Whispering-gallery wave

Whispering-gallery waves were first explained for the case of St Paul's Cathedral circa 1878[Lord Rayleigh, Theory of Sound, vol. II, 1st edition, (London, MacMillan), 1878.] by Lord Rayleigh, who revised a previous misconception[J. Tyndall, The Science of Sound (New York, Philosophical Library), 1867, p. 20.][G. B. Airy, On Sound and Atmospheric Vibrations, with the Mathematical Elements of Music (London, MacMillan), 1871, p. 145.] 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{{cite journal | last=Rayleigh | first=Lord |author-link=John William Strutt, 3rd Baron Rayleigh|title=CXII. The problem of the whispering gallery | journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science | publisher=Informa UK Limited | volume=20 | issue=120 | year=1910 | issn=1941-5982 | doi=10.1080/14786441008636993 | pages=1001–1004| url=https://zenodo.org/record/1522134 }} and 1914.{{cite journal | last=Rayleigh | first=Lord |author-link=John William Strutt, 3rd Baron Rayleigh| title=IX. Further applications of Bessel's functions of high order to the Whispering Gallery and allied problems | journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science | publisher=Informa UK Limited | volume=27 | issue=157 | year=1914 | issn=1941-5982 | doi=10.1080/14786440108635067 | pages=100–109}} 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.

Many other monuments have been shown{{cite journal|first=C. V. |last=Raman|author-link=C. V. Raman|journal= Proceedings of the Indian Association for the Cultivation of Science|volume=7|page=159|year=1921–1922|title=XV. On Whispering Galleries|url=https://babel.hathitrust.org/cgi/pt?id=mdp.39015077811514&view=1up&seq=189}} to exhibit whispering-gallery waves, such as the Gol Gumbaz in Bijapur and the Temple of Heaven in Beijing.

Whispering-gallery waves for sound exist in a wide variety of systems. Examples include the vibrations of the whole Earth[Quantitative Seismology, K. Aki and P. G. Richards (University Science Books), 2009, Ch. 8] or stars.{{cite journal | last1=Reese | first1=D. R. | last2=MacGregor | first2=K. B. | last3=Jackson | first3=S. | last4=Skumanich | first4=A. | last5=Metcalfe | first5=T. S. | title=Pulsation modes in rapidly rotating stellar models based on the self-consistent field method | journal=Astronomy & Astrophysics | publisher=EDP Sciences | volume=506 | issue=1 | date=1 March 2009 | issn=0004-6361 | doi=10.1051/0004-6361/200811510 | pages=189–201|doi-access=free| bibcode=2009A&A...506..189R | arxiv=0903.4854 }}

Such acoustic whispering-gallery waves can be used in nondestructive testing in the form of waves that creep around holes filled with liquid,{{cite journal | last1=Nagy | first1=Peter B. | last2=Blodgett | first2=Mark | last3=Golis | first3=Matthew | title=Weep hole inspection by circumferential creeping waves | journal=NDT & E International | publisher=Elsevier BV | volume=27 | issue=3 | year=1994 | issn=0963-8695 | doi=10.1016/0963-8695(94)90604-1 | pages=131–142}} for example. They have also been detected in solid cylinders{{cite journal | last1=Clorennec | first1=D | last2=Royer | first2=D | last3=Walaszek | first3=H | title=Nondestructive evaluation of cylindrical parts using laser ultrasonics | journal=Ultrasonics | publisher=Elsevier BV | volume=40 | issue=1–8 | year=2002 | issn=0041-624X | doi=10.1016/s0041-624x(02)00210-x | pmid=12160045 | pages=783–789}} and spheres,{{cite journal | last1=Ishikawa | first1=Satoru | last2=Nakaso | first2=Noritaka | last3=Takeda | first3=Nobuo | last4=Mihara | first4=Tsuyoshi | last5=Tsukahara | first5=Yusuke | last6=Yamanaka | first6=Kazushi | title=Surface acoustic waves on a sphere with divergent, focusing, and collimating beam shapes excited by an interdigital transducer | journal=Applied Physics Letters | publisher=AIP Publishing | volume=83 | issue=22 | year=2003 | issn=0003-6951 | doi=10.1063/1.1631061 | pages=4649–4651| bibcode=2003ApPhL..83.4649I }} with applications in sensing, and visualized in motion on microscopic discs .{{cite journal | last1=Tachizaki | first1=Takehiro | last2=Matsuda | first2=Osamu | last3=Maznev | first3=Alex A. | last4=Wright | first4=Oliver B. | title=Acoustic whispering-gallery modes generated and dynamically imaged with ultrashort optical pulses | journal=Physical Review B | publisher=American Physical Society (APS) | volume=81 | issue=16 | date=23 April 2010 | issn=1098-0121 | doi=10.1103/physrevb.81.165434 | page=165434| bibcode=2010PhRvB..81p5434T | hdl=2115/43062 | hdl-access=free }}

