Whispering-gallery waves, or whispering-gallery modes, are a type of wave that can travel around a concave surface. Originally discovered for sound waves in the whispering gallery of St Paul’s Cathedral, they can exist for light and for other waves, with important applications in nondestructive testing, lasing, cooling and sensing, as well as in astronomy.
Whispering-gallery waves were first explained for the case of St Paul's Cathedral circa 1878 by Lord Rayleigh, who revised a previous misconception that whispers could be heard across the dome but not at any intermediate position. He explained the phenomenon of travelling whispers with a series of specularly reflected sound rays making up chords of the circular gallery. Clinging to the walls the sound should decay in intensity only as the inverse of the distance — rather than the inverse square as in the case of a point source of sound radiating in all directions. This accounts for the whispers being audible all round the gallery.
Rayleigh developed wave theories for St Paul’s in 1910 and 1914. Fitting sound waves inside a cavity involves the physics of resonance based on wave interference; the sound can exist only at certain pitches as in the case of organ pipes. The sound forms patterns called modes, as shown in the diagram.
In the strict definition of whispering-gallery waves, they cannot exist when the guiding surface becomes straight. Mathematically this corresponds to the limit of an infinite radius of curvature. Whispering-gallery waves are guided by the effect of the wall curvature.
Other acoustic whispering-gallery waves 
Such acoustic whispering-gallery waves can be used in nondestructive testing in the form of waves that creep around holes filled with liquid, for example. They have also been detected in solid cylinders and spheres, with applications in sensing, and visualized in motion on microscopic discs .
Whispering-gallery waves for light 
Whispering-gallery waves exist for light waves. They have been produced in microscopic glass spheres or toruses, for example, with applications in lasing, optomechanical cooling, frequency comb generation and sensing. The light waves are almost perfectly guided round by optical total internal reflection, leading to Q factors in excess of 1010 being achieved. This is far greater than the best values, about 104, that can be similarly obtained in acoustics. Optical modes in a whispering gallery resonator are inherently lossy due to a mechanism similar to quantum tunneling. Strictly speaking, total internal reflection does not take place at a curved boundary between two distinct media, and light inside a whispering gallery resonator cannot be perfectly trapped, even in theoretically ideal conditions. Such a loss channel has been known from research on optical waveguide theory and is dubbed tunneling ray attenuation in the field of fiber optics. The Q factor is proportional to the decay time of the waves, which in turn is inversely proportional to both the surface scattering rate and the wave absorption in the medium making up the gallery. Whispering-gallery waves for light have been investigated in chaotic galleries, whose cross-sections deviate from a circle. And such waves have been used in quantum information applications.
Whispering-gallery waves have also been demonstrated for other electromagnetic waves such as radio waves, microwaves, terahertz radiation, infrared radiation, ultraviolet waves and x-rays.
Whispering-gallery waves for other systems 
Whispering-gallery waves have been seen in the form of matter waves for neutrons, and they have been proposed as an explanation for vibrations of a single nucleus. Analogies of whispering-gallery waves also exist for gravitational waves at the event horizon of black holes. A hybrid of waves of light and electrons known as surface plasmons has been demonstrated in the form of whispering-gallery waves, and likewise for exciton-polaritons in semiconductors. Galleries simultaneously containing both acoustic and optical whispering-gallery waves have also been made.
See also 
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- Applied Solid State Physics Laboratory at Hokkaido University, Watching Whispering-Gallery Waves
- Armani Lab, University of Southern Carolina
- Baba Lab, Yokohama National University
- Capasso Group, Harvard University
- Gallery of Whispers, Physics World 25, No. 2, Feb. 2012, p. 31
- Gong Qihuang Lab, Beijing University
- Harald Schwefel, Max Planck Institute for the Science of Light, Erlangen
- Hui Cao Research Laboratory, Yale University
- Kyungwon An Laboratory, Seoul National University
- Laboratory of Photonics and Quantum Measurements K-Lab, École Polytechnique Fédérale de Lausanne (EPFL)
- Lan Yang Laboratory, Washington University in St. Louis
- Micro-optics and Quantum Chaos Group, University of Oregon
- Steve Arnold's Microparticle Photophysics Laboratory for BioPhotonics
- St Paul's Cathedral
- The Aerosol Dynamics Research Group, University of Bristol.
- Vahala Research Group, California Institute of Technology
- Vollmer Lab of Biophotonics and Biosensing
- Ultrafast Lasers and Optical Amplifiers Lab, IIT Madras, India
- Yamanaka Lab, Tohoku University
- Yong-Hee Lee Lab, KAIST