Abstract

Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) is important for tailoring them to experimental needs. Here we report on a novel experimental mode analysis technique based on the combination of frequency analysis and far-field imaging for high mode numbers of large WGMRs. The radial mode numbers q and the angular mode numbers p = -m are identified and labeled via far-field imaging. The polar mode numbers are determined unambiguously by fitting the frequency differences between individual whispering gallery modes (WGMs). This allows for the accurate determination of the geometry and the refractive index at different temperatures of the WGMR. For future applications in classical and quantum optics, this mode analysis enables one to control the narrow-band phase-matching conditions in nonlinear processes such as second-harmonic generation or parametric down-conversion.

© 2014 Optical Society of America

Full Article  |  PDF Article

Corrections

5 December 2014: A correction was made to Ref. 4.

21 December 2015: A correction was made to Eq. (4).


OSA Recommended Articles
Dielectric tuning and coupling of whispering gallery modes using an anisotropic prism

Matthew R. Foreman, Florian Sedlmeir, Harald G. L. Schwefel, and Gerd Leuchs
J. Opt. Soc. Am. B 33(11) 2177-2195 (2016)

Observation of whispering-gallery and directional resonant laser emission in ellipsoidal microcavities

Liangmin Zhang, You-Xiong Wang, Fajian Zhang, and Richard O. Claus
J. Opt. Soc. Am. B 23(9) 1793-1800 (2006)

References

  • View by:
  • |
  • |
  • |

  1. A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum. Electron. 12, 3–14 (2006).
    [Crossref]
  2. V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
    [Crossref]
  3. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
    [Crossref] [PubMed]
  4. F. Sedlmeir, R. Zeltner, G. Leuchs, and H. G. L. Schwefel, “High-Q MgF2 whispering gallery mode resonators for refractometric sensing in aqueous environment,” Opt. Express 22(25), 30934–30942 (2014).
  5. D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
    [Crossref]
  6. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
    [Crossref] [PubMed]
  7. S. P. Vyatchanin, M. L. Gorodetsky, and V. S. Ilchenko, “Tunable narrow-band optical filters with modes of the whispering gallery type,” J. Appl. Spectrosc. 56, 182–187 (1992).
    [Crossref]
  8. M. C. Collodo, F. Sedlmeir, B. Sprenger, S. Svitlov, L. J. Wang, and H. G. L. Schwefel, “Sub-kHz lasing of a CaF2 whispering gallery mode resonator stabilized fiber ring laser,” Opt. Express 22, 19277–19283 (2014).
    [Crossref] [PubMed]
  9. J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical micro-resonators,” Adv. Atom. Mol. Opt. Phy. 58, 207–323 (2010).
    [Crossref]
  10. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
    [Crossref]
  11. J. Yu, K. Giulietti, F. Sourgen, A. Ross, J. P. Wolf, M. Ferriol, G. Foulon, C. Goutaudier, M. T. Cohen-Adad, and G. Boulon, “Second-harmonic generation in a microradius LiNbO3 cylinder with a quasi-elliptical cross section,” Opt. Lett. 24, 394–396 (1999).
    [Crossref]
  12. A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
    [Crossref]
  13. J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
    [Crossref] [PubMed]
  14. J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
    [Crossref]
  15. C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
    [Crossref]
  16. D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New J. Phys. 16, 053025 (2014).
    [Crossref]
  17. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
    [Crossref]
  18. W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
    [Crossref] [PubMed]
  19. J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
    [Crossref] [PubMed]
  20. M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
    [Crossref] [PubMed]
  21. C. S. Werner, T. Beckmann, K. Buse, and I. Breunig, “Blue-pumped whispering gallery optical parametric oscillator,” Opt. Lett. 37, 4224–4226 (2012).
    [Crossref] [PubMed]
  22. C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
    [Crossref]
  23. J. C. Knight, N. Dubreuil, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Mapping whispering-gallery modes in microspheres with a near-field probe,” Opt. Lett. 20, 1515–1517 (1995).
    [Crossref] [PubMed]
  24. A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
    [Crossref]
  25. A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
    [Crossref]
  26. G. Lin, B. Qian, F. Orucević, Y. Candela, J.-B. Jager, Z. Cai, V. Lefèvre-Seguin, and J. Hare, “Excitation mapping of whispering gallery modes in silica microcavities,” Opt. Lett. 35, 583–585 (2010).
    [Crossref] [PubMed]
  27. D. Keng, X. Tan, and S. Arnold, “Whispering gallery micro-global positioning system for nanoparticle sizing in real time,” Appl Phys. Lett. 105, 071105 (2014).
    [Crossref]
  28. M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133–143 (1994).
    [Crossref]
  29. A. Savchenkov, A. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76, 023816 (2007).
    [Crossref]
  30. T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
    [Crossref] [PubMed]
  31. C. Dong, Y. Xiao, Y. Yang, Z. Han, G. Guo, and L. Yang, “Directly mapping whispering gallery modes in a microsphere through modal coupling and directional emission,” Chin. Opt. Lett. 6, 300–302 (2008).
    [Crossref]
  32. F. Sedlmeir, M. Hauer, J. Fürst, G. Leuchs, and H. G. L. Schwefel, “Experimental characterization of an uniaxial angle cut whispering gallery mode resonator,” Opt. Express 21, 23942–23949 (2013).
    [Crossref] [PubMed]
  33. S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 1138–1140 (1991).
    [Crossref] [PubMed]
  34. S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the Terahertz frequency range,” Opt. Express 16, 7336–7343 (2008).
    [Crossref] [PubMed]
  35. J. Li, H. Lee, K. Yang, and K. Vahala, “Sideband spectroscopy and dispersion measurement in microcavities,” Opt. Express 20, 26337–26344 (2012).
    [Crossref] [PubMed]
  36. A. N. Oraevsky, “Whispering-gallery waves,” Quant. Electron. 32, 377–400 (2002).
    [Crossref]
  37. M. L. Gorodetsky and Y. A. Demchenko, “Accurate analytical estimates of eigenfrequencies and dispersion in whispering-gallery spheroidal resonators,” Proc. SPIE 8236, 823623 (2012).
    [Crossref]
  38. I. Breunig, B. Sturman, F. Sedlmeir, H. G. L. Schwefel, and K. Buse, “Whispering gallery modes at the rim of an axisymmetric optical resonator: Analytical versus numerical description and comparison with experiment,” Opt. Express 21, 30683–30692 (2013).
    [Crossref]
  39. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
    [Crossref]
  40. M. Gorodetsky and A. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Topics Quantum Electron. 12, 33–39 (2006).
    [Crossref]
  41. U. Schlarb and K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
    [Crossref]

