Whispering Gallery wave modes on elastic cylinders

Abstract

We present an analytic and numerical study of Whispering Gallery-type surface- wave modes on solid elastic cylinders imbedded in a fluid. The complex wave numbers of these waves are obtained for the case of high frequencies (ka≳15), including both their attenuation and dispersion curves for the phase velocities. It is shown that there are two different groups of Whispering Gallery modes whose wave numbers in the limit of infinite frequency or infinite cylinder radius approach the corresponding wave numbers of compressional and shear bulk waves in the cylinder material. Subject Classification: [43]40.20; [43]30.50; [43]40.55; [43]20.15; [43]35.54.

Horizontal ducting of sound by curved nonlinear internal gravity waves in the continental shelf areas

“…This type of ducting phenomenon has also been found on solid elastic cylinders imbedded in a fluid (Frisk et al, 1975;Dickey et al, 1976) and many other instances over concave surfaces. The whispering gallery effect has also been exploited beyond acoustics, e.g., laser cavities in x-rays (Braud, 1992) and a recent work on optic resonators (Righini et al, 2011).…”

Acoustic whispering-gallery modes generated and dynamically imaged with ultrashort optical pulses

“…It is now recognized that sound waves in solid or liquid spheres, cylinders, or disks can also be trapped as WG modes, [2][3][4][5] of significance in the field of nondestructive testing of bearings or pipes, in gas sensing, and in signal filtering for telecommunications. [6][7][8][9][10] Confined phonon fields such as WG or microcavity modes are of great interest because of their potential for strong acousto-optic interactions or cavity optomechanics.…”

Whispering gallery modes for elastic waves in disk resonators

“…4 For elastic waves, there are some early calculations on infinite long cylinders. 5,6 In those studies, the resonant modes appearing in infinite long cylinders were studied analytically and numerically. 5,6 There are several recent studies on micromechanical devices based on disk resonators [7][8][9] with applications in mass sensing, 7,8 and RF filters.…”

“…5,6 In those studies, the resonant modes appearing in infinite long cylinders were studied analytically and numerically. 5,6 There are several recent studies on micromechanical devices based on disk resonators [7][8][9] with applications in mass sensing, 7,8 and RF filters. 9 Also recently, stimulated Brillouin scattering (SBS) with both pump and Stokes beams in resonance with whispering gallery modes (WGM) of an ultrahigh Q calcium fluoride resonator were demonstrated.…”