Abstract

Stimulated Brillouin scattering recently allowed experimental excitation of surface acoustic resonances in micro-devices, enabling vibration at rates in the range of 50 MHz to 12 GHz. The experimental availability of such mechanical whispering gallery modes in photonic-MEMS raises questions on their structure and spectral distribution. Here we calculate the form and frequency of such vibrational surface whispering gallery modes, revealing diverse types of surface vibrations including longitudinal, transverse, and Rayleigh-type deformations. We parametrically investigate these various modes by changing their orders in the azimuthal, radial, and polar directions to reveal different vibrational structures including mechanical resonances that are localized near the interface with the environment where they can sense changes in the surroundings.

© 2011 OSA

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    [CrossRef] [PubMed]
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  43. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
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2011 (1)

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A 83(2), 021801 (2011).
[CrossRef]

2009 (7)

T. Franke, A. R. Abate, D. A. Weitz, A. Wixforth, “Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices,” Lab Chip 9(18), 2625–2627 (2009).
[CrossRef] [PubMed]

X. Jiang, Q. Lin, J. Rosenberg, K. Vahala, O. Painter, “High-Q double-disk microcavities for cavity optomechanics,” Opt. Express 17(23), 20911–20919 (2009).
[CrossRef] [PubMed]

M. Tomes, T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[CrossRef] [PubMed]

I. S. Grudinin, A. B. Matsko, L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[CrossRef] [PubMed]

M. Grech, G. Riazuelo, D. Pesme, S. Weber, V. T. Tikhonchuk, “Coherent forward stimulated-brillouin scattering of a spatially incoherent laser beam in a plasma and its effect on beam spray,” Phys. Rev. Lett. 102(15), 155001 (2009).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Optomechanics with surface-acoustic-wave whispering-gallery modes,” Phys. Rev. Lett. 103(25), 257403 (2009).
[CrossRef] [PubMed]

S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antenn. Propag. 57(8), 2242–2251 (2009).
[CrossRef]

2008 (2)

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

P. G. Malischewsky, P. C. Vinh, “Improved approximations of the Rayleigh wave velocity,” J. Thermoplastic Compos. Mater. 21(4), 337–352 (2008).
[CrossRef]

2007 (4)

A. Savchenkov, A. Matsko, V. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[CrossRef]

T. Carmon, K. J. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency,” Phys. Rev. Lett. 98(12), 123901 (2007).
[CrossRef] [PubMed]

T. Carmon, M. C. Cross, K. J. Vahala, “Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure,” Phys. Rev. Lett. 98(16), 167203 (2007).
[CrossRef] [PubMed]

T. Carmon, K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[CrossRef]

2006 (2)

P. Z. Dashti, F. Alhassen, H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[CrossRef] [PubMed]

N. Shibata, A. Nakazono, N. Taguchi, S. Tanaka, “Forward Brillouin scattering in holey fibers,” IEEE Photon. Technol. Lett. 18(2), 412–414 (2006).
[CrossRef]

2005 (5)

L. Yang, T. Carmon, B. Min, S. M. Spillane, K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005).
[CrossRef] [PubMed]

2004 (1)

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

2003 (2)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

2002 (2)

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

1998 (1)

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

1985 (1)

R. M. Shelby, M. D. Levenson, P. W. Bayer, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[CrossRef] [PubMed]

1972 (1)

E. Ippen, R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[CrossRef]

1964 (1)

R. Chiao, C. Townes, B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12(21), 592–595 (1964).
[CrossRef]

1910 (1)

L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. 20, 1001–1004 (1910).

1885 (1)

L. Rayleigh, “On waves propagated along the plane surface of an elastic solid,” Proc. Lond. Math. Soc. s1-17(1), 4–11 (1885).
[CrossRef]

Abate, A. R.

T. Franke, A. R. Abate, D. A. Weitz, A. Wixforth, “Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices,” Lab Chip 9(18), 2625–2627 (2009).
[CrossRef] [PubMed]

Alhassen, F.

P. Z. Dashti, F. Alhassen, H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[CrossRef] [PubMed]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, P. W. Bayer, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[CrossRef] [PubMed]

Capasso, F.

Carmon, T.

M. Tomes, T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[CrossRef] [PubMed]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

T. Carmon, M. C. Cross, K. J. Vahala, “Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure,” Phys. Rev. Lett. 98(16), 167203 (2007).
[CrossRef] [PubMed]

T. Carmon, K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[CrossRef]

T. Carmon, K. J. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency,” Phys. Rev. Lett. 98(12), 123901 (2007).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

L. Yang, T. Carmon, B. Min, S. M. Spillane, K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

Chiao, R.