2014 (4)

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New J. Phys. 16, 053025 (2014).
[Crossref]

D. Keng, X. Tan, and S. Arnold, “Whispering gallery micro-global positioning system for nanoparticle sizing in real time,” Appl Phys. Lett. 105, 071105 (2014).
[Crossref]

M. C. Collodo, F. Sedlmeir, B. Sprenger, S. Svitlov, L. J. Wang, and H. G. L. Schwefel, “Sub-kHz lasing of a CaF2 whispering gallery mode resonator stabilized fiber ring laser,” Opt. Express 22, 19277–19283 (2014).
[Crossref] [PubMed]

F. Sedlmeir, R. Zeltner, G. Leuchs, and H. G. L. Schwefel, “High-Q MgF2 whispering gallery mode resonators for refractometric sensing in aqueous environment,” Opt. Express 22(25), 30934–30942 (2014).

2013 (5)

F. Sedlmeir, M. Hauer, J. Fürst, G. Leuchs, and H. G. L. Schwefel, “Experimental characterization of an uniaxial angle cut whispering gallery mode resonator,” Opt. Express 21, 23942–23949 (2013).
[Crossref] [PubMed]

I. Breunig, B. Sturman, F. Sedlmeir, H. G. L. Schwefel, and K. Buse, “Whispering gallery modes at the rim of an axisymmetric optical resonator: Analytical versus numerical description and comparison with experiment,” Opt. Express 21, 30683–30692 (2013).
[Crossref]

C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (2)

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

2010 (4)

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical micro-resonators,” Adv. Atom. Mol. Opt. Phy. 58, 207–323 (2010).
[Crossref]

G. Lin, B. Qian, F. Orucević, Y. Candela, J.-B. Jager, Z. Cai, V. Lefèvre-Seguin, and J. Hare, “Excitation mapping of whispering gallery modes in silica microcavities,” Opt. Lett. 35, 583–585 (2010).
[Crossref] [PubMed]

