Abstract:
We develop a formulation for cylinder gratings in conical incidence, using a multipole method. The theory,
and its numerical implementation, is applied to two-dimensional photonic crystals consisting of a stack of
one-dimensional gratings, each characterized by its plane wave scattering matrix. These matrices are used in
combination with Bloch’s theorem to determine the band structure of the photonic crystal from the solution of
an eigenvalue problem. We show that the theory is well adapted to the difficult task of locating the complete
band gaps needed to support air-guided modes in microstructured optical fibers, that is, optical fibers in which
the confinement of light in a central air hole is achieved by photonic band-gap effects in a periodic cladding
comprising a lattice of air holes in a glass matrix.