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.{{cite journal | last1=Ishikawa | first1=Satoru | last2=Cho | first2=Hideo | last3=Yamanaka | first3=Kazushi | last4=Nakaso | first4=Noritaka | last5=Tsukahara | first5=Yusuke | title=Surface Acoustic Waves on a Sphere –Analysis of Propagation Using Laser Ultrasonics– | journal=Japanese Journal of Applied Physics | publisher=Japan Society of Applied Physics | volume=40 | issue=Part 1, No. 5B | date=30 May 2001 | issn=0021-4922 | doi=10.1143/jjap.40.3623 | bibcode=2001JaJAP..40.3623I | pages=3623–3627| s2cid=121857533 }}

Image:Whispering gallery modes sphere.png technique. The tip of an angle-cut optical fiber, visible on the right, excites the modes in the red region of the optical spectrum.{{Cite news|url=https://www.techbriefs.com/component/content/article/tb/techbriefs/physical-sciences/3160|title=Delaying Trains of Short Light Pulses in WGM Resonators|date=1 September 2018|work=Tech Briefs Media Group|access-date=2018-11-30|language=en}}]]

Whispering-gallery waves exist for light waves.{{cite journal | last=Mie | first=Gustav | title=Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen | journal=Annalen der Physik | publisher=Wiley | volume=330 | issue=3 | year=1908 | issn=0003-3804 | doi=10.1002/andp.19083300302 | pages=377–445 | language=de|doi-access=free| bibcode=1908AnP...330..377M }}{{cite journal | last=Debye | first=P. |author-link=Peter Debye| title=Der Lichtdruck auf Kugeln von beliebigem Material | journal=Annalen der Physik | publisher=Wiley | volume=335 | issue=11 | year=1909 | issn=0003-3804 | doi=10.1002/andp.19093351103 | pages=57–136 | language=de| bibcode=1909AnP...335...57D | hdl=1908/3003 | hdl-access=free }}{{cite journal | last=Oraevsky | first=Anatolii N | title=Whispering-gallery waves | journal=Quantum Electronics | publisher=IOP Publishing | volume=32 | issue=5 | date=31 May 2002 | issn=1063-7818 | doi=10.1070/qe2002v032n05abeh002205 | pages=377–400| s2cid=250792191 }} They have been produced in microscopic glass spheres or tori{{cite journal |last1=Vahala|first1=K. J. |year=2003 |title=Optical microcavities |journal=Nature |volume=424|issue=6950 |pages=839–846 |doi=10.1038/nature01939|pmid=12917698 |bibcode=2003Natur.424..839V|s2cid=4349700 }}{{cite journal | last1=Chiasera | first1=A. | last2=Dumeige | first2=Y. | last3=Féron | first3=P. | last4=Ferrari | first4=M. | last5=Jestin | first5=Y. | last6=Nunzi Conti | first6=G. | last7=Pelli | first7=S. | last8=Soria | first8=S. | last9=Righini | first9=G.C. | title=Spherical whispering-gallery-mode microresonators | journal=Laser & Photonics Reviews | publisher=Wiley | volume=4 | issue=3 | date=23 April 2010 | issn=1863-8880 | doi=10.1002/lpor.200910016 | pages=457–482| bibcode=2010LPRv....4..457C | s2cid=119484780 }} and in soap bubbles,{{cite journal |last1=Miller |first1=Johanna |title=Bubble lasers can be sturdy and sensitive |url=https://pubs.aip.org/physicstoday/article/77/3/12/3267372/Bubble-lasers-can-be-sturdy-and-sensitiveMade-of |journal=Physics Today |volume=77 |issue=3 |pages=12–14 |date=1 March 2024 |doi=10.1063/pt.xafv.lnix |publisher=American Institute of Physics|doi-access=free }} for example, with applications as optical resonators for lasing,{{cite journal | last1=Rakovich | first1=Y.P. | last2=Donegan | first2=J.F. | title=Photonic atoms and molecules | journal=Laser & Photonics Reviews | publisher=Wiley | volume=4 | issue=2 | date=2 June 2009 | issn=1863-8880 | doi=10.1002/lpor.200910001 | pages=179–191| s2cid=121561846 }} optomechanical cooling,{{cite journal | last1=Kippenberg | first1=T. J. | last2=Vahala | first2=K. J. | title=Cavity Optomechanics: Back-Action at the Mesoscale | journal=Science | publisher=American Association for the Advancement of Science (AAAS) | volume=321 | issue=5893 | date=29 August 2008 | issn=0036-8075 | doi=10.1126/science.1156032 | pmid=18755966 | pages=1172–1176| bibcode=2008Sci...321.1172K | s2cid=4620490 }} frequency comb generation{{cite journal |author1-link=Pascal Del'Haye | last1=Del’Haye | first1=P. | last2=Schliesser | first2=A. | last3=Arcizet | first3=O. | last4=Wilken | first4=T. | last5=Holzwarth | first5=R. | last6=Kippenberg | first6=T. J. | title=Optical frequency comb generation from a monolithic microresonator | journal=Nature | publisher=Springer Science and Business Media LLC | volume=450 | issue=7173 | year=2007 | issn=0028-0836 | doi=10.1038/nature06401 | pmid=18097405 | pages=1214–1217| bibcode=2007Natur.450.1214D | arxiv=0708.0611 | s2cid=4426096 }} and optical sensing.