Orthogonality relations are given for the ``four-vector'' guided modes of anisotropic uniform wave guides and for the ``six-vector'' guided modes of uniform wave guides containing unidirectional electron beams with axially independent dc velocities. In general, these orthogonality relations involve both the modes of the given wave guide and those of an appropriate ``adjoint'' wave guide. A description is given for the adjoint wave guides associated with wave guides which contain media whose characteristics are restricted only by the requirement that they be axially independent and which, if bounded, are subject to a variety of boundary conditions arising from idealizations of actual boundaries.
Absfrocr-A "nested product"(NP) algorithm is introduced to define a finite polynomial as a nested sequence of multiplications and additions. The van der Maas solution for the current distribution of a Dolph-Chebyshev array is converted to its NP equivalent. In effect, what this accomplishes is to convert the computation from a sum of many terms containing ratios of factorials of large numbers to a nested sequence of many additions and multiplications where each multiplicand is the ratio of individual factors of the factorials. Calculation of the array currents is then readily accomplished even for very large arrays.
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