Abstract

In this paper, we give a general model for analysis of multimode Whispering Gallery Mode (WGM) resonators coupled to multimode tapered fibers based on the coupled-mode theory. Such formulation takes into account the asymmetry of the taper-resonator coupling. Simulations for a microsphere show that the tapered fiber coupling mechanism induces cross-coupling between coherent orthonormal WGMs. We show that the degree of such cross-coupling depends basically on the fiber diameter, air-gap between the taper and resonator, intrinsic losses and eccentricity. The WGM cross-coupling affects the total transmission and spectral line-shape of the internal powers resulting in a controllable transformation of the line-shape to non-Lorentzian spectra. This analysis can be utilized to precisely determine the output and intra-cavity intensity of multimode microresonators, which is important in lasers, nonlinear optical signal generation and realization of optical delays.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2019 (1)

2018 (1)

2017 (2)

T. X. Hoang, S. N. Nagelberg, M. Kolle, and G. Barbastathis, “Fano resonances from coupled whispering-gallery modes in photonic molecules,” Opt. Express 25, 13125–13144 (2017).
[Crossref] [PubMed]

Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6, 789–811 (2017).
[Crossref]

2016 (4)

2015 (1)

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7, 168–240 (2015).
[Crossref]

2013 (3)

X. Wu and L. Tong, “Optical microfibers and nanofibers,” Nanophotonics 2, 407–428 (2013).
[Crossref]

J.-M. Cui, C.-H. Dong, C.-L. Zou, F.-W. Sun, Y.-F. Xiao, Z.-F. Han, and G.-C. Guo, “Controlling deformation in a high quality factor silica microsphere toward single directional emission,” Appl. Opt. 52, 298–301 (2013).
[Crossref] [PubMed]

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113, 243101 (2013).
[Crossref]

2012 (1)

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

2011 (3)

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev. 5, 553–570 (2011).
[Crossref]

2010 (2)

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

M. Sumetsky, Y. Dulashko, and R. Windeler, “Super free spectral range tunable optical microbubble resonator,” Opt. Lett. 35, 1866–1868(2010).
[Crossref] [PubMed]

2009 (2)

M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
[Crossref] [PubMed]

L. Deych and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer,” Phys. Rev. A 80, 061805 (2009).
[Crossref]

2008 (2)

2007 (2)

2006 (3)

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

M. A. Popovic, C. Manolatou, and M. R. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14, 1208–1222 (2006).
[Crossref] [PubMed]

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonators,” J. Phys. D: Appl. Phys. 39, 5133–5136 (2006).
[Crossref]

2003 (1)

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

1999 (1)

1998 (1)

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

1995 (1)

1987 (2)

C. Shun-Lien, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. 23, 499–509 (1987).
[Crossref]

C. Shun-Lien, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5, 174–183 (1987).
[Crossref]

Bakhtiari Gorajoobi, S.

Barbastathis, G.

Benson, O.

J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev. 5, 553–570 (2011).
[Crossref]

Borri, P.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113, 243101 (2013).
[Crossref]

Borri., P.

Chantada, L.

Chen, Y.-L.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Chi, M.-B.

Chiasera, A.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Cui, J.-M.

Deych, L.

L. Deych and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer,” Phys. Rev. A 80, 061805 (2009).
[Crossref]

Dinyari, K. N.

M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
[Crossref] [PubMed]

Dong, C.-H.

Dubreuil, N.

Dulashko, Y.

Dumeige, Y.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Feron, P.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Ferrari, M.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Fomin, A. E.

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

Foreman, M. R.

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7, 168–240 (2015).
[Crossref]

Gong, Q.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

Gorajoobi, S. B.

Gorodetsky, M. L.

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

Guo, G.-C.

Guo, Z.

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonators,” J. Phys. D: Appl. Phys. 39, 5133–5136 (2006).
[Crossref]

Han, Z.-F.

Hao, P.

Hare, J.

Haroche, S.

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

Haus, H. A.

Hoang, T. X.

Ilchenko, V. S.

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

Ioppolo, T.

Ivanov, A. L.

Jestin, Y.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Jiang, X.-F.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

Knight, J. C.

Kolle, M.

Kozhevnikov, M.

Laine, J.-P.