2008 (4)

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the Terahertz frequency range,” Opt. Express 16, 7336–7343 (2008).
[Crossref] [PubMed]

C. Dong, Y. Xiao, Y. Yang, Z. Han, G. Guo, and L. Yang, “Directly mapping whispering gallery modes in a microsphere through modal coupling and directional emission,” Chin. Opt. Lett. 6, 300–302 (2008).
[Crossref]

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

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref] [PubMed]

2007 (2)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

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

2006 (3)

M. Gorodetsky and A. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Topics Quantum Electron. 12, 33–39 (2006).
[Crossref]

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum. Electron. 12, 3–14 (2006).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

2005 (2)

A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
[Crossref]

2004 (1)

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

2002 (1)

A. N. Oraevsky, “Whispering-gallery waves,” Quant. Electron. 32, 377–400 (2002).
[Crossref]

1999 (2)

1998 (1)

D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
[Crossref]

1995 (1)

1994 (2)

U. Schlarb and K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133–143 (1994).
[Crossref]

1992 (2)

C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
[Crossref]

S. P. Vyatchanin, M. L. Gorodetsky, and V. S. Ilchenko, “Tunable narrow-band optical filters with modes of the whispering gallery type,” J. Appl. Spectrosc. 56, 182–187 (1992).
[Crossref]

1991 (1)

1989 (1)

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Aiello, A.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

Andersen, U.

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

Andersen, U. L.

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Arnold, S.

D. Keng, X. Tan, and S. Arnold, “Whispering gallery micro-global positioning system for nanoparticle sizing in real time,” Appl Phys. Lett. 105, 071105 (2014).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref] [PubMed]

Beckmann, T.

Benson, O.

A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
[Crossref]

Betzler, K.

U. Schlarb and K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[Crossref]

Boulon, G.

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Braginsky, V.

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

Breunig, I.

Buse, K.

Byer, R. L.

Cai, Z.

Candela, Y.

Carmon, T.

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

Chekhova, M. V.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

Cohen-Adad, M. T.

Collodo, M. C.

Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Demchenko, Y. A.

M. L. Gorodetsky and Y. A. Demchenko, “Accurate analytical estimates of eigenfrequencies and dispersion in whispering-gallery spheroidal resonators,” Proc. SPIE 8236, 823623 (2012).
[Crossref]

Döhler, G. H.

Dong, C.

Dubreuil, N.

Elser, D.

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

Ferriol, M.

Fomin, A.

M. Gorodetsky and A. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Topics Quantum Electron. 12, 33–39 (2006).
[Crossref]

Förtsch, M.

C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
[Crossref]

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

Foulon, G.

Fürst, J.

C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
[Crossref]

F. Sedlmeir, M. Hauer, J. Fürst, G. Leuchs, and H. G. L. Schwefel, “Experimental characterization of an uniaxial angle cut whispering gallery mode resonator,” Opt. Express 21, 23942–23949 (2013).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

Fürst, J. U.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

Furusawa, A.

D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
[Crossref]

Georgiades, N.

D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
[Crossref]

Giulietti, K.

Gorodetsky, M.

M. Gorodetsky and A. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Topics Quantum Electron. 12, 33–39 (2006).
[Crossref]

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Gorodetsky, M. L.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

M. L. Gorodetsky and Y. A. Demchenko, “Accurate analytical estimates of eigenfrequencies and dispersion in whispering-gallery spheroidal resonators,” Proc. SPIE 8236, 823623 (2012).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133–143 (1994).
[Crossref]

S. P. Vyatchanin, M. L. Gorodetsky, and V. S. Ilchenko, “Tunable narrow-band optical filters with modes of the whispering gallery type,” J. Appl. Spectrosc. 56, 182–187 (1992).
[Crossref]

Gossard, A. C.

Götzinger, S.

A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
[Crossref]

Goutaudier, C.

Guo, G.

Han, Z.

Hanson, M.

Hare, J.

Haroche, S.

Hauer, M.

Herr, T.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

Hofer, J.

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical micro-resonators,” Adv. Atom. Mol. Opt. Phy. 58, 207–323 (2010).
[Crossref]

Holzwarth, R.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Huang, Y.-P.

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New J. Phys. 16, 053025 (2014).
[Crossref]

Ilchenko, V.

