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'' by the br ...

wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...

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 ...

St Paul's Cathedral St Paul's Cathedral, formally the Cathedral Church of St Paul the Apostle, is an Anglican cathedral in London, England, the seat of the Bishop of London. The cathedral serves as the mother church of the Diocese of London in the Church of Engl ...

, they can exist for

light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...

and for other waves, with important applications in

nondestructive testing Nondestructive testing (NDT) is any of a wide group of analysis techniques used in science and technology industry to evaluate the properties of a material, component or system without causing damage. The terms nondestructive examination (NDE), n ...

lasing A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radi ...

cooling Cooling is removal of heat, usually resulting in a lower temperature and/or Phase transition, phase change. Temperature lowering achieved by any other means may also be called cooling. The Heat transfer, transfer of Internal energy, thermal energ ...

and sensing, as well as in

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

Introduction

Whispering-gallery waves were first explained for the case of

circa 1878 by

Lord Rayleigh John William Strutt, 3rd Baron Rayleigh ( ; 12 November 1842 – 30 June 1919), was an English physicist who received the Nobel Prize in Physics in 1904 "for his investigations of the densities of the most important gases and for his discovery ...

, 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 or chords may refer to: Art and music * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord, a chord played on a guitar, which has a particular tuning * The Chords (British band), 1970s British mod ...

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 the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental ca ...

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 is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

based on wave

interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extra ...

; 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 resonator, resonates at a specific Pitch (music), pitch when pressurized air (commonly referred to as ''wind'') is driven through it. Each pipe is tuned to a note of the musical ...

s. The sound forms patterns called

modes Mode ( 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 the setting fo ...

, 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 Confucianism, religious Confucian buildings situated in the southeastern part of central Beijing. The complex was visited by the Emperor of China, Emperors of the Ming dynasty, Ming and ...

in Beijing.

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 Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

stars A star is a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of ...

. Such acoustic whispering-gallery waves can be used in

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 Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...

(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 and in soap bubbles, for example, with applications as

optical resonator An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that confines light waves similarly to how a cavity resonator confines microwaves. Optical cavities are a major component of lasers, ...

s for

, optomechanical

frequency comb A frequency comb or spectral comb is a spectrum made of discrete and regularly spaced spectral lines. In optics, a frequency comb can be generated by certain laser sources. A number of mechanisms exist for obtaining an optical frequency comb, i ...

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

total internal reflection In physics, total internal reflection (TIR) is the 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 refl ...

, leading to

Q factor In physics and engineering, the quality factor or factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy lost ...

s in excess of 10¹⁰ being achieved. This is far greater than the best values, about 10⁴, that can be obtained in acoustics. Optical modes in a whispering gallery resonator experience some loss due to a mechanism similar to

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

, even in theoretically ideal conditions. This loss 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 ligh ...

theory and is dubbed ''tunneling ray attenuation'' in the field of

fiber optics An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at ...

. 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. 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) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ...

s such as

radio wave Radio waves (formerly called Hertzian waves) are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths g ...

microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...

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 International Telecommunicat ...

infrared radiation Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...

, ultraviolet waves and

x-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...

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 half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ...

s for

neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...

s, and electrons, and they have been proposed as an explanation for vibrations of a single

nucleus Nucleus (: nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucleu ...

. 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 wave Gravitational waves are oscillations of the gravitational field that Wave propagation, travel through space at the speed of light; they are generated by the relative motion of gravity, gravitating masses. They were proposed by Oliver Heaviside i ...

s at the

event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an outside 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 c ...

black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...

s. A hybrid of waves of light and

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

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 An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb's law, Coulomb force resulting from their opposite charges. It is an electrically neutral quasiparticle regarded as ...

polariton In physics, polaritons are bosonic quasiparticles resulting from strong coupling of electromagnetic waves (photon) with an electric or magnetic dipole-carrying excitation (state) of solid or liquid matter (such as a phonon, plasmon, or an exc ...

s in

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

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