Calculation of the scattering matrix reproduce the results published earlier by Alexander Zamolodchikov.

In this case the scattering matrix is given by:

This results in a scattering matrix that is no longer all-zeroes on the antidiagonal.

Having these results it is possible to compute the scattering matrix of a shunt node.

By modifying the scattering matrix inhomogeneous and lossy materials can be modelled.

With similar considerations as for the series node the scattering matrix of the shunt node may be derived.

The scattering matrix then pairs solutions in the "distant past" to those in the "distant future".

The overall filter response is then found from the combined scattering matrix of all the individual element matrices.

An isolator is a non-reciprocal device, with a non-symmetric scattering matrix.

The asymptotic properties of time evolution are given by the scattering matrix.