R. Chiao, C. Townes, B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12(21), 592–595 (1964).
[CrossRef]

Cross, M. C.

T. Carmon, M. C. Cross, K. J. Vahala, “Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure,” Phys. Rev. Lett. 98(16), 167203 (2007).
[CrossRef] [PubMed]

Dashti, P. Z.

P. Z. Dashti, F. Alhassen, H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[CrossRef] [PubMed]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

Franke, T.

T. Franke, A. R. Abate, D. A. Weitz, A. Wixforth, “Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices,” Lab Chip 9(18), 2625–2627 (2009).
[CrossRef] [PubMed]

Grech, M.

M. Grech, G. Riazuelo, D. Pesme, S. Weber, V. T. Tikhonchuk, “Coherent forward stimulated-brillouin scattering of a spatially incoherent laser beam in a plasma and its effect on beam spray,” Phys. Rev. Lett. 102(15), 155001 (2009).
[CrossRef] [PubMed]

Grudinin, I. S.

I. S. Grudinin, A. B. Matsko, L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[CrossRef] [PubMed]

Haroche, S.

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Ibanescu, M.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

Ilchenko, V.

A. Savchenkov, A. Matsko, V. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[CrossRef]

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A 83(2), 021801 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Optomechanics with surface-acoustic-wave whispering-gallery modes,” Phys. Rev. Lett. 103(25), 257403 (2009).
[CrossRef] [PubMed]

Ippen, E.

E. Ippen, R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[CrossRef]

Jiang, X.

Joannopoulos, J. D.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

Johnson, S. G.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

Kingsley, N. D.

S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antenn. Propag. 57(8), 2242–2251 (2009).
[CrossRef]

Kippenberg, T. J.

H. Rokhsari, T. J. Kippenberg, T. Carmon, K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Lee, H. P.

P. Z. Dashti, F. Alhassen, H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[CrossRef] [PubMed]

Lefevre-Seguin, V.

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, P. W. Bayer, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[CrossRef] [PubMed]

Lin, Q.

Loncar, M.

Maleki, L.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A 83(2), 021801 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Optomechanics with surface-acoustic-wave whispering-gallery modes,” Phys. Rev. Lett. 103(25), 257403 (2009).
[CrossRef] [PubMed]

I. S. Grudinin, A. B. Matsko, L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[CrossRef] [PubMed]

A. Savchenkov, A. Matsko, V. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[CrossRef]

Malischewsky, P. G.

P. G. Malischewsky, P. C. Vinh, “Improved approximations of the Rayleigh wave velocity,” J. Thermoplastic Compos. Mater. 21(4), 337–352 (2008).
[CrossRef]

Matsko, A.

A. Savchenkov, A. Matsko, V. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[CrossRef]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A 83(2), 021801 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Optomechanics with surface-acoustic-wave whispering-gallery modes,” Phys. Rev. Lett. 103(25), 257403 (2009).
[CrossRef] [PubMed]

I. S. Grudinin, A. B. Matsko, L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[CrossRef] [PubMed]

Min, B.

L. Yang, T. Carmon, B. Min, S. M. Spillane, K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[CrossRef]

Nakazono, A.

N. Shibata, A. Nakazono, N. Taguchi, S. Tanaka, “Forward Brillouin scattering in holey fibers,” IEEE Photon. Technol. Lett. 18(2), 412–414 (2006).
[CrossRef]

Nikolaou, S.

S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antenn. Propag. 57(8), 2242–2251 (2009).
[CrossRef]

Oxborrow, M.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

Painter, O.

Papapolymerou, J.

S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antenn. Propag. 57(8), 2242–2251 (2009).
[CrossRef]

Pesme, D.

M. Grech, G. Riazuelo, D. Pesme, S. Weber, V. T. Tikhonchuk, “Coherent forward stimulated-brillouin scattering of a spatially incoherent laser beam in a plasma and its effect on beam spray,” Phys. Rev. Lett. 102(15), 155001 (2009).
[CrossRef] [PubMed]

Ponchak, G. E.

S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antenn. Propag. 57(8), 2242–2251 (2009).
[CrossRef]

Povinelli, M. L.

Raimond, J. M.

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Rayleigh, L.

L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. 20, 1001–1004 (1910).

L. Rayleigh, “On waves propagated along the plane surface of an elastic solid,” Proc. Lond. Math. Soc. s1-17(1), 4–11 (1885).
[CrossRef]

Riazuelo, G.

