Abstract

Droplets, particularly water droplets, are abundant in both natural and artificial systems. Their capillary oscillations are governed by surface tension and are therefore distinguished from acoustic oscillations. These capillary oscillations play a major role in droplet coalescence, for example, and are also an important phenomenon in interface theories. Here, we experimentally and theoretically analyze the capillary oscillation within an optical cavity with walls of water. Our droplet benefits from an optical finesse of 520 that, accordingly, boosts its sensitivity in recording Brownian capillaries with amplitudes of 1±0.025  Å and kilohertz rates in agreement with natural-frequency calculations. Our hybrid device allows resonantly enhanced interactions between electromagnetic and capillary waves that could potentially lead to optical excitation or the cooling of droplet capillary oscillations.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Cavity Opto-Mechanics

T.J. Kippenberg and K.J. Vahala
Opt. Express 15(25) 17172-17205 (2007)

Fiber ring resonator with a nanofiber section for chiral cavity quantum electrodynamics and multimode strong coupling

Philipp Schneeweiss, Sophie Zeiger, Thomas Hoinkes, Arno Rauschenbeutel, and Jürgen Volz
Opt. Lett. 42(1) 85-88 (2017)

Fabrication of a centimeter-long cavity on a nanofiber for cavity quantum electrodynamics

Jameesh Keloth, K. P. Nayak, and K. Hakuta
Opt. Lett. 42(5) 1003-1006 (2017)

References

  • View by:
  • |
  • |
  • |

  1. M. Smoluchowski, Ann. Phys. 330, 205 (1908).
    [Crossref]
  2. A. Vrij, Adv. Colloid Interface Sci. 2, 39 (1968).
    [Crossref]
  3. M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).
    [Crossref]
  4. M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
    [Crossref]
  5. A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
    [Crossref]
  6. C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
    [Crossref]
  7. D. G. Aarts, M. Schmidt, and H. N. Lekkerkerker, Science 304, 847 (2004).
    [Crossref]
  8. A. Vrij, Discuss. Faraday Soc. 42, 23 (1966).
    [Crossref]
  9. A. Sheludko, Adv. Colloid Interface Sci. 1, 391 (1967).
    [Crossref]
  10. J. Eggers, J. R. Lister, and H. A. Stone, J. Fluid Mech. 401, 293 (1999).
    [Crossref]
  11. E. Helfand and Y. Tagami, J. Chem. Phys. 56, 3592 (1972).
    [Crossref]
  12. H. Erbil, Solid and Liquid Interfaces (Blackwell, 2006).
  13. T. Mitsui, Jpn. J. Appl. Phys. 43, 6425 (2004).
    [Crossref]
  14. R. Dahan, L. L. Martin, and T. Carmon, Optica 3, 175 (2016).
    [Crossref]
  15. V. B. Braginsky, V. B. Braginskiĭ, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, 1995), p. 137.
  16. A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
    [Crossref]
  17. A. Ashkin and J. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
    [Crossref]
  18. H.-M. Tzeng, K. F. Wall, M. Long, and R. Chang, Opt. Lett. 9, 499 (1984).
    [Crossref]
  19. M. Hossein-Zadeh and K. J. Vahala, Opt. Express 14, 10800 (2006).
    [Crossref]
  20. A. Jonáš, Y. Karadag, M. Mestre, and A. Kiraz, J. Opt. Soc. Am. B 29, 3240 (2012).
    [Crossref]
  21. U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
    [Crossref]
  22. S. Maayani, L. L. Martin, and T. Carmon, Nat. Commun. 7, 10435 (2016).
    [Crossref]
  23. L. Rayleigh, Proc. R. Soc. London 29, 71 (1879).
  24. F. Celestini and R. Kofman, Phys. Rev. E 73, 041602 (2006).
    [Crossref]
  25. J. Knight, G. Cheung, F. Jacques, and T. Birks, Opt. Lett. 22, 1129 (1997).
    [Crossref]
  26. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
    [Crossref]
  27. S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
    [Crossref]
  28. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Modern Phys. 86, 1391 (2014).
    [Crossref]
  29. F. Behroozi, J. Smith, and W. Even, Am. J. Phys. 78, 1165 (2010).
    [Crossref]
  30. S. Kaminski, L. L. Martin, and T. Carmon, Opt. Express 23, 28914 (2015).
    [Crossref]

2016 (2)

