Abstract

In the present work we study the enhancement of the nonlinear susceptibility in a quasiperiodic layered structure, comparing the optical properties of a periodic with those of a fractal structure. The considered fractal-structures are realized by following a triadic-Cantor sequence or the Fibonacci sequence. They are realized by alternating layers of two different materials (a,b) possessing linear refractive indices n, and n_b and nonlinear susceptibilities (we suppose only third-order nonlinearity) χ_a^NL and χ_b^NL, respectively. The two constituent materials are assumed to be lossless, and the response time of the composite is essentially the same as that of the nonlinear constituent. We assume that the thickness of each layer is much larger than an atomic dimension but much smaller than the incident wavelength. Consequently, the structural properties of each constituent material are essentially the same as those of a bulk sample, but the propagation of light through the structure can be described in terms of effective linear and nonlinear optical susceptibilities. We consider a TM polarization of the electric field , so that the electric field becomes nonuniformly distributed inside the layers of the composite (because the normal component of the displacement vector and not that of the electric vector is continuous at the boundary) A consequence of the fact that the electric field is nonuniformly distributed inside the layers of the structure is that, under certain circumstances, the effective susceptibility of the composite can exceed those of its constituent materials.

© 1998 IEEE