Abstract

We study free-space coupling of optical fields to the whispering-gallery-mode resonators by employing self-accelerating beams orbiting a semicircle. The best coupling condition is obtained through theoretical analysis, in accord with the numerical results. Comparing with the conventional Gaussian-like beams, much enhanced coupling efficiency is achieved with such self-accelerating beams, particularly when a large numerical aperture of an optical system is used or a higher-order azimuthal mode is considered. Conditions with slight deviation from the ideal radius of self-accelerating beams are further discussed, aiming to realize an optimized high coupling efficiency.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  3. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
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  4. W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
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  6. Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
    [Crossref] [PubMed]
  7. A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
    [Crossref] [PubMed]
  8. N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
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  12. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  22. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
    [Crossref] [PubMed]
  23. P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
    [Crossref] [PubMed]
  24. F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, “Sending femtosecond pulses in circles: highly nonparaxial accelerating beams,” Opt. Lett. 37(10), 1736–1738 (2012).
    [Crossref] [PubMed]
  25. Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
    [Crossref]
  26. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
    [Crossref] [PubMed]
  27. A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
    [Crossref] [PubMed]
  28. Z. Feng and L. Bai, “Advances of optofluidic microcavities for microlasers and biosensors,” Micromachines (Basel) 9(3), 122 (2018).
    [Crossref] [PubMed]
  29. X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
    [Crossref] [PubMed]
  30. L. Wang, C. Wang, J. Wang, F. Bo, M. Zhang, Q. Gong, M. Lončar, and Y. F. Xiao, “High-Q chaotic lithium niobate microdisk cavity,” Opt. Lett. 43(12), 2917–2920 (2018).
    [Crossref] [PubMed]

2018 (5)

L. Wang, C. Wang, J. Wang, F. Bo, M. Zhang, Q. Gong, M. Lončar, and Y. F. Xiao, “High-Q chaotic lithium niobate microdisk cavity,” Opt. Lett. 43(12), 2917–2920 (2018).
[Crossref] [PubMed]

F. Shu, X. Jiang, G. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7(8), 1455–1460 (2018).
[Crossref]

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref] [PubMed]

Z. Feng and L. Bai, “Advances of optofluidic microcavities for microlasers and biosensors,” Micromachines (Basel) 9(3), 122 (2018).
[Crossref] [PubMed]

L. Wang, C. Wang, J. Wang, F. Bo, M. Zhang, Q. Gong, M. Lončar, and Y. F. Xiao, “High-Q chaotic lithium niobate microdisk cavity,” Opt. Lett. 43(12), 2917–2920 (2018).
[Crossref] [PubMed]

2017 (2)

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
[Crossref] [PubMed]

2016 (3)

S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
[Crossref]

W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref] [PubMed]

S. X. Zhang, L. Wang, Z. Y. Li, Y. Li, Q. Gong, and Y. F. Xiao, “Free-space coupling efficiency in a high-Q deformed optical microcavity,” Opt. Lett. 41(19), 4437–4440 (2016).
[Crossref] [PubMed]

2015 (2)

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

2014 (1)

X. Fan and S. H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11(2), 141–147 (2014).
[Crossref] [PubMed]

2013 (4)

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

C. L. Zou, F. J. Shu, F. W. Sun, Z. J. Gong, Z. F. Han, and G. C. Guo, “Theory of free space coupling to high-Q whispering gallery modes,” Opt. Express 21(8), 9982–9995 (2013).
[Crossref] [PubMed]

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
[Crossref]

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

2012 (5)

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, “Sending femtosecond pulses in circles: highly nonparaxial accelerating beams,” Opt. Lett. 37(10), 1736–1738 (2012).
[Crossref] [PubMed]

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

2011 (1)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

2010 (1)

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

2005 (1)

B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report 42(162), 1–51 (2005).

2003 (1)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

1998 (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Angelescu, D.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Avino, S.

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref] [PubMed]

A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
[Crossref] [PubMed]

Baaske, M. D.

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

Bai, L.

Z. Feng and L. Bai, “Advances of optofluidic microcavities for microlasers and biosensors,” Micromachines (Basel) 9(3), 122 (2018).
[Crossref] [PubMed]

Ballard, Z.

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

Basset, P.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

Bo, F.