R. Dahan, L. L. Martin, and T. Carmon, Optica 3, 175 (2016).
[Crossref]

S. Maayani, L. L. Martin, and T. Carmon, Nat. Commun. 7, 10435 (2016).
[Crossref]

2015 (2)

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
[Crossref]

S. Kaminski, L. L. Martin, and T. Carmon, Opt. Express 23, 28914 (2015).
[Crossref]

2014 (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Modern Phys. 86, 1391 (2014).
[Crossref]

2012 (1)

2010 (1)

F. Behroozi, J. Smith, and W. Even, Am. J. Phys. 78, 1165 (2010).
[Crossref]

2006 (3)

F. Celestini and R. Kofman, Phys. Rev. E 73, 041602 (2006).
[Crossref]

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
[Crossref]

M. Hossein-Zadeh and K. J. Vahala, Opt. Express 14, 10800 (2006).
[Crossref]

2005 (1)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

2004 (2)

T. Mitsui, Jpn. J. Appl. Phys. 43, 6425 (2004).
[Crossref]

D. G. Aarts, M. Schmidt, and H. N. Lekkerkerker, Science 304, 847 (2004).
[Crossref]

2000 (1)

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

1999 (2)

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

J. Eggers, J. R. Lister, and H. A. Stone, J. Fluid Mech. 401, 293 (1999).
[Crossref]

1998 (1)

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

1997 (1)

1992 (1)

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

1991 (1)

M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).
[Crossref]

1984 (1)

1977 (1)

A. Ashkin and J. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[Crossref]

1972 (1)

E. Helfand and Y. Tagami, J. Chem. Phys. 56, 3592 (1972).
[Crossref]

1968 (1)

A. Vrij, Adv. Colloid Interface Sci. 2, 39 (1968).
[Crossref]

1967 (1)

A. Sheludko, Adv. Colloid Interface Sci. 1, 391 (1967).
[Crossref]

1966 (1)

A. Vrij, Discuss. Faraday Soc. 42, 23 (1966).
[Crossref]

1908 (1)

M. Smoluchowski, Ann. Phys. 330, 205 (1908).
[Crossref]

1879 (1)

L. Rayleigh, Proc. R. Soc. London 29, 71 (1879).

Aarts, D. G.

D. G. Aarts, M. Schmidt, and H. N. Lekkerkerker, Science 304, 847 (2004).
[Crossref]

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Alba, M.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Arazi, L.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
[Crossref]

Ashkin, A.

A. Ashkin and J. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Modern Phys. 86, 1391 (2014).
[Crossref]

Behroozi, F.

F. Behroozi, J. Smith, and W. Even, Am. J. Phys. 78, 1165 (2010).
[Crossref]

Birks, T.

Boudet, N.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Braginskii, V. B.

V. B. Braginsky, V. B. Braginskiĭ, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, 1995), p. 137.

Braginsky, V. B.

V. B. Braginsky, V. B. Braginskiĭ, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, 1995), p. 137.

Braslau, A.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Campbell, K.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
[Crossref]

Carmon, T.

S. Maayani, L. L. Martin, and T. Carmon, Nat. Commun. 7, 10435 (2016).
[Crossref]

R. Dahan, L. L. Martin, and T. Carmon, Optica 3, 175 (2016).
[Crossref]

S. Kaminski, L. L. Martin, and T. Carmon, Opt. Express 23, 28914 (2015).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

Celestini, F.

F. Celestini and R. Kofman, Phys. Rev. E 73, 041602 (2006).
[Crossref]

Chang, R.

Cheung, G.

Dahan, R.

Daillant, J.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Dayan, B.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
[Crossref]

Doerr, A.

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

Drever, R. W.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Dziedzic, J.

A. Ashkin and J. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[Crossref]

Eggers, J.

J. Eggers, J. R. Lister, and H. A. Stone, J. Fluid Mech. 401, 293 (1999).
[Crossref]

Erbil, H.

H. Erbil, Solid and Liquid Interfaces (Blackwell, 2006).

Even, W.

F. Behroozi, J. Smith, and W. Even, Am. J. Phys. 78, 1165 (2010).
[Crossref]

Fainman, Y.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
[Crossref]

Fradin, C.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Groisman, A.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
[Crossref]

Gürsel, Y.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Helfand, E.

E. Helfand and Y. Tagami, J. Chem. Phys. 56, 3592 (1972).
[Crossref]

Hossein-Zadeh, M.

Huang, K.

M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).
[Crossref]

Jacques, F.

Jonáš, A.

Kaminski, S.

Karadag, Y.

Kawamura, S.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Khalili, F. Y.

