ResonatorModen

Resonatormoden (resonator modes) are the distinct standing-wave patterns that can exist inside a resonator when it stores energy at particular frequencies. They arise as solutions to the wave equation subject to the resonator's boundary conditions. Each mode is characterized by a resonance frequency and a spatial field distribution.

In electromagnetic resonators such as microwave cavities, modes are labeled TE (transverse electric) and TM (transverse magnetic); the geometry sets the allowed mode frequencies and field patterns (for example, in a rectangular cavity the TE_mn and TM_mn modes have a specific cutoff and field distribution). In optical resonators such as Fabry-Pérot cavities, modes are often described as longitudinal modes (standing waves along the cavity length) with possible transverse modes; whispering-gallery mode resonators support circulating, high-Q modes along the periphery.

In mechanical resonators, resonator modes correspond to normal modes of vibration, such as flexural or torsional modes, with mode shapes determined by geometry and boundary conditions, e.g., a beam or a plate.

Key properties include the resonant frequency, quality factor Q (the ratio of stored to dissipated energy per cycle), mode volume, and coupling to external drives. Modes can be selectively excited or suppressed by geometry, boundary conditions, and coupling mechanisms; degeneracies can occur in symmetric structures.

Applications range from filters and lasers to sensors, clocks, and quantum devices, where specific modes enhance interaction or confinement.