The scattering of acoustic and electromagnetic waves by open cavities usually causes a resonant response, arising when the frequency of excitation approaches one of the frequencies belonging to the spectrum of eigenvalues of such a cavity. In our investigation we will focus on investigation of resonant objects widely used in practice, representing two-dimensional (2D) hollow cylinders of arbitrary shape with longitudinal slits. In the context of propagating waves, these objects are treated as waveguides; in the context of standing waves, as resonators.

Chapter Contents:

• 14.1 Introduction
• 14.1.1 Preliminary remarks
• 14.1.2 Development of a systematic approach
• 14.2 Mathematical background
• 14.2.1 Schematic description of the MAR
• 14.2.2 Scheme for finding the complex eigenvalues
• 14.3 Computation of the complex eigenvalues for various open cavities
• 14.3.1 Circular cylinder with longitudinal slit
• 14.3.2 Elliptic cavity with moveable longitudinal slit
• 14.3.3 Open rectangular cavity with finite flanges
• 14.4 Resonance response of slotted cavities
• 14.4.1 Surface current calculations
• 14.4.2 Far-field calculations
• 14.5 Conclusion
• References

Inspec keywords: acoustic wave propagation; acoustic resonance; electromagnetic wave propagation; acoustic wave scattering; eigenvalues and eigenfunctions; electromagnetic wave scattering

Other keywords: electromagnetic wave scattering; standing waves; two-dimensional arbitrary open cavities; waveguides; acoustic wave scattering; E-polarized plane waves; excitation frequency; resonators; two-dimensional hollow cylinders; resonance scattering; longitudinal slits; complex eigenvalues; propagating waves

Subjects: Nonlinear acoustics and macrosonics; Electromagnetic waves: theory; Algebra, set theory, and graph theory