V. B. Braginsky, V. B. Braginskiĭ, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, 1995), p. 137.

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Modern Phys. 86, 1391 (2014).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

Kiraz, A.

Knight, J.

Kofman, R.

F. Celestini and R. Kofman, Phys. Rev. E 73, 041602 (2006).
[Crossref]

Lekkerkerker, H. N.

D. G. Aarts, M. Schmidt, and H. N. Lekkerkerker, Science 304, 847 (2004).
[Crossref]

Levy, U.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
[Crossref]

Li, Z.

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Lister, J. R.

J. Eggers, J. R. Lister, and H. A. Stone, J. Fluid Mech. 401, 293 (1999).
[Crossref]

Long, M.

Lovsky, Y.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
[Crossref]

Luzet, D.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Maayani, S.

S. Maayani, L. L. Martin, and T. Carmon, Nat. Commun. 7, 10435 (2016).
[Crossref]

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Modern Phys. 86, 1391 (2014).
[Crossref]

Martin, L. L.

Mecke, K.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Mestre, M.

Mitsui, T.

T. Mitsui, Jpn. J. Appl. Phys. 43, 6425 (2004).
[Crossref]

Mookherjea, S.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
[Crossref]

Ocko, B.

M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).
[Crossref]

Prange, W.

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

Press, W.

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Raab, F. J.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Rafailovich, M.

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Rayleigh, L.

L. Rayleigh, Proc. R. Soc. London 29, 71 (1879).

Rokhsari, H.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

Rosenblum, S.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
[Crossref]

Sanyal, M.

M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).
[Crossref]

Schlomka, J.-P.

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Schmidt, M.

D. G. Aarts, M. Schmidt, and H. N. Lekkerkerker, Science 304, 847 (2004).
[Crossref]

Seeck, O.

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Seydel, T.

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

Sheludko, A.

A. Sheludko, Adv. Colloid Interface Sci. 1, 391 (1967).
[Crossref]

Shoemaker, D.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Sievers, L.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Sinha, S.

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).
[Crossref]

Smilgies, D.

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

Smith, J.

F. Behroozi, J. Smith, and W. Even, Am. J. Phys. 78, 1165 (2010).
[Crossref]

Smoluchowski, M.

M. Smoluchowski, Ann. Phys. 330, 205 (1908).
[Crossref]

Sokolov, J.

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Stone, H. A.

J. Eggers, J. R. Lister, and H. A. Stone, J. Fluid Mech. 401, 293 (1999).
[Crossref]

Struth, B.

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

Tagami, Y.

E. Helfand and Y. Tagami, J. Chem. Phys. 56, 3592 (1972).
[Crossref]

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

V. B. Braginsky, V. B. Braginskiĭ, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, 1995), p. 137.

Tolan, M.

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Tzeng, H.-M.

Vahala, K. J.

M. Hossein-Zadeh and K. J. Vahala, Opt. Express 14, 10800 (2006).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

Vollmer, F.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
[Crossref]

Vrij, A.

A. Vrij, Adv. Colloid Interface Sci. 2, 39 (1968).
[Crossref]

A. Vrij, Discuss. Faraday Soc. 42, 23 (1966).
[Crossref]

Wall, K. F.

Wang, J.

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

Yang, L.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

Adv. Colloid Interface Sci. (2)

A. Vrij, Adv. Colloid Interface Sci. 2, 39 (1968).
[Crossref]

A. Sheludko, Adv. Colloid Interface Sci. 1, 391 (1967).
[Crossref]

Am. J. Phys. (1)

F. Behroozi, J. Smith, and W. Even, Am. J. Phys. 78, 1165 (2010).
[Crossref]

Ann. Phys. (1)

M. Smoluchowski, Ann. Phys. 330, 205 (1908).
[Crossref]

Appl. Phys. Lett. (1)

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, Appl. Phys. Lett. 88, 111107 (2006).
[Crossref]

Discuss. Faraday Soc. (1)

A. Vrij, Discuss. Faraday Soc. 42, 23 (1966).
[Crossref]

J. Chem. Phys. (1)

E. Helfand and Y. Tagami, J. Chem. Phys. 56, 3592 (1972).
[Crossref]

J. Fluid Mech. (1)

J. Eggers, J. R. Lister, and H. A. Stone, J. Fluid Mech. 401, 293 (1999).
[Crossref]

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

T. Mitsui, Jpn. J. Appl. Phys. 43, 6425 (2004).
[Crossref]

Nat. Commun. (2)

