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 ...
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 (r ...
s in the
whispering gallery of
St Paul's Cathedral
St Paul's Cathedral is an Anglicanism, Anglican cathedral in London and is the seat of the Bishop of London. The cathedral serves as the mother church of the Diocese of London. It is on Ludgate Hill at the highest point of the City of London ...
, 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
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" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
,
cooling and
sensing, as well as in
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
.
Introduction
Whispering-gallery waves were first explained for the case of
St Paul's Cathedral
St Paul's Cathedral is an Anglicanism, Anglican cathedral in London and is the seat of the Bishop of London. The cathedral serves as the mother church of the Diocese of London. It is on Ludgate Hill at the highest point of the City of London ...
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. Amo ...
, 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
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 ...
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 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 force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillat ...
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 ...
s. The sound forms patterns called
modes, 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 t ...
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 a g ...
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 surf ...
or
stars
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
.
Such acoustic whispering-gallery waves can be used 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 ...
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
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" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
,
optomechanical
Optomechanics is the manufacture and maintenance of optical parts and devices. This includes the design and manufacture of hardware used to hold and align elements in optical systems, such as:
* Optical tables, breadboards, and rails
* Mirro ...
cooling,
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 reflecte ...
, leading to
Q factor
In physics and engineering, the quality factor or ''Q'' 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 ...
s in excess of 10
10 being achieved. This is far greater than the best values, about 10
4, 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 quantizat ...
. 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
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means ...
. 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, (visible ...
s such as
radio wave
Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz ( GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (sho ...
s,
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequency, frequencies between 300 MHz and 300 GHz respectively. Different sources define different fre ...
s,
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
Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30 PHz) to 400 nm (750 THz), shorter than that of visible light, but longer than X-rays. UV radiati ...
and
x-ray
X-rays (or rarely, ''X-radiation'') are a form of high-energy electromagnetic radiation. In many languages, it is referred to as Röntgen radiation, after the German scientist Wilhelm Conrad Röntgen, who discovered it in 1895 and named it ' ...
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 behav ...
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
Nucl ...
. 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 waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in ...
s 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 hole
A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...
s.
A hybrid of waves of light and
electron
The electron (, or in nuclear reactions) 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 partic ...
s known as
surface plasmons 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 force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and some liquids. Th ...
-
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, al ...
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.
See also
*
Whispering gallery
*
Optical ring resonator
An optical ring resonator is a set of waveguides in which at least one is a closed loop coupled to some sort of light input and output. (These can be, but are not limited to being, waveguides.) The concepts behind optical ring resonators are the ...
*
Resonator
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a reson ...
*
Architectural acoustics
Architectural acoustics (also known as building acoustics) is the science and engineering of achieving a good sound within a building and is a branch of acoustical engineering. The first application of modern scientific methods to architectura ...
References
{{reflist, 30em
External links
''Investigations of Whisper Gallery Mirrors for EUV and Soft X-Rays'', T.Y. Hung and P.L. Hagelstein
Acoustics
Waves