The resonant states in open cavities

There are considered resonant states in an open cavity i.e. where the electromagnetic field is described by a continuous spectrum. Such a situation appears when the coupling with a surrounding world is not neglected. The idea is a natural continuation of a classical potential scattering theory, but in a vector version. Formulating a scattering problem with a unitary scattering operator, (for nondissipative systems and for normalized incident and reflected waves), the energy stored in a finite volume is determined by the phase psi of the reflection coefficient being an eigenvalue of a scattering operator. The causality principle gives rise to the resonant states of the system as the real frequencies when the derivative of this phase with respect to the frequency - d psi/d omega reaches its maxima. The general statements are illustrated by tutorial examples and in the simplest form the same technique was used in the past for measurements of microwave cavities.