Physics:Whispering-gallery wave

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Snapshot of an acoustic whispering-gallery mode calculated at a frequency of 69 Hz in an enclosed cylinder of air of the same diameter (33.7 m)[1] as the whispering gallery in St Paul's Cathedral. Red and blue represent higher and lower air pressures, respectively, and the distortions in the grid lines show the displacements. In the case of the waves travelling one way round the gallery, the air particles move in elliptical trajectories.[2]
Short description: Wave that can travel around a concave surface

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.

Introduction

Whispering-gallery waves were first explained for the case of St Paul's Cathedral circa 1878[3] by Lord Rayleigh, who revised a previous misconception[4][5] 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[6] and 1914.[7] 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.[1]

Many other monuments have been shown[8] to exhibit whispering-gallery waves, such as the Gol Gumbaz in Bijapur and the Temple of Heaven in Beijing.

In the strict definition of whispering-gallery waves, they cannot exist when the guiding surface becomes straight.[9] 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[10] or stars.[11]

Such acoustic whispering-gallery waves can be used in nondestructive testing in the form of waves that creep around holes filled with liquid,[12] for example. They have also been detected in solid cylinders[13] and spheres,[14] with applications in sensing, and visualized in motion on microscopic discs .[2][15]

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.[16]

Electromagnetic waves

Optical whispering-gallery modes in a glass sphere of diameter 300 μm experimentally imaged with a fluorescence technique. The tip of an angle-cut optical fiber, visible on the right, excites the modes in the red region of the optical spectrum.[17]

Whispering-gallery waves exist for light waves.[18][19][20] They have been produced in microscopic glass spheres or tori,[21][22] for example, with applications in lasing,[23] optomechanical cooling,[24] frequency comb generation[25] and optical sensing.[26] The light waves are almost perfectly guided round by total internal reflection, leading to Q factors in excess of 1010 being achieved.[27] This is far greater than the best values, about 104, that can be similarly obtained in acoustics.[28] Optical modes in a whispering gallery resonator are inherently lossy due to a mechanism similar to quantum tunneling. 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 theory and is dubbed tunneling ray attenuation[29] 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,[30][31] whose cross-sections deviate from a circle. And such waves have been used in quantum information applications.[32]

Whispering-gallery waves have also been demonstrated for other electromagnetic waves such as radio waves,[33] microwaves,[34] terahertz radiation,[35] infrared radiation,[36] ultraviolet waves[37] and x-rays.[38] 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.[39][40] 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.[41][42]

Other systems

Whispering-gallery waves have been seen in the form of matter waves for neutrons,[43] and electrons,[44] and they have been proposed as an explanation for vibrations of a single nucleus.[45] Whispering gallery waves have also been observed in the vibrations of soap films as well as in the vibrations of thin plates [46] Analogies of whispering-gallery waves also exist for gravitational waves at the event horizon of black holes.[1] A hybrid of waves of light and electrons known as surface plasmons has been demonstrated in the form of whispering-gallery waves,[47] and likewise for exciton-polaritons in semiconductors.[48] Galleries simultaneously containing both acoustic and optical whispering-gallery waves have also been made,[49] exhibiting very strong mode coupling and coherent effects.[50] Hybrid solid-fluid-optical whispering-gallery structures have been observed as well.[51]