Bongiovanni, D.

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

Bourouina, T.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

Capasso, F.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Carmon, T.

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref] [PubMed]

S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
[Crossref]

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

Chang, R. K.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Chen, Z.

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref] [PubMed]

Courvoisier, F.

De Natale, P.

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref] [PubMed]

A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
[Crossref] [PubMed]

Di Falco, A.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
[Crossref]

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

Diehl, L.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Dong, C. H.

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Dong, M.

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

Dudley, J. M.

Edamura, T.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
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C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
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X. Fan and S. H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11(2), 141–147 (2014).
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Z. Feng and L. Bai, “Advances of optofluidic microcavities for microlasers and biosensors,” Micromachines (Basel) 9(3), 122 (2018).
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Fratalocchi, A.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
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Froehly, L.

Furfaro, L.

Gaber, N.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
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Gagliardi, G.

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
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A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
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Giorgini, A.

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
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A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
[Crossref] [PubMed]

Giust, R.

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Gong, Q.

L. Wang, C. Wang, J. Wang, F. Bo, M. Zhang, Q. Gong, M. Lončar, and Y. F. Xiao, “High-Q chaotic lithium niobate microdisk cavity,” Opt. Lett. 43(12), 2917–2920 (2018).
[Crossref] [PubMed]

L. Wang, C. Wang, J. Wang, F. Bo, M. Zhang, Q. Gong, M. Lončar, and Y. F. Xiao, “High-Q chaotic lithium niobate microdisk cavity,” Opt. Lett. 43(12), 2917–2920 (2018).
[Crossref] [PubMed]

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
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S. X. Zhang, L. Wang, Z. Y. Li, Y. Li, Q. Gong, and Y. F. Xiao, “Free-space coupling efficiency in a high-Q deformed optical microcavity,” Opt. Lett. 41(19), 4437–4440 (2016).
[Crossref] [PubMed]

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Gong, Z. J.

Guo, G. C.

Han, Z. F.

He, L.

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

Hu, Y.

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

Ilchenko, V. S.

B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report 42(162), 1–51 (2005).

Jacquot, M.

Jiang, W. C.

W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref] [PubMed]

Jiang, X.

F. Shu, X. Jiang, G. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7(8), 1455–1460 (2018).
[Crossref]

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

Jiang, X. F.

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Johnson, N. M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Kaminer, I.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

Kaminski, S.

S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
[Crossref]

Kan, H.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Khan, Y.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
[Crossref]

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

Kneissl, M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Krauss, T. F.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
[Crossref]

Lacourt, P. A.

Li, B. B.

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Li, T.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

Li, Y.

S. X. Zhang, L. Wang, Z. Y. Li, Y. Li, Q. Gong, and Y. F. Xiao, “Free-space coupling efficiency in a high-Q deformed optical microcavity,” Opt. Lett. 41(19), 4437–4440 (2016).
[Crossref] [PubMed]

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Li, Z. Y.

Lin, Q.

W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref] [PubMed]

Liu, C.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
[Crossref]

Loncar, M.

Lu, T.

W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref] [PubMed]

Maayani, S.

S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
[Crossref]

Malak, M.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Malara, P.

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref] [PubMed]

A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
[Crossref] [PubMed]

Maleki, L.

B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report 42(162), 1–51 (2005).

Martin, L. L.

S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
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Mathis, A.

Matsko, B.

B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report 42(162), 1–51 (2005).

Molinari, D.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
[Crossref]

Morandotti, R.

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

Narimanov, E. E.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

Nguyen, K. N.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Nockel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
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Ooi, B. S.

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
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Özdemir, S. K.

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
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Peng, B.

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
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Pflügl, C.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Richalot, E.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Salandrino, A.

Savchenkov, A. A.

B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report 42(162), 1–51 (2005).

Segev, M.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

Shao, L.

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
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Shu, F.

F. Shu, X. Jiang, G. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7(8), 1455–1460 (2018).
[Crossref]

Shu, F. J.

Sivco, D. L.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
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G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
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G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
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Strekalov, D.

B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report 42(162), 1–51 (2005).

Sun, F. W.

