  The problem of plane-wave diffraction on semi-infinite orthorhombic
electromagnetic (photonic) crystals of general kind is considered. Boundary
conditions are obtained in the form of infinite system of equations relating
amplitudes of incident wave, eigenmodes excited in the crystal and scattered
spatial harmonics. Generalized Ewald-Oseen extinction principle is formulated
on the base of deduced boundary conditions. The knowledge of properties of
infinite crystal's eigenmodes provides option to solve the diffraction problem
for the corresponding semi-infinite crystal numerically. In the case when the
crystal is formed by small inclusions which can be treated as point dipolar
scatterers with fixed direction the problem admits complete rigorous analytical
solution. The amplitudes of excited modes and scattered spatial harmonics are
expressed in terms of the wave vectors of the infinite crystal by closed-form
analytical formulae. The result is applied for study of reflection properties
of metamaterial formed by cubic lattice of split-ring resonators.
