Abstract

Third-harmonic generation can be realized via both χ(3) and cascaded χ(2) nonlinear processes in a triply-resonant microcavity. It is still unknown how these processes interfere with each other and the optimization of the conversion efficiency still remains as a question. In this work, the interplay between the direct third-harmonic generation and the cascaded process combining of the second-harmonic generation and the sum-frequency generation are investigated. It is found that the interference effect between these two processes can be used to improve the conversion efficiency. By optimizing the cavity resonance and the external coupling conditions, the saturation of the nonlinear conversion is mitigated and the third-harmonic conversion efficiency is increased. A design rule is provided for achieving efficient third-harmonic generation in an optical microcavity, which can be generalized further to the high-order harmonic generations.

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

Full Article  |  PDF Article
OSA Recommended Articles
Cascaded third-harmonic generation of ultrashort optical pulses in two-dimensional quasi-phase-matching gratings

Nobuhide Fujioka, Satoshi Ashihara, Hidenobu Ono, Tsutomu Shimura, and Kazuo Kuroda
J. Opt. Soc. Am. B 24(9) 2394-2405 (2007)

χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities

Alejandro Rodriguez, Marin Soljačić, J. D. Joannopoulos, and Steven G. Johnson
Opt. Express 15(12) 7303-7318 (2007)

References

  • View by:
  • |
  • |
  • |

  1. R. W. Boyd, Nonlinear Optics (Academic2003).
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic2007).
  3. C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
    [Crossref] [PubMed]
  4. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
    [Crossref]
  5. M. Li, L. Zhang, L. M. Tong, and D. X. Dai, “Hybrid silicon nonlinear photonics,” Photonics Res. 6, B13–B22 (2018).
    [Crossref]
  6. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [Crossref] [PubMed]
  7. 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]
  8. G. Lin, A. Coillet, and Y. K. Chembo, “Nonlinear photonics with high-Q whispering-gallery-mode resonators,” Adv. Opt. Photon. 9, 828–890 (2017).
    [Crossref]
  9. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
    [Crossref] [PubMed]
  10. H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
    [Crossref]
  11. D. H. Leach, R. K. Chang, W. P. Acker, and S. C. Hill, “Third-order sum-frequency generation in droplets: experimental results,” J. Opt. Soc. Am. B 10, 34–35 (1993).
    [Crossref]
  12. J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
    [Crossref]
  13. T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3, 430–435 (2007).
    [Crossref]
  14. R. Ismaeel, T. Lee, M. Ding, N. G. R. Broderick, and G. Brambilla, “Nonlinear microfiber loop resonators for resonantly enhanced third harmonic generation,” Opt. Lett. 37, 5121–5123 (2012).
    [Crossref] [PubMed]
  15. D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
    [Crossref] [PubMed]
  16. M. Asano, S. Komori, R. Ikuta, N. Imoto, Ş. K. Özdemir, and T. Yamamoto, “Visible light emission from a silica microbottle resonator by second- and third-harmonic generation,” Opt. Lett. 41, 5793–5796 (2016).
    [Crossref] [PubMed]
  17. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19, 11415–11421 (2011),
    [Crossref] [PubMed]
  18. M. Galli, D. Gerace, K. Welna, T. F. Krauss, L. O’Faolain, G. Guizzetti, and L. C. Andreani, “Low-power continuous-wave generation of visible harmonics in silicon photonic crystal nanocavities,” Opt. Express 18, 26613–26624 (2010).
    [Crossref] [PubMed]
  19. J. B. Surya, X. Guo, C. L. Zou, and H. X. Tang, “Efficient third-harmonic generation in composite aluminum nitride/silicon nitride microrings,” Optica 5, 103–108 (2018).
    [Crossref]
  20. X. Guo, C. Zou, and H. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500 %/W conversion efficiency,” Optica 3, 1126–1131 (2016).
    [Crossref]
  21. Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
    [Crossref]
  22. K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
    [Crossref] [PubMed]
  23. Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
    [Crossref]
  24. K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO:LiNbO3 disk resonator,” Appl. Phys. Express 2, 122401 (2009).
    [Crossref]
  25. S. Liu, Y. Zheng, and X. Chen, “Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk,” Opt. Lett. 42, 3626–3629 (2017).
    [Crossref] [PubMed]
  26. A. Chen-Jinnai, T. Kato, S. Fujii, T. Nagano, T. Kobatake, and T. Tanabe, “Broad bandwidth third-harmonic generation via four-wave mixing and stimulated raman scattering in a microcavity,” Opt. Express 24, 26322–26331 (2016).
    [Crossref] [PubMed]
  27. W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
    [Crossref]
  28. L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
    [Crossref]
  29. S. Fujii, T. Kato, R. Suzuki, and T. Tanabe, “Third-harmonic blue light generation from kerr clustered combs and dispersive waves,” Opt. Lett. 42, 2010-2013 (2017).
    [Crossref] [PubMed]
  30. H.-T. Tan and H. Huang, “Bright quadripartite entanglement from competing χ(2) nonlinearities,” Phys. Rev. A 83, 015802 (2011).
    [Crossref]
  31. V. Ulvila, C. Phillips, L. Halonen, and M. Vainio, “Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearitiesl,” Opt. Lett. 38, 4281–4284 (2013).
    [Crossref] [PubMed]
  32. H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single ir pump in aln microring resonator,” Optica 1, 396–399 (2014).
    [Crossref]
  33. R. Wolf, I. Breunig, H. Zappe, and K. Buse, “Cascaded second-order optical nonlinearities in on-chip micro rings,” Opt. Express 25, 29927–29933 (2017).
    [Crossref] [PubMed]
  34. M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
    [Crossref]
  35. X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
    [Crossref]
  36. X. Guo, C. L. Zou, H. Jung, and H. X. Tang, “On-Chip Strong Coupling and Efficient Frequency Conversion between Telecom and Visible Optical Modes,” Phys. Rev. Lett. 117, 123902 (2016).
    [Crossref] [PubMed]
  37. X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
    [Crossref] [PubMed]
  38. M. Zhang, C. Wang, R. Cheng, A. Shams-Ansari, and M. Lončar, “Monolithic ultra-high-Q lithium niobate microring resonator,” Optica 4, 1536–1537 (2017).
    [Crossref]
  39. D. F. Walls and G. J. Milburn, Quantum optics (Springer Science & Business Media2007).
  40. R. Yu, C. Ding, J. Wang, and D. Zhang, “Enhanced visible light generation in an active microcavity via third-harmonic conversion beyond the non-depletion approximation,” J. Appl. Phys. 122, 244303 (2017).
    [Crossref]
  41. J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
    [Crossref] [PubMed]
  42. J. Moore, M. Tomes, T. Carmon, and M. Jarrahi, “Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator,” Opt. Express 19, 24139–24146 (2011).
    [Crossref] [PubMed]