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum. Electron. 12, 3–14 (2006).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
[Crossref]

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Ilchenko, V. S.

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref] [PubMed]

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

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133–143 (1994).
[Crossref]

S. P. Vyatchanin, M. L. Gorodetsky, and V. S. Ilchenko, “Tunable narrow-band optical filters with modes of the whispering gallery type,” J. Appl. Spectrosc. 56, 182–187 (1992).
[Crossref]

Jager, J.-B.

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

Keng, D.

D. Keng, X. Tan, and S. Arnold, “Whispering gallery micro-global positioning system for nanoparticle sizing in real time,” Appl Phys. Lett. 105, 071105 (2014).
[Crossref]

Kimble, H.

D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
[Crossref]

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Kippenberg, T. J.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical micro-resonators,” Adv. Atom. Mol. Opt. Phy. 58, 207–323 (2010).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Knight, J. C.

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

Kowligy, A. S.

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New J. Phys. 16, 053025 (2014).
[Crossref]

Kumar, P.

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New J. Phys. 16, 053025 (2014).
[Crossref]

Lam, C. C.

Lassen, M.

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

Lee, H.

Lefèvre-Seguin, V.

Leuchs, G.

F. Sedlmeir, R. Zeltner, G. Leuchs, and H. G. L. Schwefel, “High-Q MgF2 whispering gallery mode resonators for refractometric sensing in aqueous environment,” Opt. Express 22(25), 30934–30942 (2014).

F. Sedlmeir, M. Hauer, J. Fürst, G. Leuchs, and H. G. L. Schwefel, “Experimental characterization of an uniaxial angle cut whispering gallery mode resonator,” Opt. Express 21, 23942–23949 (2013).
[Crossref] [PubMed]

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
[Crossref]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

Leung, P. T.

Li, J.

Liang, W.

Lin, G.

Maleki, L.

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref] [PubMed]

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

A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Malzer, S.

Marquardt, C.

C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
[Crossref]

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

Matsko, A.

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

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum. Electron. 12, 3–14 (2006).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Matsko, A. B.

Mazzei, A.

A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
[Crossref]

Menezes, L. S.

A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
[Crossref]

Mohageg, M.

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Oraevsky, A. N.

A. N. Oraevsky, “Whispering-gallery waves,” Quant. Electron. 32, 377–400 (2002).
[Crossref]

Orucevic, F.

Oxborrow, M.

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

Parkins, A. S.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Preu, S.

Qian, B.

Raimond, J. M.

Ross, A.

Sandoghdar, V.

A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
[Crossref]

J. C. Knight, N. Dubreuil, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Mapping whispering-gallery modes in microspheres with a near-field probe,” Opt. Lett. 20, 1515–1517 (1995).
[Crossref] [PubMed]

Savchenkov, A.

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

A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Savchenkov, A. A.

Schiller, S.

Schlarb, U.

U. Schlarb and K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[Crossref]

Schliesser, A.

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical micro-resonators,” Adv. Atom. Mol. Opt. Phy. 58, 207–323 (2010).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Schwefel, H. G. L.

Sedlmeir, F.

Seidel, D.

Silberhorn, C.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

Sourgen, F.

Sprenger, B.

Stone, A. D.

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

Strekalov, D.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
[Crossref]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

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

A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
[Crossref]

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Strekalov, D. V.

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New J. Phys. 16, 053025 (2014).
[Crossref]

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

Sturman, B.

Svitlov, S.

Tan, X.

D. Keng, X. Tan, and S. Arnold, “Whispering gallery micro-global positioning system for nanoparticle sizing in real time,” Appl Phys. Lett. 105, 071105 (2014).
[Crossref]

Vahala, K.

Vahala, K. J.

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

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Vernooy, D.

D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
[Crossref]

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref] [PubMed]

Vyatchanin, S. P.

S. P. Vyatchanin, M. L. Gorodetsky, and V. S. Ilchenko, “Tunable narrow-band optical filters with modes of the whispering gallery type,” J. Appl. Spectrosc. 56, 182–187 (1992).
[Crossref]

Wang, C. Y.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

Wang, L. J.

Werner, C. S.

Wilcut, E.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Wittmann, C.

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

Wolf, J. P.

Xiao, Y.

Yang, K.

Yang, L.