See also

References

  1. ↑ 1.0 1.1 1.2 Wright, Oliver B. (2012). "Gallery of whispers". Physics World 25 (2): 31–36. doi:10.1088/2058-7058/25/02/36. Bibcode: 2012PhyW...25b..31W. 
  2. ↑ 2.0 2.1 Oliver, Wright B.; Matsuda, Oliver. "Watching whispering-gallery waves". http://kino-ap.eng.hokudai.ac.jp/WG.html. 
  3. ↑ [Lord Rayleigh, Theory of Sound, vol. II, 1st edition, (London, MacMillan), 1878.]
  4. ↑ [J. Tyndall, The Science of Sound (New York, Philosophical Library), 1867, p. 20.]
  5. ↑ [G. B. Airy, On Sound and Atmospheric Vibrations, with the Mathematical Elements of Music (London, MacMillan), 1871, p. 145.]
  6. ↑ Rayleigh, Lord (1910). "CXII. The problem of the whispering gallery". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (Informa UK Limited) 20 (120): 1001–1004. doi:10.1080/14786441008636993. ISSN 1941-5982. https://zenodo.org/record/1522134. 
  7. ↑ Rayleigh, Lord (1914). "IX. Further applications of Bessel's functions of high order to the Whispering Gallery and allied problems". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (Informa UK Limited) 27 (157): 100–109. doi:10.1080/14786440108635067. ISSN 1941-5982. 
  8. ↑ Raman, C. V. (1921–1922). "XV. On Whispering Galleries". Proceedings of the Indian Association for the Cultivation of Science 7: 159. https://babel.hathitrust.org/cgi/pt?id=mdp.39015077811514&view=1up&seq=189. 
  9. ↑ [L. M. Brekhovskikh, Sov. Phys. Acoust. 13, 462, 1968]
  10. ↑ [Quantitative Seismology, K. Aki and P. G. Richards (University Science Books), 2009, Ch. 8]
  11. ↑ Reese, D. R.; MacGregor, K. B.; Jackson, S.; Skumanich, A.; Metcalfe, T. S. (1 March 2009). "Pulsation modes in rapidly rotating stellar models based on the self-consistent field method". Astronomy & Astrophysics (EDP Sciences) 506 (1): 189–201. doi:10.1051/0004-6361/200811510. ISSN 0004-6361. Bibcode: 2009A&A...506..189R. 
  12. ↑ Nagy, Peter B.; Blodgett, Mark; Golis, Matthew (1994). "Weep hole inspection by circumferential creeping waves". NDT & E International (Elsevier BV) 27 (3): 131–142. doi:10.1016/0963-8695(94)90604-1. ISSN 0963-8695. 
  13. ↑ Clorennec, D; Royer, D; Walaszek, H (2002). "Nondestructive evaluation of cylindrical parts using laser ultrasonics". Ultrasonics (Elsevier BV) 40 (1–8): 783–789. doi:10.1016/s0041-624x(02)00210-x. ISSN 0041-624X. PMID 12160045. 
  14. ↑ Ishikawa, Satoru; Nakaso, Noritaka; Takeda, Nobuo; Mihara, Tsuyoshi; Tsukahara, Yusuke; Yamanaka, Kazushi (2003). "Surface acoustic waves on a sphere with divergent, focusing, and collimating beam shapes excited by an interdigital transducer". Applied Physics Letters (AIP Publishing) 83 (22): 4649–4651. doi:10.1063/1.1631061. ISSN 0003-6951. Bibcode: 2003ApPhL..83.4649I. 
  15. ↑ Tachizaki, Takehiro; Matsuda, Osamu; Maznev, Alex A.; Wright, Oliver B. (23 April 2010). "Acoustic whispering-gallery modes generated and dynamically imaged with ultrashort optical pulses". Physical Review B (American Physical Society (APS)) 81 (16): 165434. doi:10.1103/physrevb.81.165434. ISSN 1098-0121. Bibcode: 2010PhRvB..81p5434T. 
  16. ↑ Ishikawa, Satoru; Cho, Hideo; Yamanaka, Kazushi; Nakaso, Noritaka; Tsukahara, Yusuke (30 May 2001). "Surface Acoustic Waves on a Sphere –Analysis of Propagation Using Laser Ultrasonics–". Japanese Journal of Applied Physics (Japan Society of Applied Physics) 40 (Part 1, No. 5B): 3623–3627. doi:10.1143/jjap.40.3623. ISSN 0021-4922. Bibcode: 2001JaJAP..40.3623I. 