M. Grech, G. Riazuelo, D. Pesme, S. Weber, V. T. Tikhonchuk, “Coherent forward stimulated-brillouin scattering of a spatially incoherent laser beam in a plasma and its effect on beam spray,” Phys. Rev. Lett. 102(15), 155001 (2009).
[CrossRef] [PubMed]

Rokhsari, H.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

Rosenberg, J.

Savchenkov, A.

A. Savchenkov, A. Matsko, V. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[CrossRef]

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A 83(2), 021801 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Optomechanics with surface-acoustic-wave whispering-gallery modes,” Phys. Rev. Lett. 103(25), 257403 (2009).
[CrossRef] [PubMed]

Scherer, A.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

Schwefel, H. G. L.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

Seidel, D.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A 83(2), 021801 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Optomechanics with surface-acoustic-wave whispering-gallery modes,” Phys. Rev. Lett. 103(25), 257403 (2009).
[CrossRef] [PubMed]

Shelby, R. M.

R. M. Shelby, M. D. Levenson, P. W. Bayer, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[CrossRef] [PubMed]

Shibata, N.

N. Shibata, A. Nakazono, N. Taguchi, S. Tanaka, “Forward Brillouin scattering in holey fibers,” IEEE Photon. Technol. Lett. 18(2), 412–414 (2006).
[CrossRef]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

Smythe, E. J.

Spillane, S. M.

L. Yang, T. Carmon, B. Min, S. M. Spillane, K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Stoicheff, B.

R. Chiao, C. Townes, B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12(21), 592–595 (1964).
[CrossRef]

Stolen, R.

E. Ippen, R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[CrossRef]

Stone, A. D.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

Strekalov, D.

A. Savchenkov, A. Matsko, V. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[CrossRef]

Taguchi, N.

N. Shibata, A. Nakazono, N. Taguchi, S. Tanaka, “Forward Brillouin scattering in holey fibers,” IEEE Photon. Technol. Lett. 18(2), 412–414 (2006).
[CrossRef]

Tanaka, S.

N. Shibata, A. Nakazono, N. Taguchi, S. Tanaka, “Forward Brillouin scattering in holey fibers,” IEEE Photon. Technol. Lett. 18(2), 412–414 (2006).
[CrossRef]

Tentzeris, M. M.

S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antenn. Propag. 57(8), 2242–2251 (2009).
[CrossRef]

Tikhonchuk, V. T.

M. Grech, G. Riazuelo, D. Pesme, S. Weber, V. T. Tikhonchuk, “Coherent forward stimulated-brillouin scattering of a spatially incoherent laser beam in a plasma and its effect on beam spray,” Phys. Rev. Lett. 102(15), 155001 (2009).
[CrossRef] [PubMed]

Tomes, M.

M. Tomes, T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[CrossRef] [PubMed]

Townes, C.

R. Chiao, C. Townes, B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12(21), 592–595 (1964).
[CrossRef]

Treussart, F.

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Vahala, K.

Vahala, K. J.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

T. Carmon, M. C. Cross, K. J. Vahala, “Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure,” Phys. Rev. Lett. 98(16), 167203 (2007).
[CrossRef] [PubMed]

T. Carmon, K. J. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency,” Phys. Rev. Lett. 98(12), 123901 (2007).
[CrossRef] [PubMed]

T. Carmon, K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

L. Yang, T. Carmon, B. Min, S. M. Spillane, K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Velichansky, V.

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Vinh, P. C.

P. G. Malischewsky, P. C. Vinh, “Improved approximations of the Rayleigh wave velocity,” J. Thermoplastic Compos. Mater. 21(4), 337–352 (2008).
[CrossRef]

Volikov, P.

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Weber, S.

M. Grech, G. Riazuelo, D. Pesme, S. Weber, V. T. Tikhonchuk, “Coherent forward stimulated-brillouin scattering of a spatially incoherent laser beam in a plasma and its effect on beam spray,” Phys. Rev. Lett. 102(15), 155001 (2009).
[CrossRef] [PubMed]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

Weitz, D. A.

T. Franke, A. R. Abate, D. A. Weitz, A. Wixforth, “Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices,” Lab Chip 9(18), 2625–2627 (2009).
[CrossRef] [PubMed]

Wixforth, A.

