## Kerr frequency comb generation in overmoded resonators |

Optics Express, Vol. 20, Issue 24, pp. 27290-27298 (2012)

http://dx.doi.org/10.1364/OE.20.027290

Acrobat PDF (1712 KB)

### Abstract

We show that scattering-based interaction among nearly degenerate optical modes is the key factor in low threshold generation of Kerr frequency combs in nonlinear optical resonators with small group velocity dispersion (GVD). Mode interaction is capable of producing drastic changes in the local GVD, resulting in either a significant reduction, or an increase, in the oscillation threshold. Furthermore, we show that mode interaction is also responsible for majority of observed optical frequency combs in resonators characterized with large normal GVD. We present results of our numerical simulations together with supporting experimental data.

© 2012 OSA

## 1. Introduction

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

3. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A **76**(4), 043837 (2007). [CrossRef]

7. 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,” Nature Photonics **6**, 480–487 (2012). [CrossRef]

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

17. S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A **84**, 053833 (2011). [CrossRef]

18. 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**, 093902 (2008). [CrossRef] [PubMed]

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

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

7. 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,” Nature Photonics **6**, 480–487 (2012). [CrossRef]

7. 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,” Nature Photonics **6**, 480–487 (2012). [CrossRef]

15. W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF_{2} whispering gallery mode resonator,” Opt. Lett. **36**, 2290–2292 (2011). [CrossRef] [PubMed]

17. S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A **84**, 053833 (2011). [CrossRef]

20. F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express **20**, 21033–21043 (2012). [CrossRef]

21. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A **85**, 023830 (2012). [CrossRef]

22. A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal GVD Kerr frequency comb,” Opt. Lett. **37**, 43–45 (2012). [CrossRef] [PubMed]

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

24. 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**, 143903 (2010). [CrossRef]

25. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nature Photonics **5**, 293–296 (2011). [CrossRef]

## 2. Theoretical model

31. A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, “Group velocity dispersion and stability of resonant hyper-parametric oscillations,” in *Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD)* (Optical Society of America, 2011), paper NWD2.

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

32. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: threshold and phase diffusion,” Phys. Rev. A **71**, 033804 (2005). [CrossRef]

*V*̂ = −

*h*̄

*g*(

*ê*

^{†})

^{2}

*ê*

^{2}/2 is the interaction Hamiltonian,

*ω*are mode frequencies,

_{j}*â*is the annihilation operator of the field in the mode),

_{j}*ω*

_{11}is frequency of the pumped mode,

*n*

_{0}and

*n*

_{2}are linear and nonlinear refractive indexes of the material, 𝒱 is mode volume,

*δ*

_{11,j}is Kronecker’s delta;

*γ*

_{0}=

*γ*

_{0}

*+*

_{c}*γ*

_{0i}is half width at half maximum for optical modes, assumed to be the same for all modes involved; and

*γ*

_{0c}and

*γ*

_{0i}stand for coupling loss and intrinsic loss. The optical pump exciting the comb is given by

*F*

_{0}= (2

*γ*

_{0c}

*P*/(

*h*̄

*ω*

_{11}))1/2, where

*P*is the value of the power of cw pump light.

*a*

_{12}) interacts with another mode of the resonator (

*c*) having the same loaded Q-factor, but belonging to a different mode family. While it is possible for many modes (

*c*) to interact linearly with

_{j}*a*

_{12}, only one mode usually dominates. The interaction, described by Hamiltonian

*a*

_{12}. The splitting may be considered as a pure frequency shift of the mode

*a*

_{12}expressed as

*ω*̃

_{12}=

*ω*

_{12}−

*κ*

^{2}/Δ in the asymptotic case of a large difference between the eigenfrequencies of the interacting modes, Δ =

*ω*−

_{c}*ω*

_{12}, compared with the interaction constant

*κ*, |Δ| ≫

*κ*.

*a*

_{12}resulting from interaction with mode

*c*leads to modification of the effective GVD value for the pumped mode and the first two sideband modes, According to Eq. (2), it is enough to have

*κ*

^{2}≈ −Δ

*γ*

_{0}to achieve the desirable value of the GVD in any resonator with a small intrinsic dispersion.

*c*. In our experiments we observe frequency shifts of modes exceeding

*κ*

^{2}/Δ

*γ*

_{0}= 10

^{3}occurring due to mode interaction. This means that the value of dimensionless parameter

*κ*/

*γ*

_{0}can exceed 30. By selecting

*κ*/

*γ*

_{0}= 20 we found that soft excitation of the fundamental Kerr comb is possible for a wide range of frequency detunings: −50

*γ*

_{0}> Δ > −140

*γ*

_{0}. The Kerr comb for Δ = −70

*γ*

_{0}and

*ω*

_{11}−

*ω*= −2.4

*γ*

_{0}is shown in Fig. 1(a). It has a slightly asymmetric spectrum and a fast roll-off for higher order harmonics. The comb starts from zero fluctuations of the field with essentially zero initial conditions. Since such excitation regime of the comb is absent in the case where no mode interaction is available, we conclude that mode interaction is the actual cause, as predicted by the reasoning discussed above. It is worth noting that selection of

*κ*/

*γ*

_{0}= 20 is not critical; the comb is generated for a broad range of parameters. A detailed study of the dependence of the comb properties on parameters

*κ*/

*γ*

_{0}and Δ/

*γ*

_{0}will be presented elsewhere.