  17. ↑ "Delaying Trains of Short Light Pulses in WGM Resonators" (in en). Tech Briefs Media Group. 1 September 2018. https://www.techbriefs.com/component/content/article/tb/techbriefs/physical-sciences/3160. 
  18. ↑ Mie, Gustav (1908). "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen" (in de). Annalen der Physik (Wiley) 330 (3): 377–445. doi:10.1002/andp.19083300302. ISSN 0003-3804. Bibcode: 1908AnP...330..377M. 
  19. ↑ Debye, P. (1909). "Der Lichtdruck auf Kugeln von beliebigem Material" (in de). Annalen der Physik (Wiley) 335 (11): 57–136. doi:10.1002/andp.19093351103. ISSN 0003-3804. Bibcode: 1909AnP...335...57D. 
  20. ↑ Oraevsky, Anatolii N (31 May 2002). "Whispering-gallery waves". Quantum Electronics (IOP Publishing) 32 (5): 377–400. doi:10.1070/qe2002v032n05abeh002205. ISSN 1063-7818. 
  21. ↑ Vahala, K. J. (2003). "Optical microcavities". Nature 424 (6950): 839–846. doi:10.1038/nature01939. PMID 12917698. Bibcode: 2003Natur.424..839V. 
  22. ↑ Chiasera, A.; Dumeige, Y.; Féron, P.; Ferrari, M.; Jestin, Y.; Nunzi Conti, G.; Pelli, S.; Soria, S. et al. (23 April 2010). "Spherical whispering-gallery-mode microresonators". Laser & Photonics Reviews (Wiley) 4 (3): 457–482. doi:10.1002/lpor.200910016. ISSN 1863-8880. Bibcode: 2010LPRv....4..457C. 
  23. ↑ Rakovich, Y.P.; Donegan, J.F. (2 June 2009). "Photonic atoms and molecules". Laser & Photonics Reviews (Wiley) 4 (2): 179–191. doi:10.1002/lpor.200910001. ISSN 1863-8880. 
  24. ↑ Kippenberg, T. J.; Vahala, K. J. (29 August 2008). "Cavity Optomechanics: Back-Action at the Mesoscale". Science (American Association for the Advancement of Science (AAAS)) 321 (5893): 1172–1176. doi:10.1126/science.1156032. ISSN 0036-8075. PMID 18755966. Bibcode: 2008Sci...321.1172K. 
  25. ↑ Del’Haye, P.; Schliesser, A.; Arcizet, O.; Wilken, T.; Holzwarth, R.; Kippenberg, T. J. (2007). "Optical frequency comb generation from a monolithic microresonator". Nature (Springer Science and Business Media LLC) 450 (7173): 1214–1217. doi:10.1038/nature06401. ISSN 0028-0836. PMID 18097405. Bibcode: 2007Natur.450.1214D. 
  26. ↑ Arnold, S.; Khoshsima, M.; Teraoka, I.; Holler, S.; Vollmer, F. (15 February 2003). "Shift of whispering-gallery modes in microspheres by protein adsorption". Optics Letters (The Optical Society) 28 (4): 272–4. doi:10.1364/ol.28.000272. ISSN 0146-9592. PMID 12653369. Bibcode: 2003OptL...28..272A. 
  27. ↑ Grudinin, Ivan S.; Ilchenko, Vladimir S.; Maleki, Lute (8 December 2006). "Ultrahigh optical Q factors of crystalline resonators in the linear regime". Physical Review A (American Physical Society (APS)) 74 (6): 063806. doi:10.1103/physreva.74.063806. ISSN 1050-2947. Bibcode: 2006PhRvA..74f3806G. 
  28. ↑ Yamanaka, K.; Ishikawa, S.; Nakaso, N.; Takeda, N.; Sim, Dong Youn et al. (2006). "Ultramultiple roundtrips of surface acoustic wave on sphere realizing innovation of gas sensors". IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 53 (4): 793–801. doi:10.1109/TUFFC.2006.1621507. PMID 16615584. 
  29. ↑ Pask, Colin (1 December 1977). "Generalized parameters for tunneling ray attenuation in optical fibers". Journal of the Optical Society of America (The Optical Society) 68 (1): 110. doi:10.1364/josa.68.000110. ISSN 0030-3941. 
