IMPURITY MODES FROM IMPURITY CLUSTERS IN PHOTONIC BAND STRUCTURES

A Green function calculation for the impurity modes of single impuriti es and clusters of impurities in a photonic band structure is given. S pecifically, a truncated two-dimensional periodic dielectric medium co mposed from a square lattice array of dielectric rods placed perpendic ularly between two parallel perfectly conducting plates is studied. Im purities are introduced into this system substitutionally by replacing one (single impurity case) or a number (cluster impurity case) of the rods in the periodic system by impurity rods. Exact expressions for t he impurity mode frequencies are obtained in terms of the Green functi ons of the pure system. These expressions are then evaluated for the c ase of impurities with small cross-sectional areas using numerically d etermined Green functions. Linear frequency-independent, linear freque ncy dependent and non-linear impurity dielectric media are treated.