## Impact of cavity spectrum on span in microresonator frequency combs |

Optics Express, Vol. 21, Issue 22, pp. 26929-26935 (2013)

http://dx.doi.org/10.1364/OE.21.026929

Acrobat PDF (1140 KB)

### Abstract

We experimentally study the factors that limit the span in frequency combs derived from the crystalline whispering gallery mode resonators. We observe that cavity dispersion is the key property that governs the parameters of the combs resulting from cascaded four wave mixing process. Two different regimes of comb generation are observed depending on the precise cavity dispersion behavior at the pump wavelength. In addition, the comb generation efficiency is found to be affected by the crossing of modes of different families. The influence of Raman lasing and its dependence on temperature is discussed.

© 2013 Optical Society of America

## 1. Introduction

1. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature **450**(7173), 1214–1217 (2007). [CrossRef] [PubMed]

3. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. **101**(9), 093902 (2008). [CrossRef] [PubMed]

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

14. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. **38**(1), 37–39 (2013). [CrossRef] [PubMed]

6. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics **6**(7), 480–487 (2012). [CrossRef]

15. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. **36**(17), 3398–3400 (2011). [CrossRef] [PubMed]

16. P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. **107**(6), 063901 (2011). [CrossRef] [PubMed]

_{2}WGM resonators of various size and shape. Each resonator has its axis aligned with the crystalline optical axis (z–cut). We use analytical approximations and finite element method (FEM) [17

17. O. Pironneau, F. Hecht, A. Le Hyaric, and J. Morice, “FreeFem++,” http://www.freefem.org/

## 2. Finite element modeling

18. A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Morphology-dependent photonic circuit elements,” Opt. Lett. **31**(9), 1313–1315 (2006). [CrossRef] [PubMed]

19. I. S. Grudinin and N. Yu, “Finite-element modeling of coupled optical microdisk resonators for displacement sensing,” J. Opt. Soc. Am. B **29**(11), 3010–3014 (2012). [CrossRef]

20. M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes” IEEE. J. Sel. Top. Quantum Electron. **12**(1), 33–39 (2006). [CrossRef]

## 3. Experimental study

6. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics **6**(7), 480–487 (2012). [CrossRef]

11. Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A **82**(3), 033801 (2010). [CrossRef]

13. Y. K. Chembo, D. V. Strekalov, and N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. **104**(10), 103902 (2010). [CrossRef] [PubMed]

2. I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF_{2} resonator,” Opt. Lett. **34**(7), 878–880 (2009). [CrossRef] [PubMed]

3. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. **101**(9), 093902 (2008). [CrossRef] [PubMed]

21. A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal group-velocity dispersion Kerr frequency comb,” Opt. Lett. **37**(1), 43–45 (2012). [CrossRef] [PubMed]

## 4. Spectral features

_{2}cavity increased 50% with the 4-fold increase in the pump power from 100 mW to 400 mW at 1560 nm wavelength. The comb was 165 nm wide and did not reach the ZDW.

22. P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics **3**(9), 529–533 (2009). [CrossRef]

10. M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs” arXiv:1305.4921. [CrossRef]

15. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. **36**(17), 3398–3400 (2011). [CrossRef] [PubMed]

23. C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. St. J. Russell, “Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser,” Opt. Lett. **30**(15), 1980–1982 (2005). [CrossRef] [PubMed]

24. S. Coen and M. Erkintalo, “Universal scaling laws of Kerr frequency combs,” Opt. Lett. **38**(11), 1790–1792 (2013). [CrossRef] [PubMed]

## 5. Influence of Raman lasing

25. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. **93**(8), 083904 (2004). [CrossRef] [PubMed]

_{2}resonators only parametric comb generation is observed, while in smaller resonators the Raman lasing notably competes with the generation of combs. To study the concurrent FWM and Raman lasing experimentally, we fabricated a MgF

_{2}microcavity with FSR comparable to Raman gain linewidth, then changed the cavity temperature to tune the relative offset of the Raman line and mode positions. This cavity is nearly single mode and its dispersion can be modeled with an ellipsoid having the major axis a = 190 μm and minor axis b = 105 μm. The GVD of such an ellipsoid is shown in Fig. 5.

_{2}at temperatures 296 and 307.7 K is a lorentzian having a linewidth of 241 and 253 GHz and offset from the pump of 12.148 and 12.139 THz respectively [26

26. A. Perakis, E. Sarantopoulou, Y. S. Raptis, and C. Raptis, “Temperature dependence of Raman scattering and anharmonicity study of MgF_{2},” Phys. Rev. B **59**(2), 775–782 (1999). [CrossRef]

27. W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Passively mode-locked raman laser,” Phys. Rev. Lett. **105**(14), 143903 (2010). [CrossRef] [PubMed]

28. I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express **20**(6), 6604–6609 (2012). [CrossRef] [PubMed]

_{2}resonators also in the normal GVD regime [2

2. I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF_{2} resonator,” Opt. Lett. **34**(7), 878–880 (2009). [CrossRef] [PubMed]

3. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. **101**(9), 093902 (2008). [CrossRef] [PubMed]

## 6. Conclusion

## Acknowledgments

## References and links

1. | P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature |

2. | I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF |

3. | A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. |

4. | T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science |

5. | T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Modelocking in an optical microresonator via soliton formation” arXiv:1211.0733. |