Langbein, W.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113, 243101 (2013).
[Crossref]

L. Chantada, N. I. Nikolaev, A. L. Ivanov, P. Borri., and W. Langbein, “Optical resonances in microcylinders: response to perturbations for biosensing,” J. Opt. Soc. Am. B 25, 1312–1321 (2008).
[Crossref]

Larsson, M.

M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
[Crossref] [PubMed]

Lefevre, V.

Lefevre-Seguin, V.

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

Leuchs, G.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Leventhal, D. K.

Li, B.-B.

Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6, 789–811 (2017).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

Li, Y.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

Liao, J.

Little, B. E.

Liu, L.

Liu, Y.-C.

Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6, 789–811 (2017).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

Lutti, J.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113, 243101 (2013).
[Crossref]

Manolatou, C.

Marquardt, C.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Matsko, A. B.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Min, B.

B. Min, L. Yang, and K. Vahala, “Perturbative analytic theory of an ultrahigh-Q toroidal microcavity,” Phys. Rev. A 76, 013823 (2007).
[Crossref]

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Nunzi Conti, G.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Otugen, M. V.

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

Park, Y.-S.

Pau, S.

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonators,” J. Phys. D: Appl. Phys. 39, 5133–5136 (2006).
[Crossref]

Pelli, S.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Popovic, M. A.

Quan, H.

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonators,” J. Phys. D: Appl. Phys. 39, 5133–5136 (2006).
[Crossref]

Raimond, J. M.

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

Righini, G. C.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

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L. Deych and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer,” Phys. Rev. A 80, 061805 (2009).
[Crossref]

Sandoghdar, V.

Schmitzer, H.

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113, 243101 (2013).
[Crossref]

Schwefel, H. G.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

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Sheverev, V.

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C. Shun-Lien, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. 23, 499–509 (1987).
[Crossref]

C. Shun-Lien, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5, 174–183 (1987).
[Crossref]

Soria, S.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

Stepaniuk, V.

Strekalov, D. V.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Sumetsky, M.

Sun, F.-W.

J.-M. Cui, C.-H. Dong, C.-L. Zou, F.-W. Sun, Y.-F. Xiao, Z.-F. Han, and G.-C. Guo, “Controlling deformation in a high quality factor silica microsphere toward single directional emission,” Appl. Opt. 52, 298–301 (2013).
[Crossref] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

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M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7, 168–240 (2015).
[Crossref]

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X. Wu and L. Tong, “Optical microfibers and nanofibers,” Nanophotonics 2, 407–428 (2013).
[Crossref]

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

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B. Min, L. Yang, and K. Vahala, “Perturbative analytic theory of an ultrahigh-Q toroidal microcavity,” Phys. Rev. A 76, 013823 (2007).
[Crossref]

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S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

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

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

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M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7, 168–240 (2015).
[Crossref]

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H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113, 243101 (2013).
[Crossref]

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M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
[Crossref] [PubMed]

Wang, Y.

Ward, J.

J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev. 5, 553–570 (2011).
[Crossref]

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Windeler, R.

Wu, X.

Wu, Y.-H.

Xiao, Y.-F.

Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6, 789–811 (2017).
[Crossref]

J.-M. Cui, C.-H. Dong, C.-L. Zou, F.-W. Sun, Y.-F. Xiao, Z.-F. Han, and G.-C. Guo, “Controlling deformation in a high quality factor silica microsphere toward single directional emission,” Appl. Opt. 52, 298–301 (2013).
[Crossref] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

Y.-F. Xiao, C.-H. Dong, Z.-F. Han, G.-C. Guo, and Y.-S. Park, “Directional escape from a high-Q deformed microsphere induced by short CO2 laser pulses,” Opt. Lett. 32, 644–646 (2007).
[Crossref] [PubMed]

Xu, L.

Yang, L.

B. Min, L. Yang, and K. Vahala, “Perturbative analytic theory of an ultrahigh-Q toroidal microcavity,” Phys. Rev. A 76, 013823 (2007).
[Crossref]

Yi, X.

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Zervas, M. N.

Zhang, K.

Zhou, S.

Zou, C.-L.