  30. ↑ Gmachl, C. (5 June 1998). "High-Power Directional Emission from Microlasers with Chaotic Resonators". Science 280 (5369): 1556–1564. doi:10.1126/science.280.5369.1556. ISSN 0036-8075. PMID 9616111. Bibcode: 1998Sci...280.1556G. 
  31. ↑ Baryshnikov, Yuliy; Heider, Pascal; Parz, Wolfgang; Zharnitsky, Vadim (22 September 2004). "Whispering Gallery Modes Inside Asymmetric Resonant Cavities". Physical Review Letters (American Physical Society (APS)) 93 (13): 133902. doi:10.1103/physrevlett.93.133902. ISSN 0031-9007. PMID 15524720. Bibcode: 2004PhRvL..93m3902B. 
  32. ↑ Tanaka, Akira; Asai, Takeshi; Toubaru, Kiyota; Takashima, Hideaki; Fujiwara, Masazumi; Okamoto, Ryo; Takeuchi, Shigeki (24 January 2011). "Phase shift spectra of a fiber–microsphere system at the single photon level". Optics Express (The Optical Society) 19 (3): 2278–85. doi:10.1364/oe.19.002278. ISSN 1094-4087. PMID 21369045. Bibcode: 2011OExpr..19.2278T. 
  33. ↑ Budden, K. G.; Martin, H. G. (6 February 1962). "The ionosphere as a whispering gallery". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (The Royal Society) 265 (1323): 554–569. doi:10.1098/rspa.1962.0042. ISSN 2053-9169. Bibcode: 1962RSPSA.265..554B. 
  34. ↑ Stanwix, P. L. (2005). "Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators". Physical Review Letters 95 (4): 040404. doi:10.1103/PhysRevLett.95.040404. PMID 16090785. Bibcode: 2005PhRvL..95d0404S. 
  35. ↑ Mendis, R.; Mittleman, M. (2010). "Whispering-gallery-mode terahertz pulse propagation on a curved metallic plate". Applied Physics Letters 97 (3): 031106. doi:10.1063/1.3466909. Bibcode: 2010ApPhL..97c1106M. 
  36. ↑ Albert, F.; Braun, T.; Heindel, T.; Schneider, C.; Reitzenstein, S.; Höfling, S.; Worschech, L.; Forchel, A. (6 September 2010). "Whispering gallery mode lasing in electrically driven quantum dot micropillars". Applied Physics Letters (AIP Publishing) 97 (10): 101108. doi:10.1063/1.3488807. ISSN 0003-6951. Bibcode: 2010ApPhL..97j1108A. 
  37. ↑ Hyun, J. K.; Couillard, M.; Rajendran, P.; Liddell, C. M.; Muller, D. A. (15 December 2008). "Measuring far-ultraviolet whispering gallery modes with high energy electrons". Applied Physics Letters (AIP Publishing) 93 (24): 243106. doi:10.1063/1.3046731. ISSN 0003-6951. Bibcode: 2008ApPhL..93x3106H. 
  38. ↑ Liu, Chien; Golovchenko, Jene A. (4 August 1997). "Surface Trapped X Rays: Whispering-Gallery Modes atλ=0.7Å". Physical Review Letters (American Physical Society (APS)) 79 (5): 788–791. doi:10.1103/physrevlett.79.788. ISSN 0031-9007. Bibcode: 1997PhRvL..79..788L. http://nrs.harvard.edu/urn-3:HUL.InstRepos:29406252. 
  39. ↑ M.R. Foreman (2015). "Whispering gallery mode sensors". Advances in Optics and Photonics 7 (2): 168–240. doi:10.1364/AOP.7.000168. PMID 26973759. PMC 4786191. Bibcode: 2015AdOP....7..168F. https://www.osapublishing.org/aop/abstract.cfm?uri=aop-7-2-168. 
  40. ↑ Y. Wang (2020). "Microfluidic whispering gallery mode optical sensors for biological applications". Laser & Photonics Reviews 14 (12): 2000135–56. doi:10.1002/lpor.202000135. Bibcode: 2020LPRv...1400135W. https://www.researchgate.net/publication/346314054. 
  41. ↑ T. Reynolds (2017). "Fluorescent and lasing whispering gallery mode microresonators for sensing applications". Laser & Photonics Reviews 11 (2): 1600265–76. doi:10.1002/lpor.201600265. Bibcode: 2017LPRv...1100265R. https://onlinelibrary.wiley.com/doi/abs/10.1002/lpor.201600265. 