C. L. Zou, F. J. Shu, F. W. Sun, Z. J. Gong, Z. F. Han, and G. C. Guo, “Theory of free space coupling to high-Q whispering gallery modes,” Opt. Express 21(8), 9982–9995 (2013).
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X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Tomes, M.

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

Tureci, H. E.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

Unterhinninghofen, J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
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Vollmer, F.

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
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Wang, C.

Wang, J.

Wang, L.

Wang, Q. J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Wiersig, J.

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Xiao, Y. F.

L. Wang, C. Wang, J. Wang, F. Bo, M. Zhang, Q. Gong, M. Lončar, and Y. F. Xiao, “High-Q chaotic lithium niobate microdisk cavity,” Opt. Lett. 43(12), 2917–2920 (2018).
[Crossref] [PubMed]

L. Wang, C. Wang, J. Wang, F. Bo, M. Zhang, Q. Gong, M. Lončar, and Y. F. Xiao, “High-Q chaotic lithium niobate microdisk cavity,” Opt. Lett. 43(12), 2917–2920 (2018).
[Crossref] [PubMed]

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

S. X. Zhang, L. Wang, Z. Y. Li, Y. Li, Q. Gong, and Y. F. Xiao, “Free-space coupling efficiency in a high-Q deformed optical microcavity,” Opt. Lett. 41(19), 4437–4440 (2016).
[Crossref] [PubMed]

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Yamanishi, M.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Yan, C.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Yang, L.

F. Shu, X. Jiang, G. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7(8), 1455–1460 (2018).
[Crossref]

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Yannai, M.

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref] [PubMed]

Yi, X.

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

Yilmaz, H.

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

Yin, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

Yu, N.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Yu, W.

W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref] [PubMed]

Yuan, X.

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Yun, S. H.

X. Fan and S. H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11(2), 141–147 (2014).
[Crossref] [PubMed]

Zhang, M.

Zhang, P.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

Zhang, S. X.

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

S. X. Zhang, L. Wang, Z. Y. Li, Y. Li, Q. Gong, and Y. F. Xiao, “Free-space coupling efficiency in a high-Q deformed optical microcavity,” Opt. Lett. 41(19), 4437–4440 (2016).
[Crossref] [PubMed]

Zhang, X.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37(14), 2820–2822 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

Zhao, G.

F. Shu, X. Jiang, G. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7(8), 1455–1460 (2018).
[Crossref]

Zhu, J.

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

Zou, C. L.

C. L. Zou, F. J. Shu, F. W. Sun, Z. J. Gong, Z. F. Han, and G. C. Guo, “Theory of free space coupling to high-Q whispering gallery modes,” Opt. Express 21(8), 9982–9995 (2013).
[Crossref] [PubMed]

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Adv. Mater. (1)

X. F. Jiang, Y. F. Xiao, C. L. Zou, L. He, C. H. Dong, B. B. Li, Y. Li, F. W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24(35), 260–264 (2012).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 (2003).
[Crossref]

IPN Progress Report (1)

B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report 42(162), 1–51 (2005).

Lab Chip (1)

N. Gaber, M. Malak, X. Yuan, K. N. Nguyen, P. Basset, E. Richalot, D. Angelescu, and T. Bourouina, “On the free-space Gaussian beam coupling to droplet optical resonators,” Lab Chip 13(5), 826–833 (2013).
[Crossref] [PubMed]

Micromachines (Basel) (1)

Z. Feng and L. Bai, “Advances of optofluidic microcavities for microlasers and biosensors,” Micromachines (Basel) 9(3), 122 (2018).
[Crossref] [PubMed]

Nanophotonics (1)

F. Shu, X. Jiang, G. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7(8), 1455–1460 (2018).
[Crossref]

Nat. Commun. (1)

W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref] [PubMed]

Nat. Methods (1)

X. Fan and S. H. Yun, “The potential of optofluidic biolasers,” Nat. Methods 11(2), 141–147 (2014).
[Crossref] [PubMed]

Nat. Photonics (2)

S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
[Crossref]

C. Liu, A. Di Falco, D. Molinari, Y. Khan, B. S. Ooi, T. F. Krauss, and A. Fratalocchi, “Enhanced energy storage in chaotic optical resonators,” Nat. Photonics 7(6), 473–478 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (1)

