Abstract
Abstract : A study to develop and apply a generalized theory of the coupling of the modes of propagation such as occur in distributed microwave devices is reported. A review of some of the concepts and principal theorems of Lie algebras is presented. As a result of this work, we are able to classify such problems according to whether the covering algebra is semi-simple or not. If it is not, then it contains a ''solvable ideal'' and at least that part of the problem is, in principle, fully soluble, giving an explicit solution obtained by successive quadrature. If, on the other hand, it is semi-simple, then we can apply Cartan's structure theorems to provide a meaningful and useful definition of the ''modes'' of the system, and to map out the coupling between these modes. The analysis of the statistical effect of random coupling in uniform systems is in progress. The randomness can be with respect to time, as in the parametric amplifier or maser that is pumped with a noisy signal. Or it can be with respect to distance, as in the study of the effect of randomly located dislocations or other inhomogeneities in a laser crystal. If the random coupling can be considered as a perturbation on a constant system matrix, then the resultant effect on the matricant solution is expressed in terms of the correlation coefficients of the perturbing matrix. (Author)
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