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Resonances of the open cavity

Zagrodziński J.

Journal of Technical Physics

2001

Vol. 42, no 1

109-113

Resonant states in an open cavity, i.e. where the electromagnetic field is described by a continuous spectrum, are considered. Such a situation appears when 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 the 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 some examples and, in the simplest form, the same technique was used in the past for measurements of microwave cavities.