1.5 Frequency domain analysis

In most cases we are either interested in the fields at one particular location, for example, on the surface of an optical element, or we want to know the fields at all places in the interferometer but at one particular point in time. The latter is usually true for the steady state approach: assuming that the interferometer is in a steady state, all solutions must be independent of time so that we can perform all computations at t = 0 without loss of generality. In that case, the scalar plane wave can be written as
E = E0 exp(− ikz ). (3 )
The frequency domain is of special interest as numerical models of gravitational-wave detectors tend to be much faster to compute in the frequency domain than in the time domain.

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