Electromagnetic Transmission Characteristics of a Lattice of Infinitely Long Conducting Cylinders

This investigation is primarily concerned with the study of electromagnetic transmission characteristics of a lattice of infinitely long conducting cylinders. Four approaches to the general problem have been employed and the advantages, disadvantages, and realms of validity of each have been studied. Several of these methods constitute a substantial improvement over previous analyses and are supported by wave-guide and free-space experimental work. The four approaches are: (1) A molecular analogy with a consideration of dipole interactions leading to the Clausius-Mosotti relations, (2) A transmission line formulation which considers the thick obstacle for both polarizations, (3) An analysis based on the summation of scattered fields which demonstrates that the Clausius-Mosotti relations are a special case of a more general relation which accounts for the effects of higher order multipoles, and (4) A solution formally valid for all values of spacing and cylinder radius based on integral equation formulation of variational principle.