6. | T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics |

7. | S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A |

8. | J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. |

9. | A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, “Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,” Opt. Lett. |

10. | M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs” arXiv:1305.4921. [CrossRef] |

11. | Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A |

12. | Y. K. Chembo and N. Yu, “On the generation of octave-spanning optical frequency combs using monolithic whispering-gallery-mode microresonators,” Opt. Lett. |

13. | Y. K. Chembo, D. V. Strekalov, and N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. |

14. | S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. |

15. | Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. |

16. | P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. |

17. | O. Pironneau, F. Hecht, A. Le Hyaric, and J. Morice, “FreeFem++,” http://www.freefem.org/ |

18. | A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Morphology-dependent photonic circuit elements,” Opt. Lett. |

19. | I. S. Grudinin and N. Yu, “Finite-element modeling of coupled optical microdisk resonators for displacement sensing,” J. Opt. Soc. Am. B |

20. | M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes” IEEE. J. Sel. Top. Quantum Electron. |

21. | A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal group-velocity dispersion Kerr frequency comb,” Opt. Lett. |

22. | P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics |

23. | C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. St. J. Russell, “Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser,” Opt. Lett. |

24. | S. Coen and M. Erkintalo, “Universal scaling laws of Kerr frequency combs,” Opt. Lett. |

25. | T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. |

26. | A. Perakis, E. Sarantopoulou, Y. S. Raptis, and C. Raptis, “Temperature dependence of Raman scattering and anharmonicity study of MgF |

27. | W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Passively mode-locked raman laser,” Phys. Rev. Lett. |

28. | I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(230.5750) Optical devices : Resonators

(260.1180) Physical optics : Crystal optics

(240.3990) Optics at surfaces : Micro-optical devices

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 19, 2013

Revised Manuscript: October 23, 2013

Manuscript Accepted: October 24, 2013

Published: October 30, 2013

**Citation**

Ivan S. Grudinin, Lukas Baumgartel, and Nan Yu, "Impact of cavity spectrum on span in microresonator frequency combs," Opt. Express **21**, 26929-26935 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26929

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### References

- P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007). [CrossRef] [PubMed]
- I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF2 resonator,” Opt. Lett.34(7), 878–880 (2009). [CrossRef] [PubMed]
- A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett.101(9), 093902 (2008). [CrossRef] [PubMed]
- T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332(6029), 555–559 (2011). [CrossRef] [PubMed]
- T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Modelocking in an optical microresonator via soliton formation” arXiv:1211.0733.
- T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012). [CrossRef]
- S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A84(5), 053833 (2011). [CrossRef]
- J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett.109(23), 233901 (2012). [CrossRef] [PubMed]
- A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, “Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,” Opt. Lett.38(4), 525–527 (2013). [CrossRef] [PubMed]
- M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs” arXiv:1305.4921. [CrossRef]
- Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A82(3), 033801 (2010). [CrossRef]
- Y. K. Chembo and N. Yu, “On the generation of octave-spanning optical frequency combs using monolithic whispering-gallery-mode microresonators,” Opt. Lett.35(16), 2696–2698 (2010). [CrossRef] [PubMed]
- Y. K. Chembo, D. V. Strekalov, and N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett.104(10), 103902 (2010). [CrossRef] [PubMed]
- S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett.38(1), 37–39 (2013). [CrossRef] [PubMed]
- Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett.36(17), 3398–3400 (2011). [CrossRef] [PubMed]
- P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett.107(6), 063901 (2011). [CrossRef] [PubMed]
- O. Pironneau, F. Hecht, A. Le Hyaric, and J. Morice, “FreeFem++,” http://www.freefem.org/
- A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Morphology-dependent photonic circuit elements,” Opt. Lett.31(9), 1313–1315 (2006). [CrossRef] [PubMed]
- I. S. Grudinin and N. Yu, “Finite-element modeling of coupled optical microdisk resonators for displacement sensing,” J. Opt. Soc. Am. B29(11), 3010–3014 (2012). [CrossRef]
- M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes” IEEE. J. Sel. Top. Quantum Electron.12(1), 33–39 (2006). [CrossRef]
- A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal group-velocity dispersion Kerr frequency comb,” Opt. Lett.37(1), 43–45 (2012). [CrossRef] [PubMed]
- P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009). [CrossRef]
- C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. St. J. Russell, “Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser,” Opt. Lett.30(15), 1980–1982 (2005). [CrossRef] [PubMed]
- S. Coen and M. Erkintalo, “Universal scaling laws of Kerr frequency combs,” Opt. Lett.38(11), 1790–1792 (2013). [CrossRef] [PubMed]
- T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett.93(8), 083904 (2004). [CrossRef] [PubMed]
- A. Perakis, E. Sarantopoulou, Y. S. Raptis, and C. Raptis, “Temperature dependence of Raman scattering and anharmonicity study of MgF2,” Phys. Rev. B59(2), 775–782 (1999). [CrossRef]
- W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Passively mode-locked raman laser,” Phys. Rev. Lett.105(14), 143903 (2010). [CrossRef] [PubMed]
- I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express20(6), 6604–6609 (2012). [CrossRef] [PubMed]

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