Whispering-gallery waves, or whispering-gallery modes, are a type of wave that can travel around a concave surface. Originally discovered for

sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' b ...

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...

s in the

whispering gallery The Whispering Gallery of St Paul's Cathedral, London A whispering gallery is usually a circular, hemispherical, elliptical or ellipsoidal enclosure, often beneath a dome or a vault, in which whispers can be heard clearly in other parts of t ...

of St Paul's Cathedral, they can exist for

light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...

and for other waves, with important applications in nondestructive testing, lasing,

cooling Cooling is removal of heat, usually resulting in a lower temperature and/or phase change. Temperature lowering achieved by any other means may also be called cooling.ASHRAE Terminology, https://www.ashrae.org/technical-resources/free-resources/as ...

and sensing, as well as in

astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

Introduction

Whispering-gallery waves were first explained for the case of St Paul's Cathedral circa 1878 by

Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Am ...

, 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

rays making up

chords Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a particular tuning * Chord (geometry), a line segment joining two points on a curve * Chord ( ...

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 In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understoo ...

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 Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...

based on wave interference; the sound can exist only at certain pitches as in the case of

organ pipe An organ pipe is a sound-producing element of the pipe organ that resonates at a specific pitch when pressurized air (commonly referred to as ''wind'') is driven through it. Each pipe is tuned to a specific note of the musical scale. A set o ...

s. The sound forms patterns called

modes Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...

, as shown in the diagram. Many other monuments have been shown to exhibit whispering-gallery waves, such as the

Gol Gumbaz Gol Gumbaz (), also written Gol Gumbad, is a 17th-century mausoleum located in Bijapur, a city in Karnataka, India. It houses the remains of Mohammad Adil Shah, seventh sultan of the Adil Shahi dynasty, and some of his relatives. Begun in the ...

in Bijapur and the

Temple of Heaven The Temple of Heaven () is a complex of imperial religious buildings situated in the southeastern part of central Beijing. The complex was visited by the Emperors of the Ming and Qing dynasties for annual ceremonies of prayer to Heaven for ...

in Beijing. 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.

Acoustic waves

Whispering-gallery waves for sound exist in a wide variety of systems. Examples include the vibrations of the whole

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

stars A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ma ...

. 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 are more efficiently guided in spheres than in cylinders because the effects of acoustic diffraction (lateral wave spreading) are then completely compensated.

Electromagnetic waves

Whispering-gallery waves exist for light waves. They have been produced in microscopic glass spheres or tori, for example, with applications in lasing, optomechanical

frequency comb In optics, a frequency comb is a laser source whose spectrum consists of a series of discrete, equally spaced frequency lines. Frequency combs can be generated by a number of mechanisms, including periodic modulation (in amplitude and/or phase) of a ...

generation and sensing. The light waves are almost perfectly guided round by optical

total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflect ...

, 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 In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...

. As a result, light inside a whispering gallery mode experiences a degree of radiation loss even in theoretically ideal conditions. Such a loss channel has been known from research on

optical waveguide An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid light ...

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 Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both t ...

applications. Whispering-gallery waves have also been demonstrated for other

electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...

s such as radio waves,

microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...

terahertz radiation Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of fre ...

infrared radiation Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...

, ultraviolet waves and

x-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...

s. More recently, with the rapid development of microfluidic technologies, many integrated whispering gallery mode sensors, by combining the portability of lab‐on‐chip devices and the high sensitivity of whispering gallery mode resonators have emerged. The capabilities of efficient sample handling and multiplexed analyte detection offered by these systems have led to many biological and chemical sensing applications, especially for the detection of single particle or biomolecule.

Other systems

Whispering-gallery waves have been seen in the form of

matter wave Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wav ...

s for

neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...

s, and electrons, and they have been proposed as an explanation for vibrations of a single nucleus. Whispering gallery waves have also been observed in the vibrations of soap films as well as in the vibrations of thin plates Analogies of whispering-gallery waves also exist for gravitational waves at the

event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact ob ...

of black holes. A hybrid of waves of light and

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

s known as

surface plasmon Surface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such ...

s has been demonstrated in the form of whispering-gallery waves, and likewise for exciton-

polariton In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also ...

s in

semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. ...

s. Galleries simultaneously containing both acoustic and optical whispering-gallery waves have also been made, exhibiting very strong mode coupling and coherent effects. Hybrid solid-fluid-optical whispering-gallery structures have been observed as well.

References

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External links