Resonances in Open Systems

In a short introduction examples of open resonators with acoustic, electromagnetic, elastic and water waves are given. A simple one-dimensional model problem is used to introduce the concept of 'leaky modes' which radiate energy. Numerically we employ 'perfectly matched layers (PML)' to solve such radiation problems. In wave guide problems so-called 'trapped modes' can occur in addition to leaky modes. Trapped modes do not radiate energy and are therefore important in applications. A well known example are the 'Parker modes' in wind tunnel testing, heat exchangers or turbomachinery cascades. Finally, as an example of a two-dimensional open resonator we compute the resonances in a classical laser cavity. The acoustic analogon is the 'gap tone' problem which is of importance in airframe noise. Two examples of the latter, namely 'cavity noise' and 'slat noise' are discussed briefly. The latter is still part of ongoing research