2018 (4)

M. Li, L. Zhang, L. M. Tong, and D. X. Dai, “Hybrid silicon nonlinear photonics,” Photonics Res. 6, B13–B22 (2018).
[Crossref]

M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

J. B. Surya, X. Guo, C. L. Zou, and H. X. Tang, “Efficient third-harmonic generation in composite aluminum nitride/silicon nitride microrings,” Optica 5, 103–108 (2018).
[Crossref]

2017 (7)

2016 (10)

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

X. Guo, C. Zou, and H. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500 %/W conversion efficiency,” Optica 3, 1126–1131 (2016).
[Crossref]

A. Chen-Jinnai, T. Kato, S. Fujii, T. Nagano, T. Kobatake, and T. Tanabe, “Broad bandwidth third-harmonic generation via four-wave mixing and stimulated raman scattering in a microcavity,” Opt. Express 24, 26322–26331 (2016).
[Crossref] [PubMed]

M. Asano, S. Komori, R. Ikuta, N. Imoto, Ş. K. Özdemir, and T. Yamamoto, “Visible light emission from a silica microbottle resonator by second- and third-harmonic generation,” Opt. Lett. 41, 5793–5796 (2016).
[Crossref] [PubMed]

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

X. Guo, C. L. Zou, H. Jung, and H. X. Tang, “On-Chip Strong Coupling and Efficient Frequency Conversion between Telecom and Visible Optical Modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref] [PubMed]

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

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]

2015 (1)

2014 (2)

H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single ir pump in aln microring resonator,” Optica 1, 396–399 (2014).
[Crossref]

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (2)

2011 (3)

2010 (2)

2009 (2)

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[Crossref]

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO:LiNbO3 disk resonator,” Appl. Phys. Express 2, 122401 (2009).
[Crossref]

2007 (1)

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

2005 (1)

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

2003 (1)

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

1997 (1)

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

1993 (1)

Acker, W. P.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic2007).

