Non-constant scattering matrices and applications

The formulation of sections 3 and 4 can be restated for the more general case in which the scattering matrix has elements which are functions of .

In this case the scattering relationship is

(86) |

In the more general case of passive propagation, the scattering junction is said to be lossless if

By adding (89) to its conjugate transpose we get

When the medium is passive we have , and a spectral factorization does exist. The normalized scattering matrix is then

(91) |

A real-coefficient matrix
which is analytic for
and which satisfies (93) is called *Lossless Bounded
Real* [63,112]. The condition (93) implies
that the elements of any column of
are power complementary,
i.e.,

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