C. Dong, Y. Xiao, Y. Yang, Z. Han, G. Guo, and L. Yang, “Directly mapping whispering gallery modes in a microsphere through modal coupling and directional emission,” Chin. Opt. Lett. 6, 300–302 (2008).
[Crossref]

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

Yang, Y.

Young, K.

Yu, J.

Zeltner, R.

Zimmerman, J. D.

Adv. Atom. Mol. Opt. Phy. (1)

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical micro-resonators,” Adv. Atom. Mol. Opt. Phy. 58, 207–323 (2010).
[Crossref]

Appl Phys. Lett. (1)

D. Keng, X. Tan, and S. Arnold, “Whispering gallery micro-global positioning system for nanoparticle sizing in real time,” Appl Phys. Lett. 105, 071105 (2014).
[Crossref]

Chin. Opt. Lett. (1)

Electron. Lett. (1)

A. Savchenkov, A. Matsko, D. Strekalov, V. Ilchenko, and L. Maleki, “Mode filtering in optical whispering gallery resonators,” Electron. Lett. 41, 495 (2005).
[Crossref]

IEEE J. Sel. Top. Quantum. Electron. (1)

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes-part I: basics,” IEEE J. Sel. Top. Quantum. Electron. 12, 3–14 (2006).
[Crossref]

IEEE J. Sel. Topics Quantum Electron. (1)

M. Gorodetsky and A. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Topics Quantum Electron. 12, 33–39 (2006).
[Crossref]

J. Appl. Spectrosc. (1)

S. P. Vyatchanin, M. L. Gorodetsky, and V. S. Ilchenko, “Tunable narrow-band optical filters with modes of the whispering gallery type,” J. Appl. Spectrosc. 56, 182–187 (1992).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

M. Förtsch, J. U. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 4, 1818 (2013).
[Crossref] [PubMed]

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref] [PubMed]

Nat. Photonics (1)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

Nature (2)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

New J. Phys. (1)

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New J. Phys. 16, 053025 (2014).
[Crossref]

Opt. Commun. (2)

A. Mazzei, S. Götzinger, L. S. Menezes, V. Sandoghdar, and O. Benson, “Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe,” Opt. Commun. 250, 428–433 (2005).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113, 133–143 (1994).
[Crossref]

Opt. Express (6)

Opt. Lett. (6)

Opt. Photon. News (1)

C. Marquardt, D. Strekalov, J. Fürst, M. Förtsch, and G. Leuchs, “Nonlinear optics in crystalline whispering gallery resonators,” Opt. Photon. News 24, 38–45 (2013).
[Crossref]

Phys. Lett. A (1)

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Phys. Rev. A (2)

D. Vernooy, A. Furusawa, N. Georgiades, V. Ilchenko, and H. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, 2293–2296 (1998).
[Crossref]

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

Phys. Rev. B (1)

U. Schlarb and K. Betzler, “Influence of the defect structure on the refractive indices of undoped and Mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[Crossref]

Phys. Rev. Lett. (5)

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

A. Savchenkov, A. Matsko, D. Strekalov, M. Mohageg, V. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

J. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref] [PubMed]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. Fürst, D. Strekalov, D. Elser, A. Aiello, U. Andersen, C. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
[Crossref] [PubMed]

Proc. SPIE (1)

M. L. Gorodetsky and Y. A. Demchenko, “Accurate analytical estimates of eigenfrequencies and dispersion in whispering-gallery spheroidal resonators,” Proc. SPIE 8236, 823623 (2012).
[Crossref]

Quant. Electron. (1)

A. N. Oraevsky, “Whispering-gallery waves,” Quant. Electron. 32, 377–400 (2002).
[Crossref]

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 (6)