Andreani, L. C.

Asano, M.

Barucci, A.

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

Bennemann, K. H.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Berneschi, S.

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

Boucaud, P.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Boutou, V.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Bowers, J. E.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic2003).

Brambilla, G.

Breunig, I.

Brimont, C.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Broderick, N. G. R.

Bromberg, Y.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Bruch, A.

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

Burkhart, J.

Buse, K.

Carmon, T.

J. Moore, M. Tomes, T. Carmon, and M. Jarrahi, “Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator,” Opt. Express 19, 24139–24146 (2011).
[Crossref] [PubMed]

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

Caspani, L.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Chang, L.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Chang, R. K.

Checoury, X.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Chembo, Y. K.

Chen, T.

Chen, X.

Cheng, R.

M. Zhang, C. Wang, R. Cheng, A. Shams-Ansari, and M. Lončar, “Monolithic ultra-high-Q lithium niobate microring resonator,” Optica 4, 1536–1537 (2017).
[Crossref]

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref] [PubMed]

Chen-Jinnai, A.

Choi, J.-H.

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Chu, S. T.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Cohen, O.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

Coillet, A.

Dai, D. X.

M. Li, L. Zhang, L. M. Tong, and D. X. Dai, “Hybrid silicon nonlinear photonics,” Photonics Res. 6, B13–B22 (2018).
[Crossref]

M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
[Crossref]

Dewitz, J. P.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Ding, C.

R. Yu, C. Ding, J. Wang, and D. Zhang, “Enhanced visible light generation in an active microcavity via third-harmonic conversion beyond the non-depletion approximation,” J. Appl. Phys. 122, 244303 (2017).
[Crossref]

Ding, M.

Dong, C. H.

M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
[Crossref]

El Kurdi, M.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Fang, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

Farnesi, D.

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

Fischer, D.

Foster, M. A.

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Fujii, S.

Gaeta, A. L.

Galli, M.

Gayral, B.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Gerace, D.

Gong, Z.

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

Grazioso, F.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Guillet, T.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Guizzetti, G.

Guo, H.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Guo, X.

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

J. B. Surya, X. Guo, C. L. Zou, and H. X. Tang, “Efficient third-harmonic generation in composite aluminum nitride/silicon nitride microrings,” Optica 5, 103–108 (2018).
[Crossref]

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref] [PubMed]

X. Guo, C. L. Zou, H. Jung, and H. X. Tang, “On-Chip Strong Coupling and Efficient Frequency Conversion between Telecom and Visible Optical Modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref] [PubMed]

X. Guo, C. Zou, and H. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500 %/W conversion efficiency,” Optica 3, 1126–1131 (2016).
[Crossref]

H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single ir pump in aln microring resonator,” Optica 1, 396–399 (2014).
[Crossref]

Hak, D.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

Halonen, L.

Han, Z.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Hashemi, H.

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[Crossref]

Hill, S. C.

Huang, H.

H.-T. Tan and H. Huang, “Bright quadripartite entanglement from competing χ(2) nonlinearities,” Phys. Rev. A 83, 015802 (2011).
[Crossref]

Hübner, W.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Hwang, M.-S.

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Ikuta, R.

Ilchenko, V. S.

Imoto, N.

Ismaeel, R.

Jarrahi, M.

Jiang, L.

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

Joannopoulos, J. D.

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[Crossref]

Johnson, S. G.

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[Crossref]

Johnston, T.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Jones, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

Jung, H.

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref] [PubMed]

X. Guo, C. L. Zou, H. Jung, and H. X. Tang, “On-Chip Strong Coupling and Efficient Frequency Conversion between Telecom and Visible Optical Modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref] [PubMed]

H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single ir pump in aln microring resonator,” Optica 1, 396–399 (2014).
[Crossref]

Kasparian, J.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Kato, T.