T. Franke, A. R. Abate, D. A. Weitz, A. Wixforth, “Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices,” Lab Chip 9(18), 2625–2627 (2009).
[CrossRef] [PubMed]

Yang, L.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

L. Yang, T. Carmon, B. Min, S. M. Spillane, K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

L. Yang, T. Carmon, B. Min, S. M. Spillane, K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol-gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[CrossRef]

E. Ippen, R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

N. Shibata, A. Nakazono, N. Taguchi, S. Tanaka, “Forward Brillouin scattering in holey fibers,” IEEE Photon. Technol. Lett. 18(2), 412–414 (2006).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antenn. Propag. 57(8), 2242–2251 (2009).
[CrossRef]

J. Thermoplastic Compos. Mater. (1)

P. G. Malischewsky, P. C. Vinh, “Improved approximations of the Rayleigh wave velocity,” J. Thermoplastic Compos. Mater. 21(4), 337–352 (2008).
[CrossRef]

Lab Chip (1)

T. Franke, A. R. Abate, D. A. Weitz, A. Wixforth, “Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices,” Lab Chip 9(18), 2625–2627 (2009).
[CrossRef] [PubMed]

Nat. Phys. (1)

T. Carmon, K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[CrossRef]

Nature (3)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Philos. Mag. (1)

L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. 20, 1001–1004 (1910).

Phys. Rev. A (2)

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A 83(2), 021801 (2011).
[CrossRef]

A. Savchenkov, A. Matsko, V. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

Phys. Rev. Lett. (13)

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[CrossRef] [PubMed]

T. Carmon, K. J. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency,” Phys. Rev. Lett. 98(12), 123901 (2007).
[CrossRef] [PubMed]

T. Carmon, M. C. Cross, K. J. Vahala, “Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure,” Phys. Rev. Lett. 98(16), 167203 (2007).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

R. Chiao, C. Townes, B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12(21), 592–595 (1964).
[CrossRef]

P. Z. Dashti, F. Alhassen, H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, P. W. Bayer, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54(9), 939–942 (1985).
[CrossRef] [PubMed]

M. Grech, G. Riazuelo, D. Pesme, S. Weber, V. T. Tikhonchuk, “Coherent forward stimulated-brillouin scattering of a spatially incoherent laser beam in a plasma and its effect on beam spray,” Phys. Rev. Lett. 102(15), 155001 (2009).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Optomechanics with surface-acoustic-wave whispering-gallery modes,” Phys. Rev. Lett. 103(25), 257403 (2009).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Illustration of the mechanical whispering gallery resonance in a sphere. Deformation of the outer surface describes the exaggerated mechanical deformation. The cuts reveal also the internal deformation as indicated by colors.

Fig. 2
Fig. 2

Rayleigh, transverse, and longitudinal whispering gallery modes where energy is confined within a wavelength distance from the interface. The major deformation is either radial, polar, or azimuthal as indicated by arrows. Mϕ in this calculation is 20, indicating that 20 acoustical wavelengthes are resonating along the spehre circumference. Color represents absolute value of the deformation.

Fig. 3
Fig. 3

High-order mechanical whispering gallery modes. Top: Increasing the mode order in the radial and polar directions for mechanical whispering gallery modes in a silica sphere. Color represents deformation. Mϕ = 20. Bottom: We depict several of the top modes and present them in 3D. The presented section is one acoustic wavelength in the azimuthal direction. The equator is seen to deform into a sine where the Rayleigh mode the deformation is in the radial direction and for the transverse mode the deformation is in the polar direction.

Fig. 4
Fig. 4

High-order mechanical whispering gallery modes. The calculated speed of sound is shown as a function of the azimuthal mode order, Mϕ . The first three transverse orders are given for the Rayleigh-, transverse-, and longitudinal families. At large Mϕ , the speed of sound asymptotically converges to the relevant speed of sound in bulk media (see Table 1).

Fig. 5
Fig. 5

Vibration frequencies for the various modes in a r = 100 micron silica sphere as a function of their azimuthal mode order. Left, with Mϕ typical to forward Brillouin excitation. Right, with Mϕ typical to backward Brillouin excitation. The shadowed regions estimate how high resonance frequencies can go for each of these modes via relying on high order transverse members of this mode family. The shadowed region is bounded in the Mϕ direction as estimation from momentum conservation consideration. We assume excitation with 1.5-micron telecom pump.

Tables (1)

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Table 1 Analytically and Numerically Calculated Speeds of Sound a

Equations (2)

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ρ ˜ = A a ( t ) T a ( θ , r ) e i ( M φ a φ ϖ a t ) , E ˜ p = A p ( t ) T p ( θ , r ) e i ( M φ p φ ϖ p t ) , E ˜ S = A S ( t ) T S ( θ , r ) e i ( M φ S φ ϖ S t ) .
2 ρ ˜ t 2 V 2 ρ ˜ b t 2 ρ ˜ = 1 2 ε 0 γ θ 2 ( E ˜ p + E ˜ S ) 2 .

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