18. 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**, 093902 (2008). [CrossRef] [PubMed]

18. 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**, 093902 (2008). [CrossRef] [PubMed]

15. W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF_{2} whispering gallery mode resonator,” Opt. Lett. **36**, 2290–2292 (2011). [CrossRef] [PubMed]

## 3. Experiment

*ω*nearly equal to the FSR of the resonator. The modulated light was fed into the resonator and then sent to a photodiode. The photocurrent was analyzed using an oscilloscope (channel 2 in Fig. 2).

_{RF}*ω*−

_{l}*ω*

_{l}_{−1}−

*ω*and

_{RF}*ω*

_{l}_{+1}−

*ω*−

_{l}*ω*. The difference of those frequencies corresponds to the dispersion coefficient

_{RF}*D*. The accuracy of measurement is approximately one tenth of the full width at half maximum (FWHM) of the resonator mode. According to Fig. 3, this accuracy is good enough to observe that some mode families have a nearly equidistant spectrum, while other mode families have significantly non-equidistant spectra.

*D*/

*γ*

_{0}exceeded unity. This observation supports our theoretical prediction.

*D*/

*γ*

_{0}), and observed generation of frequency combs with envelopes similar to those predicted by the theory. In this experiment we used a CaF

_{2}resonator with a diameter of about 6.7 mm. The resonator had approximately 9.9 GHz FSR with loaded quality factor exceeding 10

^{9}. We pumped the resonator with 1545 nm light from a semiconductor laser. The optical power emitted by the laser was 15 mW, and 3.2-1 mW of the light entered the selected modes of the resonator (the value depends on the selected mode). The output light was collected using a fiber and introduced to an optical spectrum analyzer. The resultant optical spectra are shown in Fig. 6.

## 4. Conclusion

## Acknowledgment

## References and links

1. | O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in |

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

3. | I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A |

4. | I. H. Agha, Y. Okawachi, and A. L. Gaeta, “Theoretical and experimental investigation of broadband cascaded four-wave mixing in high-Q microspheres,” Opt. Express |

5. | 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. |

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

7. | 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,” Nature Photonics |

8. | F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express |

9. | A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A |

10. | A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal GVD Kerr frequency comb,” Opt. Lett. |

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

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

13. | A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nature Photonics |

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

15. | W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF |

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

18. | 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. |

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

20. | F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express |

21. | A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A |

22. | A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal GVD Kerr frequency comb,” Opt. Lett. |

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

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

25. | A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nature Photonics |

26. | 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,” Nature Photonics |

27. | F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. Tom Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nature Photonics |

28. | A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A |

29. | T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. |

30. | 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. | A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, “Group velocity dispersion and stability of resonant hyper-parametric oscillations,” in |

32. | A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: threshold and phase diffusion,” Phys. Rev. A |

**OCIS Codes**

(190.3970) Nonlinear optics : Microparticle nonlinear optics

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

**ToC Category:**

Frequency Comb Generation

**History**

Original Manuscript: August 10, 2012

Revised Manuscript: September 17, 2012

Manuscript Accepted: September 18, 2012

Published: November 19, 2012

**Virtual Issues**

Nonlinear Photonics (2012) *Optics Express*

**Citation**

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, "Kerr frequency comb generation in overmoded resonators," Opt. Express **20**, 27290-27298 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27290

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### References

- O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsko, ed. (CRC Press, 2009), Chap. 11.
- T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332, 555–559 (2011). [CrossRef] [PubMed]
- I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A76(4), 043837 (2007). [CrossRef]
- I. H. Agha, Y. Okawachi, and A. L. Gaeta, “Theoretical and experimental investigation of broadband cascaded four-wave mixing in high-Q microspheres,” Opt. Express17, 16209–16215 (2009). [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, 103902 (2010). [CrossRef] [PubMed]
- Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A82, 033801 (2010). [CrossRef]
- 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,” Nature Photonics6, 480–487 (2012). [CrossRef]
- F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express20, 21033–21043 (2012). [CrossRef]
- A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A85, 023830 (2012). [CrossRef]
- A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal GVD Kerr frequency comb,” Opt. Lett.37, 43–45 (2012). [CrossRef] [PubMed]
- I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express20, 6604–6609 (2012). [CrossRef] [PubMed]
- 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, 143903 (2010). [CrossRef]
- A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nature Photonics5, 293–296 (2011). [CrossRef]
- P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007). [CrossRef]
- W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett.36, 2290–2292 (2011). [CrossRef] [PubMed]
- 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, 063901 (2011). [CrossRef]
- S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A84, 053833 (2011). [CrossRef]
- 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, 093902 (2008). [CrossRef] [PubMed]
- I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF2 resonator,” Opt. Lett.34, 878–880 (2009). [CrossRef] [PubMed]
- F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express20, 21033–21043 (2012). [CrossRef]
- A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A85, 023830 (2012). [CrossRef]
- A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal GVD Kerr frequency comb,” Opt. Lett.37, 43–45 (2012). [CrossRef] [PubMed]
- I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express20, 6604–6609 (2012). [CrossRef] [PubMed]
- 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, 143903 (2010). [CrossRef]
- A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nature Photonics5, 293–296 (2011). [CrossRef]
- 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,” Nature Photonics3, 529–533 (2009). [CrossRef]
- F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. Tom Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nature Photonics5, 770–776 (2011). [CrossRef]
- A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A76, 023816 (2007). [CrossRef]
- T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett.100, 103905 (2008). [CrossRef] [PubMed]
- A. 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, 1313–1315 (2006). [CrossRef] [PubMed]
- A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, “Group velocity dispersion and stability of resonant hyper-parametric oscillations,” in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.
- A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: threshold and phase diffusion,” Phys. Rev. A71, 033804 (2005). [CrossRef]

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