Sum rules and physical bounds for a particulate slab

Two different sum rules for transmission of the coherent electromagnetic field by a particulate slab are established. The particles are assumed spherical, dielectric, and randomly located, and the slab is illuminated by a plane wave at normal incidence. These sum rules are obtained assuming that the particles are passive scatterers and satisfy causality conditions. The sum rules are then employed to generate physical bounds on a combination of bandwidth and thickness of the slab for a given transmission level. A potential check of the accuracy of the numerical computations is also admitted by the exact sum rules. A series of numerical computations illustrates the results obtained in this chapter.