  42. ↑ A. Bozzola (2017). "Hybrid plasmonic–photonic whispering gallery mode resonators for sensing: a critical review". Analyst 142 (6): 883–898. doi:10.1039/C6AN02693A. PMID 28225100. Bibcode: 2017Ana...142..883B. 
  43. ↑ Nesvizhevsky, Valery V.; Voronin, Alexei Yu.; Cubitt, Robert; Protasov, Konstantin V. (13 December 2009). "Neutron whispering gallery". Nature Physics (Springer Science and Business Media LLC) 6 (2): 114–117. doi:10.1038/nphys1478. ISSN 1745-2473. 
  44. ↑ Reecht, Gaël; Bulou, Hervé; Scheurer, Fabrice; Speisser, Virginie; Carrière, Bernard; Mathevet, Fabrice; Schull, Guillaume (29 January 2013). "Oligothiophene Nanorings as Electron Resonators for Whispering Gallery Modes". Physical Review Letters (American Physical Society (APS)) 110 (5): 056802. doi:10.1103/physrevlett.110.056802. ISSN 0031-9007. PMID 23414040. Bibcode: 2013PhRvL.110e6802R. 
  45. ↑ Dragún, Olga; Überall, Herbert (1980). "Nuclear Rayleigh and whispering gallery waves excited in heavy ion collisions". Physics Letters B (Elsevier BV) 94 (1): 24–27. doi:10.1016/0370-2693(80)90816-3. ISSN 0370-2693. Bibcode: 1980PhLB...94...24D. 
  46. ↑ Arcos, E.; Báez, G.; Cuatláyol, P. A.; Prian, M. L. H.; Méndez-Sánchez, R. A.; Hernández-Saldaña, H. (1998). "Vibrating soap films: An analog for quantum chaos on billiards". American Journal of Physics (American Association of Physics Teachers (AAPT)) 66 (7): 601–607. doi:10.1119/1.18913. ISSN 0002-9505. Bibcode: 1998AmJPh..66..601A. 
  47. ↑ Min, Bumki; Ostby, Eric; Sorger, Volker; Ulin-Avila, Erick; Yang, Lan; Zhang, Xiang; Vahala, Kerry (2009). "High-Q surface-plasmon-polariton whispering-gallery microcavity". Nature (Springer Science and Business Media LLC) 457 (7228): 455–458. doi:10.1038/nature07627. ISSN 0028-0836. PMID 19158793. Bibcode: 2009Natur.457..455M. 
  48. ↑ Sun, Liaoxin; Chen, Zhanghai; Ren, Qijun; Yu, Ke; Bai, Lihui; Zhou, Weihang; Xiong, Hui; Zhu, Z. Q. et al. (16 April 2008). "Direct Observation of Whispering Gallery Mode Polaritons and their Dispersion in a ZnO Tapered Microcavity". Physical Review Letters 100 (15): 156403. doi:10.1103/physrevlett.100.156403. ISSN 0031-9007. PMID 18518134. Bibcode: 2008PhRvL.100o6403S. 
  49. ↑ Tomes, Matthew; Carmon, Tal (19 March 2009). "Photonic Micro-Electromechanical Systems Vibrating atX-band (11-GHz) Rates". Physical Review Letters (American Physical Society (APS)) 102 (11): 113601. doi:10.1103/physrevlett.102.113601. ISSN 0031-9007. PMID 19392199. Bibcode: 2009PhRvL.102k3601T. 
  50. ↑ Kim, JunHwan; Kuzyk, Mark C.; Han, Kewen; Wang, Hailin; Bahl, Gaurav (26 January 2015). "Non-reciprocal Brillouin scattering induced transparency". Nature Physics (Springer Science and Business Media LLC) 11 (3): 275–280. doi:10.1038/nphys3236. ISSN 1745-2473. Bibcode: 2015NatPh..11..275K. 
  51. ↑ Bahl, Gaurav; Kim, Kyu Hyun; Lee, Wonsuk; Liu, Jing; Fan, Xudong; Carmon, Tal (7 June 2013). "Brillouin cavity optomechanics with microfluidic devices". Nature Communications (Springer Science and Business Media LLC) 4 (1): 1994. doi:10.1038/ncomms2994. ISSN 2041-1723. PMID 23744103. Bibcode: 2013NatCo...4.1994B. 

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