{{cite journal | last1=Arnold | first1=S. | last2=Khoshsima | first2=M. | last3=Teraoka | first3=I. | last4=Holler | first4=S. | last5=Vollmer | first5=F. | title=Shift of whispering-gallery modes in microspheres by protein adsorption | journal=Optics Letters | publisher=The Optical Society | volume=28 | issue=4 | pages=272–4 | date=15 February 2003 | issn=0146-9592 | doi=10.1364/ol.28.000272 | pmid=12653369 | bibcode=2003OptL...28..272A }} The light waves are guided around almost perfectly by total internal reflection, leading to Q factors in excess of 10¹⁰ being achieved.{{cite journal | last1=Grudinin | first1=Ivan S. | last2=Ilchenko | first2=Vladimir S. | last3=Maleki | first3=Lute | title=Ultrahigh optical Q factors of crystalline resonators in the linear regime | journal=Physical Review A | publisher=American Physical Society (APS) | volume=74 | issue=6 | date=8 December 2006 | issn=1050-2947 | doi=10.1103/physreva.74.063806 | page=063806| bibcode=2006PhRvA..74f3806G }} This is far greater than the best values, about 10⁴, that can be obtained in acoustics.{{cite journal|first1=K. |last1=Yamanaka |first2=S.|last2=Ishikawa|first3=N.|last3=Nakaso|first4=N.|last4=Takeda|first5=Dong Youn|last5=Sim|first6=T.|last6=Mihara|display-authors=5|journal=IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control |volume=53|issue=4|year=2006|doi=10.1109/TUFFC.2006.1621507|title=Ultramultiple roundtrips of surface acoustic wave on sphere realizing innovation of gas sensors|pages=793–801 |pmid=16615584 |s2cid=22051539 }} Optical modes in a whispering gallery resonator experience some loss due to a mechanism similar to quantum tunneling, even in theoretically ideal conditions. This loss has been known from research on optical waveguide theory and is dubbed tunneling ray attenuation in the field of fiber optics.{{cite journal | last=Pask | first=Colin | authorlink = Colin Pask | title=Generalized parameters for tunneling ray attenuation in optical fibers | journal=Journal of the Optical Society of America | publisher=The Optical Society | volume=68 | issue=1 | date=1 December 1977 | issn=0030-3941 | doi=10.1364/josa.68.000110 | page=110}} 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,{{cite journal | last=Gmachl | first=C. | title=High-Power Directional Emission from Microlasers with Chaotic Resonators | journal=Science | volume=280 | issue=5369 | date=5 June 1998 | issn=0036-8075 | doi=10.1126/science.280.5369.1556 | pmid=9616111 | pages=1556–1564| bibcode=1998Sci...280.1556G | arxiv=cond-mat/9806183 | s2cid=502055 }}{{cite journal | last1=Baryshnikov | first1=Yuliy | last2=Heider | first2=Pascal | last3=Parz | first3=Wolfgang | last4=Zharnitsky | first4=Vadim | title=Whispering Gallery Modes Inside Asymmetric Resonant Cavities | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=93 | issue=13 | date=22 September 2004 | issn=0031-9007 | doi=10.1103/physrevlett.93.133902 | pmid=15524720 | page=133902| bibcode=2004PhRvL..93m3902B }} whose cross-sections deviate from a circle. Such waves have been used in quantum information applications.{{cite journal | last1=Tanaka | first1=Akira | last2=Asai | first2=Takeshi | last3=Toubaru | first3=Kiyota | last4=Takashima | first4=Hideaki | last5=Fujiwara | first5=Masazumi | last6=Okamoto | first6=Ryo | last7=Takeuchi | first7=Shigeki | title=Phase shift spectra of a fiber–microsphere system at the single photon level | journal=Optics Express | publisher=The Optical Society | volume=19 | issue=3 | pages=2278–85 | date=24 January 2011 | issn=1094-4087 | doi=10.1364/oe.19.002278 | pmid=21369045 | bibcode=2011OExpr..19.2278T | arxiv=1101.5198 | s2cid=31604481 }}