J.-M. Cui, C.-H. Dong, C.-L. Zou, F.-W. Sun, Y.-F. Xiao, Z.-F. Han, and G.-C. Guo, “Controlling deformation in a high quality factor silica microsphere toward single directional emission,” Appl. Opt. 52, 298–301 (2013).
[Crossref] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

Adv. Opt. Photonics (1)

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7, 168–240 (2015).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[Crossref]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Shun-Lien, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. 23, 499–509 (1987).
[Crossref]

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

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

J. Appl. Phys. (1)

H. P. Wagner, H. Schmitzer, J. Lutti, P. Borri, and W. Langbein, “Effects of uniaxial pressure on polar whispering gallery modes in microspheres,” J. Appl. Phys. 113, 243101 (2013).
[Crossref]

J. Lightwave Technol. (2)

C. Shun-Lien, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5, 174–183 (1987).
[Crossref]

B. E. Little, J.-P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17, 704 (1999).
[Crossref]

J. Opt. (1)

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. D: Appl. Phys. (1)

Z. Guo, H. Quan, and S. Pau, “Near-field gap effects on small microcavity whispering-gallery mode resonators,” J. Phys. D: Appl. Phys. 39, 5133–5136 (2006).
[Crossref]

Laser Photon. Rev. (2)

J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev. 5, 553–570 (2011).
[Crossref]

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
[Crossref]

Nano Lett. (1)

M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
[Crossref] [PubMed]

Nanophotonics (2)

Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6, 789–811 (2017).
[Crossref]

X. Wu and L. Tong, “Optical microfibers and nanofibers,” Nanophotonics 2, 407–428 (2013).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. A (3)

B. Min, L. Yang, and K. Vahala, “Perturbative analytic theory of an ultrahigh-Q toroidal microcavity,” Phys. Rev. A 76, 013823 (2007).
[Crossref]

L. Deych and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer,” Phys. Rev. A 80, 061805 (2009).
[Crossref]

X. Yi, Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Multiple-rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator,” Phys. Rev. A 83, 023803 (2011).
[Crossref]

Phys. Rev. Lett. (1)

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 a) Schematic of the taper-coupled microresonator system showing the inputs and outputs of the coupling region, and b) typical calculated electric of the 1st, 7th and 15th order WGMs with radial order of one for a silica microsphere with radius of30μm.
Fig. 2
Fig. 2 Spectra of transmission, internal power enhancement and internal WGM phase of tapered fiber coupled microsphere considering degenerate modes of 1st, 3rd and 5th orders as a function of fiber-to-sphere air-gap. The intrinsic Q of all modes is set to 106 and the tapered fiber diameter is 2μm (dashed lines show the position of the isolated microsphere resonance wavelength).
Fig. 3
Fig. 3 Internal power enhancement, transmission and phase spectra of tapered fiber-coupled microsphere with zero air-gap, taper diameter of 2μm and intrinsic Q of 106. Results are shown for WGMs with N + 1=1, 3 and 5 when the cavity operates in single-mode (dashed lines) or multimode (solid lines) regimes.
Fig. 4
Fig. 4 Transmission and internal/input power spectra of the taper-coupled microsphere at zero air-gap and fixed taper diameter of 2μm when the intrinsic Q of the modes varies from 5×104 to 108 (insets show magnified view of the results for higher Q’s)
Fig. 5
Fig. 5 Transmission and internal/input power spectra of the taper-coupled microsphere at zero air-gap and fixed intrinsic Q of 106 when the taper diameter varies from 1.2μm to 9.2μm (dashed lines show the position of the isolated microsphere resonance wavelength).
Fig. 6
Fig. 6 a) Transmission, internal/input power and phase spectra of microsphere with a fixed intrinsic Q of 106 as a function of eccentricity showing various level of WGM interactions, and b) transmission spectra corresponding to eccentricities of zero and 0.2% as function of intrinsic Q factor (Q = 1, 5, 10, 20 and 50 ×105), coupled to a tapered fiber at zero air-gap with diameter of 2μm (dashed lines show the position of the isolated perfect microsphere resonance wavelength).

Equations (1)

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Λ = [ Λ i j ] ( N + P ) × ( N + P ) = [ [ V 1 ] P × P [ V 2 ] P × N [ V 3 ] N × P [ V 4 ] N × N ]

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