Kim, H.-R.

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Kim, K.-H.

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Kippenberg, T. J.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Kobatake, T.

Komori, S.

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Krämer, B.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Krauss, T. F.

Kues, M.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Leach, D. H.

Lee, H.

Lee, T.

Leisner, T.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[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]

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Levy, J. S.

Li, J.

Li, M.

M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
[Crossref]

M. Li, L. Zhang, L. M. Tong, and D. X. Dai, “Hybrid silicon nonlinear photonics,” Photonics Res. 6, B13–B22 (2018).
[Crossref]

Liang, W.

Liang, X.

Lin, G.

Lin, Z.

Lipson, M.

Little, B. E.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Liu, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

Liu, S.

Loncar, M.

Maleki, L.

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]

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

McMillan, J. F.

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum optics (Springer Science & Business Media2007).

Moore, J.

Morandotti, R.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Moss, D. J.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Nagano, T.

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

No, Y.-S.

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Nunzi Conti, G.

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

O’Faolain, L.

Özdemir, S. K.

Paniccia, M.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

Park, H.-G.

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Pfeiffer, M. H.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Phillips, C.

Rairoux, P.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Reimer, C.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Ren, X. F.

M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
[Crossref]

Righini, G. C.

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

Rodriguez, A. W.

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[Crossref]

Roland, I.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Rong, H.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

Roztocki, P.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Sasagawa, K.

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO:LiNbO3 disk resonator,” Appl. Phys. Express 2, 122401 (2009).
[Crossref]

Sauvage, S.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Savchenkov, A. A.

Schuck, C.

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref] [PubMed]

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]

Semond, F.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Shams-Ansari, A.

Soljacic, M.

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[Crossref]

Soria, S.

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

Stoll, R.

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]

Surya, J. B.

Suzuki, R.

Tan, H.-T.

H.-T. Tan and H. Huang, “Bright quadripartite entanglement from competing χ(2) nonlinearities,” Phys. Rev. A 83, 015802 (2011).
[Crossref]

Tanabe, T.

Tang, H.

Tang, H. X.

J. B. Surya, X. Guo, C. L. Zou, and H. X. Tang, “Efficient third-harmonic generation in composite aluminum nitride/silicon nitride microrings,” Optica 5, 103–108 (2018).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref] [PubMed]

X. Guo, C. L. Zou, H. Jung, and H. X. Tang, “On-Chip Strong Coupling and Efficient Frequency Conversion between Telecom and Visible Optical Modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref] [PubMed]

H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single ir pump in aln microring resonator,” Optica 1, 396–399 (2014).
[Crossref]

Tomes, M.

Tong, L. M.

M. Li, L. Zhang, L. M. Tong, and D. X. Dai, “Hybrid silicon nonlinear photonics,” Photonics Res. 6, B13–B22 (2018).
[Crossref]

Tsuchiya, M.

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO:LiNbO3 disk resonator,” Appl. Phys. Express 2, 122401 (2009).
[Crossref]

Ulvila, V.

Vahala, K. J.

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
[Crossref] [PubMed]

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

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

Vainio, M.

Vajda, S.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Vezin, B.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Volet, N.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum optics (Springer Science & Business Media2007).

Wang, C.

Wang, J.

R. Yu, C. Ding, J. Wang, and D. Zhang, “Enhanced visible light generation in an active microcavity via third-harmonic conversion beyond the non-depletion approximation,” J. Appl. Phys. 122, 244303 (2017).
[Crossref]

Wang, L.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Welna, K.

Wetzel, B.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Wolf, J. P.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Wolf, R.

Wong, C. W.

Wöste, L.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Xie, Z.

Yamamoto, T.

Yu, R.

R. Yu, C. Ding, J. Wang, and D. Zhang, “Enhanced visible light generation in an active microcavity via third-harmonic conversion beyond the non-depletion approximation,” J. Appl. Phys. 122, 244303 (2017).
[Crossref]

Zappe, H.

Zeng, Y.

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Zervas, M.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Zhang, D.