Whispering-gallery waves have also been demonstrated for other electromagnetic waves such as radio waves,{{cite journal |first1=K. G.|last1=Budden|first2=H. G.|last2=Martin| title=The ionosphere as a whispering gallery | journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences | publisher=The Royal Society | volume=265 | issue=1323 | date=6 February 1962 | issn=2053-9169 | doi=10.1098/rspa.1962.0042 | pages=554–569|bibcode=1962RSPSA.265..554B|s2cid=120311101}} microwaves,{{cite journal |last1=Stanwix|first1=P. L. |year=2005 |title=Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators |journal=Physical Review Letters|volume=95|issue=4 |pages=040404 |doi=10.1103/PhysRevLett.95.040404 |pmid=16090785 |display-authors=etal|arxiv=hep-ph/0506074|bibcode=2005PhRvL..95d0404S|s2cid=14255475 }} terahertz radiation,{{cite journal |last1=Mendis|first1=R. |last2=Mittleman|first2=M. |year=2010 |title=Whispering-gallery-mode terahertz pulse propagation on a curved metallic plate |journal=Applied Physics Letters |volume=97|issue=3 |pages=031106 |doi=10.1063/1.3466909|bibcode=2010ApPhL..97c1106M}} infrared radiation,{{cite journal | last1=Albert | first1=F. | last2=Braun | first2=T. | last3=Heindel | first3=T. | last4=Schneider | first4=C. | last5=Reitzenstein | first5=S. | last6=Höfling | first6=S. | last7=Worschech | first7=L. | last8=Forchel | first8=A. | title=Whispering gallery mode lasing in electrically driven quantum dot micropillars | journal=Applied Physics Letters | publisher=AIP Publishing | volume=97 | issue=10 | date=6 September 2010 | issn=0003-6951 | doi=10.1063/1.3488807 | page=101108| bibcode=2010ApPhL..97j1108A }} ultraviolet waves{{cite journal | last1=Hyun | first1=J. K. | last2=Couillard | first2=M. | last3=Rajendran | first3=P. | last4=Liddell | first4=C. M. | last5=Muller | first5=D. A. | title=Measuring far-ultraviolet whispering gallery modes with high energy electrons | journal=Applied Physics Letters | publisher=AIP Publishing | volume=93 | issue=24 | date=15 December 2008 | issn=0003-6951 | doi=10.1063/1.3046731 | page=243106| bibcode=2008ApPhL..93x3106H }} and x-rays.{{cite journal | last1=Liu | first1=Chien | last2=Golovchenko | first2=Jene A. | title=Surface Trapped X Rays: Whispering-Gallery Modes atλ=0.7Å | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=79 | issue=5 | date=4 August 1997 | issn=0031-9007 | doi=10.1103/physrevlett.79.788 | pages=788–791| bibcode=1997PhRvL..79..788L | s2cid=121253766 | url=http://nrs.harvard.edu/urn-3:HUL.InstRepos:29406252 | url-access=subscription }} 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.{{cite journal|author=M.R. Foreman|title=Whispering gallery mode sensors |journal=Advances in Optics and Photonics|volume=7 |pages=168–240|date=2015|issue=2 |doi=10.1364/AOP.7.000168|pmid=26973759 |url=https://www.osapublishing.org/aop/abstract.cfm?uri=aop-7-2-168 |pmc=4786191|bibcode=2015AdOP....7..168F }}{{cite journal|author=Y. Wang|title=Microfluidic whispering gallery mode optical sensors for biological applications |journal=Laser & Photonics Reviews|volume=14 |pages=2000135–56|date=2020|issue=12 |doi=10.1002/lpor.202000135|bibcode=2020LPRv...1400135W |s2cid=228850737 |url=https://www.researchgate.net/publication/346314054 }} 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.{{cite journal|author=T. Reynolds|title=Fluorescent and lasing whispering gallery mode microresonators for sensing applications |journal=Laser & Photonics Reviews|volume=11 |pages=1600265–76|date=2017|issue=2 |doi=10.1002/lpor.201600265|bibcode=2017LPRv...1100265R |url=https://onlinelibrary.wiley.com/doi/abs/10.1002/lpor.201600265 |hdl=2027.42/136528|s2cid=125481589 |hdl-access=free}}{{cite journal|author=A. Bozzola|title=Hybrid plasmonic–photonic whispering gallery mode resonators for sensing: a critical review |journal=Analyst|volume=142 |pages=883–898|date=2017|issue=6 |doi=10.1039/C6AN02693A|pmid=28225100 |bibcode=2017Ana...142..883B |doi-access=free}}

