Authors: G.M. Gallatin
Affilation: Bell Labs, Lucent Technologies, United States
Pages: 318 - 321
Keywords: Greens function, scattering, diffraction, patterned, imperfect, multilayers
The 3D electromagnetic Greens function Gij(x,x) for planar multilayers is constructed from the eigenmodes of Maxwellís equations in the multilayer structure. Other approaches hav been used to derive the Greens function and the derivation here is similar to that given in . Once obtained, this Greens function can be used to perform detailed perturbative calculations of the scattering and diffraction from an arbitrary nonplanar multilayer in either of two relevant regimes: imperfect or patterned multilayers. For the imperfect case two types of imperfection are considered: multiple ìpointî defects and statistically defined index fluctuations. For patterned multilayers we consider the full structure to be built of 2 differenct basic types of planar structure. Then using the physical optics approximation as the starting or unperturbed field, we show that the Greens function easily generates the corrections to this approximation needed to satisfy boundary conditions at the interface between the two planar structure types. Other types of problems can and have been treated by this approach such as mode coupling in linear  and nonlinear waveguides . The advantage of using the planar multilayer Greens function follows directly from the fact that it is analytic which provides insight as well as numerical results and the planar eigenmodes can be evaluated rapidly even in 3D so it can be fast.