R. Yu, C. Ding, J. Wang, and D. Zhang, “Enhanced visible light generation in an active microcavity via third-harmonic conversion beyond the non-depletion approximation,” J. Appl. Phys. 122, 244303 (2017).
[Crossref]

Zhang, L.

M. Li, L. Zhang, L. M. Tong, and D. X. Dai, “Hybrid silicon nonlinear photonics,” Photonics Res. 6, B13–B22 (2018).
[Crossref]

Zhang, M.

Zheng, Y.

Zou, C.

Zou, C. L.

J. B. Surya, X. Guo, C. L. Zou, and H. X. Tang, “Efficient third-harmonic generation in composite aluminum nitride/silicon nitride microrings,” Optica 5, 103–108 (2018).
[Crossref]

M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
[Crossref]

X. Guo, C. L. Zou, H. Jung, and H. X. Tang, “On-Chip Strong Coupling and Efficient Frequency Conversion between Telecom and Visible Optical Modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref] [PubMed]

Zou, C.-L.

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref] [PubMed]

ACS Photonics (1)

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, F. Semond, and P. Boucaud, “Imaging of photonic crystal localized modes through third-harmonic generation,” ACS Photonics 3, 1240–1247 (2016).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. Express (1)

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO:LiNbO3 disk resonator,” Appl. Phys. Express 2, 122401 (2009).
[Crossref]

J. Appl. Phys. (1)

R. Yu, C. Ding, J. Wang, and D. Zhang, “Enhanced visible light generation in an active microcavity via third-harmonic conversion beyond the non-depletion approximation,” J. Appl. Phys. 122, 244303 (2017).
[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 (1)

Laser Photonics Rev. (1)

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photonics Rev. 10, 631–638 (2016).
[Crossref]

Light Sci. Appl. (1)

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref] [PubMed]

Nat. Commun. (1)

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, and H.-G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[Crossref]

Nat. Phys. (1)

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

Nature (2)

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon raman laser,” Nature 433, 292–294 (2005).
[Crossref] [PubMed]

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

Opt. Express (6)

Opt. Lett. (5)

Optica (6)

Photonics Res. (1)

M. Li, L. Zhang, L. M. Tong, and D. X. Dai, “Hybrid silicon nonlinear photonics,” Photonics Res. 6, B13–B22 (2018).
[Crossref]

Phys. Rev. A (3)

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[Crossref]

H.-T. Tan and H. Huang, “Bright quadripartite entanglement from competing χ(2) nonlinearities,” Phys. Rev. A 83, 015802 (2011).
[Crossref]

M. Li, C. L. Zou, C. H. Dong, X. F. Ren, and D. X. Dai, “Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity,” Phys. Rev. A 98, 013854 (2018).
[Crossref]

Phys. Rev. Applied (1)

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient Generation of a Near-visible Frequency Comb via Cherenkov-like Radiation from a Kerr Microcomb,” Phys. Rev. Applied 10, 014012 (2018).
[Crossref]

Phys. Rev. Lett. (3)

X. Guo, C. L. Zou, H. Jung, and H. X. Tang, “On-Chip Strong Coupling and Efficient Frequency Conversion between Telecom and Visible Optical Modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref] [PubMed]

D. Farnesi, A. Barucci, G. C. Righini, S. Berneschi, S. Soria, and G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, and K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952 (1997).
[Crossref]

Science (1)

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref] [PubMed]

Other (3)

R. W. Boyd, Nonlinear Optics (Academic2003).

G. P. Agrawal, Nonlinear Fiber Optics (Academic2007).

D. F. Walls and G. J. Milburn, Quantum optics (Springer Science & Business Media2007).

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 (4)

