) of the wave. The
immittance is used to investigate transmission and reflection at a surface or
an interface of the PC. In particular, the general properties of immittance are
useful for clarifying the wave propagation characteristics. We give a general
proof that the immittance of EM Bloch waves on a plane in infinite one- and
two-dimensional (2D) PCs is real when the plane is a reflection plane of the PC
and the Bloch wavevector is perpendicular to the plane. We also show that the
pure-real feature of immittance on a reflection plane for an infinite
three-dimensional PC is good approximation based on the numerical calculations.
The analytical proof indicates that the method used for immittance matching is
extremely simplified since only the real part of the immittance function is
needed for analysis without numerical verification. As an application of the
proof, we describe a method based on immittance matching for qualitatively
evaluating the reflection at the surface of a semi-infinite 2D PC, at the
interface between a semi-infinite slab waveguide (WG) and a semi-infinite 2D PC
line-defect WG, and at the interface between a semi-infinite channel WG and a
semi-infinite 2D PC slab line-defect WG.
