Scattering by quasi-periodic and quasi-random distributions

We consider the scattering of plane electromagnetic waves by parallel, coplanar, arbitrary cylinders distributed essentially as in a "one-dimensional liquid" of elastic objects. Green\´s function methods are used to generalize and extend results obtained previously by separations of variables for circular cylinders. Taking into account coherent multiple scattering, we obtain a general form for the coherent field and a corresponding approximation for the incoherent scattering. The field depends critically on the normalized difference between the average and minimum separations of scatterer centers; say on which equals the relative "elbow room" per scatterer. If , then the distribution is periodic and the results reduce to those for the general grating; thus the range corresponds to the quasi-periodic case. Similarly, at the other limit , the results reduce to those for the random "rare gas" case, and the range may be called quasi-random. Thus, as the parameter is varied from 1 to 0 (or as the distribution of scatterers is "compressed"), the result exhibit successively the effects expected for gaseous, liquid, and crystalline distributions.