METHOD OF INTEGRAL-EQUATIONS AND AN EXTINCTION THEOREM FOR 2-DIMENSIONAL PROBLEMS IN NONLINEAR OPTICS

An approach using the generalized method of integral equations by substitution of the variables in the integral equation is applied to two- and quasi-two-dimensional systems. As a result, the connection between the integral and Maxwell equations as well as an extinction theorem for this case are established. The technique developed may be applied to any composite medium with a columnlike mesostructure. By use of the elementary cylinder radiator (''mesoscopic atom'') concept we reduce the problem of finding the optical properties of such media to the calculation of the susceptibility of a dense two-dimensional gas. The calculated optical anisotropy depends dramatically not only on the concentration but also on the form of the inclusions (mesostructure). Our calculations of the dielectric permittivity tensor for a two-dimensional composite medium with wire mesostructure show excellent agreement with the experimental measurements of the long-wavelength dielectric constants for two orthogonal polarizations in a photonic crystal made of dielectric rods [W. M. Robertson et al., J. Opt. Soc. Am. B 10, 322 (1993)].