Whispering-gallery waves have been seen in the form of matter waves for neutrons,{{cite journal | last1=Nesvizhevsky | first1=Valery V. | last2=Voronin | first2=Alexei Yu. | last3=Cubitt | first3=Robert | last4=Protasov | first4=Konstantin V. | title=Neutron whispering gallery | journal=Nature Physics | publisher=Springer Science and Business Media LLC | volume=6 | issue=2 | date=13 December 2009 | issn=1745-2473 | doi=10.1038/nphys1478 | pages=114–117| doi-access=free }} and electrons,{{cite journal | last1=Reecht | first1=Gaël | last2=Bulou | first2=Hervé | last3=Scheurer | first3=Fabrice | last4=Speisser | first4=Virginie | last5=Carrière | first5=Bernard | last6=Mathevet | first6=Fabrice | last7=Schull | first7=Guillaume | title=Oligothiophene Nanorings as Electron Resonators for Whispering Gallery Modes | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=110 | issue=5 | date=29 January 2013 | issn=0031-9007 | doi=10.1103/physrevlett.110.056802 | pmid=23414040 | page=056802| bibcode=2013PhRvL.110e6802R | arxiv=1301.4860 | s2cid=40257448 }} and they have been proposed as an explanation for vibrations of a single nucleus.{{cite journal | last1=Dragún | first1=Olga | last2=Überall | first2=Herbert | title=Nuclear Rayleigh and whispering gallery waves excited in heavy ion collisions | journal=Physics Letters B | publisher=Elsevier BV | volume=94 | issue=1 | year=1980 | issn=0370-2693 | doi=10.1016/0370-2693(80)90816-3 | pages=24–27| bibcode=1980PhLB...94...24D }} Whispering gallery waves have also been observed in the vibrations of soap films as well as in the vibrations of thin plates {{cite journal | last1=Arcos | first1=E. | last2=Báez | first2=G. | last3=Cuatláyol | first3=P. A. | last4=Prian | first4=M. L. H. | last5=Méndez-Sánchez | first5=R. A. | last6=Hernández-Saldaña | first6=H. | title=Vibrating soap films: An analog for quantum chaos on billiards | journal=American Journal of Physics | publisher=American Association of Physics Teachers (AAPT) | volume=66 | issue=7 | year=1998 | issn=0002-9505 | doi=10.1119/1.18913 | pages=601–607| bibcode=1998AmJPh..66..601A | arxiv=chao-dyn/9903002 | s2cid=52106857 }} 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,{{cite journal | last1=Min | first1=Bumki | last2=Ostby | first2=Eric | last3=Sorger | first3=Volker | last4=Ulin-Avila | first4=Erick | last5=Yang | first5=Lan | last6=Zhang | first6=Xiang | last7=Vahala | first7=Kerry | title=High-Q surface-plasmon-polariton whispering-gallery microcavity | journal=Nature | publisher=Springer Science and Business Media LLC | volume=457 | issue=7228 | year=2009 | issn=0028-0836 | doi=10.1038/nature07627 | pmid=19158793 | pages=455–458| bibcode=2009Natur.457..455M | s2cid=4411541 }} and likewise for exciton-polaritons in semiconductors.