S. Maayani, L. L. Martin, and T. Carmon, Nat. Commun. 7, 10435 (2016).
[Crossref]

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, Nat. Commun. 6, 6788 (2015).
[Crossref]

Nature (1)

C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant, Nature 403, 871 (2000).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Optica (1)

Phys. Rev. E (1)

F. Celestini and R. Kofman, Phys. Rev. E 73, 041602 (2006).
[Crossref]

Phys. Rev. Lett. (5)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

A. Ashkin and J. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[Crossref]

M. Sanyal, S. Sinha, K. Huang, and B. Ocko, Phys. Rev. Lett. 66, 628 (1991).
[Crossref]

M. Tolan, O. Seeck, J.-P. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M. Rafailovich, and J. Sokolov, Phys. Rev. Lett. 81, 2731 (1998).
[Crossref]

A. Doerr, M. Tolan, W. Prange, J.-P. Schlomka, T. Seydel, W. Press, D. Smilgies, and B. Struth, Phys. Rev. Lett. 83, 3470 (1999).
[Crossref]

Proc. R. Soc. London (1)

L. Rayleigh, Proc. R. Soc. London 29, 71 (1879).

Rev. Modern Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Modern Phys. 86, 1391 (2014).
[Crossref]

Science (2)

D. G. Aarts, M. Schmidt, and H. N. Lekkerkerker, Science 304, 847 (2004).
[Crossref]

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, and K. S. Thorne, Science 256, 325 (1992).
[Crossref]

Other (2)

V. B. Braginsky, V. B. Braginskiĭ, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, 1995), p. 137.

H. Erbil, Solid and Liquid Interfaces (Blackwell, 2006).

Supplementary Material (3)

NameDescription
» Visualization 1: AVI (449 KB)      Calculated first droplet eigenmode. The shape of the first capillary mode.
» Visualization 2: AVI (7178 KB)      Calculated second droplet eigenmode. The shape of the second capillary mode.
» Visualization 3: AVI (6237 KB)      Listening to droplet thermal fluctuations (soundtrack) while sweeping the laser via two resonances (movie). The fluctuation in droplet radius is converted to audio as-is and with no signal processing or frequency conversion.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Experimental setup: (a) Micrograph of the water microdroplet along with its calculated fundamental optical mode shape (inset). (b) A Lorentzian transfer function (black) converts radius drifts (red) into changes in the optical transmission (blue). (c) Monitoring droplet resonator transmission while scanning a wavelength through the resonance reveals its optical quality factor. (d) Experimental setup scheme. Laser wavelength is 980 nm.

Fig. 2.
Fig. 2.

Experimental results: Droplet fluctuations are shown in the (a) temporal and (b) frequency domains, where the oscillation frequencies that dominate over their vicinity are linked to calculated droplet modes (inset); see Visualization 2 and Visualization 3. The blue arrows lead to a zoomed-in plot where each of the points represents the transmission average over a 125 ns period. The error bar represents the standard deviation for each average. Presenting the capillary spectrum on a (c) log–log scale reveals a drop at high frequencies where the black line represents a Lorentzian fit. The Lorentzian “skirt” dominates at the high frequencies on the right-hand side of (c). The stem holding the droplets has a radius of 5 μm and the droplet radius is 16 μm and the optical wavelength is 980 nm. Deformation in the three-dimensional plots is exaggerated in the graphics.

Fig. 3.
Fig. 3.

Experimentally reaching maximal optocapillary coupling at the region where the optical resonance has the steepest transmission slope. (a) Slowly scanning the laser frequency while light is coupled to the optical resonance reveals its spectral transmission. Spectral transmission is then split into (b) AC components representing transmission oscillations (by capillaries) and to (c) DC representing the Lorentzian shape of the optical resonance. (d) The optocapillary coupling is measured through the amplitude of the AC transmission oscillation. (e) As one can see in (f), optocapillary coupling (F, black) is maximal at the green background regions [in (a)–(f)] where cavity transmission is the steepest. The points in (d) represent averaging over the oscillation amplitude (in this region), and the error bars represent the standard deviation of the oscillation amplitude. The diameter of the droplet is 118 μm and its optical quality factor is 19500.

Tables (1)

Tables Icon

Table 1. Different Waves Possible in Water a

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Δ T = Q r Δ r ,
f = 2 γ / ( π 2 ρ r 3 ) k / ( 2 3 π r 3 ρ ) ,
k B T = k Δ r 2 ,

Metrics