Fig. 1
Fig. 1 Spatial structure of WGMs. The coordinate system for the electric field distributions defined by Eq. (1) is based on the radial distance u of the observation point to the surface of the WGMR, the polar angle θ, and the azimuthal angle ϕ. The intensity distributions on the right-hand side are shown for various radial mode numbers q and angular mode numbers p=-m.
Fig. 2
Fig. 2 Illustration of a WGMR mode spectrum. As for all resonators, the free spectral range is the characteristic mode spacing for one mode family. Here, we show two mode families (dashed and solid lines), whose respective free spectral ranges (FSR,1 ≠ FSRℓ′,2, see Eq. (7)) are determined by geometric dispersion. In addition to equatorial WGMs {q ≥ 1, p = 0}, each mode family contains non-equatorial WGMs {q ≥ 1, p ≠ 0} at an offset frequency given by Eq. (9). Within a given spectral observation window, the frequency differences of the WGMs belonging to different mode families allow to unambiguously identify the polar mode number .
Fig. 3
Fig. 3 Illustration of the experimental setup showing the spectral and spatial mode analysis detection.
Fig. 4
Fig. 4 Labeled transmission spectra. Transmission spectra at λ = 532 nm of the macroscopic WGMR (major radius R = 1.59 mm) measured at T = 70°C (a) and T = 57°C (c). The radial mode numbers q and the angular mode numbers p = − m are assigned according to the far-field emission patterns (see Fig. 5). Frequencies are specified relative to the frequency ν,q=1,p=0 of the fundamental WGM {q=1,p=0}, which is highlighted in grey. Non-equatorial WGMs {q ≥ 1, p ≠ 0} exhibit a fixed frequency difference to the respective equatorial WGM {q ≥ 1, p=0} (see Fig. (a) and Eq. (9)). Fig. (b) shows measured (square markers) and calculated (vertical lines) frequency differences Δν,1,0, Δq, Δp = 0) according to Eq. (5) for different equatorial WGMs {q ≥ 1, p=0} at different temperatures. Temperature tuning of these WGMs exhibits different slopes due to their different FSR,q given by Eq. (7). The frequency spectrum at a given temperature is then directly related to the polar mode number ( = m for equatorial WGMs) of the fundamental WGM shown on the right axis.
Fig. 5
Fig. 5 a) Far-field emission patterns of various low-order WGMs (see Fig. 4(a) for the corresponding frequency spectrum). The WGMs {q=2,p=0} and {3,2} exhibit distortions in the far-field images, which probably originate from their frequency degeneracy to other WGMs. The horizontal center positions of the intensity distributions shift to the left (towards smaller Φ) for higher radial mode numbers q. b) Averaged vertical cross section for WGMs with the same p but different q. This gives information on the distribution of the WGMs in θ-direction, which allows a distinction between different angular mode numbers p. c) Distinction of different radial mode numbers q of equatorial WGMs (p=0) according to the coupling angle Φ. Within our spectral observation window, the higher the radial mode number q, the smaller is and Φ. The exact polar mode numbers used for the calculated out-coupling angles Φ (see Eq. (2)) are derived from an analysis of the spectrum.
Fig. 6
Fig. 6 Evaluation of the measured frequency spectrum (see Fig. 4(a)). a) The mismatch between measured and computed frequency differences (see Eq. (5)) over a broad range of numbers of the fundamental WGM {q=1,p=0}. The frequency mismatches of a selection of equatorial WGMs are shown. The individual mismatches reach zero at multiple values of , however, all together they reach zero at the unique value of = 41903 in b).

Equations (10)

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

E e 1 2 ( θ θ m ) 2 H p ( θ θ m ) e i m ϕ angular part Ai ( u u m α q ) radial part ,
θ m = ( R / ρ ) 3 / 4 m 1 / 2 , u m = R / 2 1 / 3 m 2 / 3 ,
sin Φ = λ n prism 2 π R ,
Δ Φ 2 = n 2 1 λ n prism 2 2 π R cos 2 Φ .
ν , q , p = c 2 π n R 1 / x [ + α q ( 2 ) 1 / 3 + p ( R ρ 1 ) χ n n 2 1 + 1 2 R ρ + 3 α q 2 20 ( 2 ) 1 / 3 + O ( 2 / 3 ) ] ,
Δ ν , q , p ( Δ , Δ q , Δ p ) = ν + Δ , q + Δ q , p + Δ p ν , q , p
x d = x ( 1 + ν , q , p n n ν | ν , q , p ) ,
Δ ν , q , p ( Δ = 1 , 0 , 0 ) FSR , q 1 x d [ 1 + α q 6 ( 2 ) 2 3 ] .
Δ ν , q , p ( 0 , Δ q , 0 ) 1 x d ( α q + Δ q α q ) ( 2 ) 1 3
Δ ν , q , p ( 0 , 0 , Δ p ) 1 x d ( R ρ 1 ) Δ p ,

Metrics