{{cite journal | last1=Sun | first1=Liaoxin | last2=Chen | first2=Zhanghai | last3=Ren | first3=Qijun | last4=Yu | first4=Ke | last5=Bai | first5=Lihui | last6=Zhou | first6=Weihang | last7=Xiong | first7=Hui | last8=Zhu | first8=Z. Q. | last9=Shen | first9=Xuechu | title=Direct Observation of Whispering Gallery Mode Polaritons and their Dispersion in a ZnO Tapered Microcavity | journal=Physical Review Letters | volume=100 | issue=15 | date=16 April 2008 | issn=0031-9007 | doi=10.1103/physrevlett.100.156403 | pmid=18518134 | page=156403| bibcode=2008PhRvL.100o6403S | arxiv=0710.5334 | s2cid=28537857 }} Galleries simultaneously containing both acoustic and optical whispering-gallery waves have also been made,{{cite journal | last1=Tomes | first1=Matthew | last2=Carmon | first2=Tal | title=Photonic Micro-Electromechanical Systems Vibrating atX-band (11-GHz) Rates | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=102 | issue=11 | date=19 March 2009 | issn=0031-9007 | doi=10.1103/physrevlett.102.113601 | pmid=19392199 | page=113601| bibcode=2009PhRvL.102k3601T }} exhibiting very strong mode coupling and coherent effects.{{cite journal | last1=Kim | first1=JunHwan | last2=Kuzyk | first2=Mark C. | last3=Han | first3=Kewen | last4=Wang | first4=Hailin | last5=Bahl | first5=Gaurav | title=Non-reciprocal Brillouin scattering induced transparency | journal=Nature Physics | publisher=Springer Science and Business Media LLC | volume=11 | issue=3 | date=26 January 2015 | issn=1745-2473 | doi=10.1038/nphys3236 | pages=275–280| bibcode=2015NatPh..11..275K | arxiv=1408.1739 | s2cid=119173646 }} Hybrid solid-fluid-optical whispering-gallery structures have been observed as well.{{cite journal | last1=Bahl | first1=Gaurav | last2=Kim | first2=Kyu Hyun | last3=Lee | first3=Wonsuk | last4=Liu | first4=Jing | last5=Fan | first5=Xudong | last6=Carmon | first6=Tal | title=Brillouin cavity optomechanics with microfluidic devices | journal=Nature Communications | publisher=Springer Science and Business Media LLC | volume=4 | issue=1 | pages=1994 | date=7 June 2013 | issn=2041-1723 | doi=10.1038/ncomms2994 | pmid=23744103 |doi-access=free| bibcode=2013NatCo...4.1994B | arxiv=1302.1949 }}

• Whispering gallery
• Optical ring resonator
• Resonator
• Architectural acoustics

{{reflist|30em}}

• [https://ieeexplore.ieee.org/document/135280 Investigations of Whisper Gallery Mirrors for EUV and Soft X-Rays, T.Y. Hung and P.L. Hagelstein]

Category:Acoustics

Category:Waves