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping,” Phys. Rev. A 88(4), 043809 (2013).
[Crossref]

Phys. Rev. Lett. (4)

A. Giorgini, S. Avino, P. Malara, P. De Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin cavity optomechanics in liquid droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108(16), 163901 (2012).
[Crossref] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109(19), 193901 (2012).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. 107(52), 22407–22412 (2010).
[Crossref] [PubMed]

Sci. Rep. (2)

J. Zhu, S. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4(1), 6396 (2015).
[Crossref] [PubMed]

A. Giorgini, S. Avino, P. Malara, P. De Natale, and G. Gagliardi, “Fundamental limits in high-Q droplet microresonators,” Sci. Rep. 7(1), 41997 (2017).
[Crossref] [PubMed]

Science (3)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
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T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
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X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358(6361), 344–347 (2017).
[Crossref] [PubMed]

Sensors (Basel) (1)

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

Other (1)

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Self-accelerating Airy beams: generation, control, and applications, in Nonlinear photonics and novel optical phenomena, Z. Chen and R. Morandotti, eds, (Springer, 2012), 1–46.

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Figures (5)

Fig. 1
Fig. 1 Configuration of free-space coupling to a cylindrical resonator (right) via a Gaussian-like beam (top left) and a self-accelerating beam (bottom left), where the small empty circles mark the beam locations.
Fig. 2
Fig. 2 Analysis of coupling efficiency to the microcavity (the quality factor is 3.216 × 105 for the mode under test) for (a,c) accelerating beams and (b,d) Gaussian-like beams as a function of different beam locations, characterized by (a, b) the calculated values of mode coefficients |c92|2 via Eq. (6), and (c, d) the computed energy in the resonator via COMSOL. The plotted values in (a,b) and (c,d) are normalized by the maximum value in (a) and (c), respectively.
Fig. 3
Fig. 3 The weight (|cm|2) of each Bessel component for the case of (a) the self-accelerating beam and (b) the Gaussian-like beam under the optimal coupling condition in Fig. 2, where NA = 0.85 is employed. Notice the difference in the y-axis scale.
Fig. 4
Fig. 4 Optimized value of |cm|2 as a function of NA for accelerating beams (dashed line) and Gaussian-like beams (solid lines).
Fig. 5
Fig. 5 Influence of the radius of the accelerating beams on the coupling efficiency (m′ = 92 is under test). (a) Horizontal shift needed to allow the optimized coupling at different offsets of the radius with respect to the ideal case; (b) Slope of the linear relationship in (a) for different NAs, where the numerical values are obtained by a linear fitting in the range of ε in (a); (c, d) Optimized coupling efficiency for (c) various radius offsets when NA = 0.85 and (d) various NAs when the offset is set to be 1 μm.

Equations (12)

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{ E zi = m a m J m (nkr)exp(imϕ) (rR), E zo = m [ b m H m (1) (kr)+ c m H m (2) (kr) ]exp(imϕ) (r>R),
E( x,z )= 1 P k xmin k xmax e i[ k x x+ k z z+ρ( k x ) ] d k x ,
ρ( k x )= k x d 1 k z d 2 + r 0 karcsin( k x /k ),
E( r,ϕ )= 1 P θ min θ max e i[ krcos( θϕ )+ρ( θ ) ] d( ksinθ ) ,
E( r,ϕ )= m= + c m J m ( kr ) exp( imϕ ),
c m = 1 P exp( i π 2 m ) θ min θ max e i[ mθ+ρ( θ ) ] kcosθdθ .
ksinθ d 1 kcosθ d 2 +( r 0 k m )θ=0.
| c m | optimal 2 =NA/π.
c m = 1 P exp( i π 2 m ) θ min θ max e i( ksinθα+εkθ ) kcosθdθ .
c m = 1 P exp( i π 2 m )( 2ksin θ max +A α 2 +Bα+C ),
A= k 3 sin 3 θ max /3, B=[ sin( 2 θ max )2 θ max cos( 2 θ max ) ] k 3 ε/4, C= k 3 [ ( θ max 2 2 )sin θ max +2 θ max cos θ max ] ε 2 ,
s= 3[ sin( 2 θ max )2 θ max cos( 2 θ max ) ]/ ( 8 sin 3 θ max ) ,

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