Fig. 1
Fig. 1 THG in a microcavity. Schematic diagram of a micro-cavity coupled with a waveguide. The microcavity is driven by a continuous laser on the fundamental mode a. In the microcavity, a couples with b via SHG, a, b couple with c via SFG, a couple with c via DTHG. The DTHG and cascaded SHG-SFG can both generate photons in the TH mode c. The intrinsic and external decay rates of mode i are κi,0 and κi,1, respectively.
Fig. 2
Fig. 2 Interference between DTHG and SHG-SFG process. (a) The intensity of the TH mode generated from three different processes with δb = 0.5κb. (b) The relation between the normalized intensity of the TH mode and the detuning of the SH mode. The intensities are normalized to that of the DTHG process with P i T H / P D T H G T H (i represents the intensity of the TH mode from DTHG, SHG-SFG and the combined process). The parameters used in the calculations are g3/2π = 10 Hz, g2/2π = 0.1 MHz, κb/2π = 1 GHz, κa,0/2π = 0.4 × 109 Hz, κb,0 = 4κa,0, κc,0 = 10κa,0. All the three modes are critically coupled to the waveguide.
Fig. 3
Fig. 3 Saturation effects in TH light generation. (a) Relation between the conversion efficiency from the fundamental frequency to the TH frequency for three different processes. The cascaded SHG-SFG saturates first when increasing the pump power. (b) Interference fringes for different pump powers. The saturation of the SHG-SFG process destroys the constructive interference significantly. (c) Optimal detuning (Blue line) of the SH mode for TH light generation and the corresponding maximum enhancement factor (Orange line) over the DTHG process. When the pump increases, the optimal detuning shifts to larger values and the constructive interference is destroyed. In the high-pump regime, THG is dominated by the DTHG process.
Fig. 4
Fig. 4 Optimization of the conversion efficiency. (a) Relationship between the conversion efficiency and the external coupling rates κa,1 and κc,1. Left: P p = 10 mW. Right: Pp = 1000mW. In the high-pump regime, the cavity modes should be designed over-coupled to the waveguide to achieve optimal efficiency. (b) Relationship between the optimal THG efficiency and the pump power. Black line: the detuning δb, external coupling rates κa,1 and κc,1 are optimized; Red line: efficiency of DTHG with all the modes critical-coupled to the waveguide. Orange: optimal external coupling rate of the fundamental mode a. Blue: optimal external coupling rate of the TH mode c. The external coupling rates shown in this figure are normalized to the corresponding intrinsic decay rates κi,0.

Equations (19)

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

H = H 0 + H ( 2 ) + H ( 3 ) + H d ,
H 0 = ω a , 0 a a + ω b , 0 b b + ω c , 0 c c ,
H ( 2 ) = g 22 ( a 2 b + a 2 b ) + g 21 ( a b c + a b c ) ,
H ( 3 ) = g 3 ( a 3 c + a 3 c ) ,
H d = ϵ a ( a e i ω a t + a e i ω a t ) ,
H 0 = δ a a a + δ b b b + δ c c c ,
d a d t = α a a i 3 g 3 a 2 c i 2 g 22 a b i g 21 b c i ϵ a
d b d t = α b b i g 22 a 2 i g 21 a c
d c d t = α c c i g 3 a 3 i g 21 a b ,
P TH = 2 ω c κ c , 1 | c s | 2 ,
η = P TH / P p ,
H = δ b b b + δ c c c + g 3 | a s | 3 ( c + c ) + g 22 | a s | 2 ( b + b ) + g 21 | a s | ( b c + b c ) ,
d b d t = ( i δ b κ b ) b i g 22 | a s | 2 i g 21 | a s | c
d c d t = ( i δ c κ c ) c i g 3 | a s | 3 i g 21 | a s | b .
c s = i g 3 g 21 g 22 α b α c + g 21 2 α b | a s | 2 | a s | 3 ( i g 3 α c g 21 g 22 α b α c ) | a s | 3 .
Q cr = ω 2 g 3 g 21 g 22 .
[ g 21 2 α b * i g 3 g 21 g 22 α b * α c * + g 21 2 α b * | a | 2 i g 3 g 21 g 22 α b α c + g 21 2 α b | a | 2 | a | 6 + 2 g 22 2 α b | a | 2 ( i 3 g 3 2 g 21 g 22 α b + g 21 g 22 α b * ) i g 3 g 21 g 22 α b α c + g 21 2 α b | a | 2 | a | 4 + α a ] = i ϵ a
c = i g 3 g 21 g 22 α b α c + g 21 2 α b | a | 2 a 3
b = i α b ( g 22 + g 21 i g 3 g 21 g 22 α b α c + g 21 2 α b | a | 2 | a | 2 ) a 2 .

Metrics