  We report a new computational method based on the recursive Green's function
technique for calculation of light propagation in photonic crystal structures.
The advantage of this method in comparison to the conventional
finite-difference time domain (FDTD) technique is that it computes Green's
function of the photonic structure recursively by adding slice by slice on the
basis of Dyson's equation. This eliminates the need for storage of the wave
function in the whole structure, which obviously strongly relaxes the memory
requirements and enhances the computational speed. The second advantage of this
method is that it can easily account for the infinite extension of the
structure both into the air and into the space occupied by the photonic crystal
by making use of the so-called "surface Green's functions". This eliminates the
spurious solutions (often present in the conventional FDTD methods) related to
e.g. waves reflected from the boundaries defining the computational domain. The
developed method has been applied to study scattering and propagation of the
electromagnetic waves in the photonic band-gap structures including cavities
and waveguides. A particular attention has been paid to surface modes residing
on a termination of a semi-infinite photonic crystal. We demonstrate that
coupling of the surface states with incoming radiation may result in enhanced
intensity of an electromagnetic field on the surface and very high Q factor of
the surface state. This effect can be employed as an operational principle for
surface-mode lasers and sensors.
