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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26935–26941
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Broadband parametric frequency comb generation with a 1-μm pump source

Kasturi Saha, Yoshitomo Okawachi, Jacob S. Levy, Ryan K. W. Lau, Kevin Luke, Mark A. Foster, Michal Lipson, and Alexander L. Gaeta  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 26935-26941 (2012)
http://dx.doi.org/10.1364/OE.20.026935


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Abstract

We report the first experimental demonstration of broadband frequency comb generation from a single-frequency pump laser at 1-μm using parametric oscillation in a high-Q silicon-nitride ring resonator. The resonator dispersion is engineered to have a broad anomalous group velocity dispersion region near the pump wavelength for efficient parametric four-wave mixing. The comb spans 55 THz with a 230-GHz free spectral range. These results demonstrate the powerful advantage of dispersion engineering in chip-based devices for producing combs with a wide range of pump wavelengths.

© 2012 OSA

1. Introduction

Optical frequency synthesizers with discrete, precisely equidistant frequencies over a large bandwidth can be applied to a wide array of research areas such as spectroscopy, sensing, and optical clocks [1

1. Th. Udem, R. Holzwart, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). [CrossRef] [PubMed]

3

3. M. J. Thorpe and J. Ye, “Cavity enhanced direct frequency comb spctroscopy,” Appl. Phys. B 91, 397–414 (2008). [CrossRef]

]. A highly promising route to such optical comb generation, utilizes ultra-broadband cascaded parametric four-wave mixing (FWM) oscillation in high-Q microresonators [4

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

12

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

]. While there has been significant experimental [13

13. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011). [CrossRef] [PubMed]

19

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

] and theoretical [20

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

23

23. 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]

] development of ultra-broadband, microresonator-based comb generation, most of the emphasis has been on generating frequency combs with a pump in the telecommunication window. Broadband frequency combs pumped at near-IR wavelengths centered at 1 μm can offer several advantages such as the existence of commercially available technology for f–2f stabilization, the potential spectral overlap with optical frequency standards and to generate frequency-doubled comb in the visible spectrum for astronomical applications [24

24. F. Quinlan, G. Ycas, S. Osterman, and S. A Diddams, “A 12.5 GHz-spaced optical frequency comb spanning ¿400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum. 81, 063105 (2010). [CrossRef] [PubMed]

].

It has been established that dispersion engineering of microresonator geometries allows for using pump waves at different wavelengths to generate a frequency combs [25

25. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Nature Photon. 5, 293–296 (2011). [CrossRef]

27

27. J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, and T. J. Kippenberg, “Dispersion engineered high-Q silicon nitride ring-resonators via atomic layer deposition,” arXiv:1207.3841v1.

] over distinct wavelength ranges, but it still remains a challenge to design a device using the same device platform with the flexibility of pumping at different wavelengths and generating an ultra-broadband frequency comb in the visible or near-IR wavelength range with a desired comb spacing. For example, parametric comb generation was demonstrated in a CaF2 cylindrical and spheroid resonators with a 794-nm pump but with a relatively narrow ∼2 THz bandwidth [25

25. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Nature Photon. 5, 293–296 (2011). [CrossRef]

]. In a microtoroid [26

26. C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hansch, N. Picque, and T. J. Kippenberg, “Mid-Infrared optical frequency combs based on crystalline microresonators,” arXiv:119.2716v1.

] or microsphere [7

7. 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 17, 16209–16215 (2009). [CrossRef] [PubMed]

] geometry, the dispersion is dependent on the size and shape of the cavity. Since the free spectral range (FSR) is determined by the cavity size, it is difficult to design a structure where the pump wavelength and FSR can be freely determined. In contrast, in a silicon-nitride microring resonator, the dispersion and FSR can be controlled separately, and we have recently shown ultra-broadband (octave-spanning) comb generation with a pump at 1550 nm [14

14. 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, 3398–3400 (2011). [CrossRef] [PubMed]

] and have established that this system provides unmatched flexibility for tuning the FSR [28

28. A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lipson, and A. L. Gaeta, “Chip-based frequency combs with sub-100 GHz repetition rates,” Opt. Lett. 37, 875–877 (2012). [CrossRef] [PubMed]

].

Here, we show the multi-wavelength pumping functionality of the silicon-nitride microresonator platform and report the first demonstration of optical parametric oscillation and generation of an ultra-broadband frequency comb at 1-μm in a silicon-nitride ring resonator by dispersion engineering FWM gain in the 0.8–1.5 μm wavelength range.

2. Dispersion engineering for comb generation

In parametric comb generation, the pump power builds up in the resonator, resulting in parametric oscillation of a signal-idler pair. As the pump power is increased, the power in the signal-idler pair builds up further and leads to additional higher-order FWM processes that result in multiple components near the peaks of the cavity modes. Parametric oscillation in a cavity geometry arises from the interplay between the nonlinearity and the group-velocity dispersion (GVD), which is characterized by the phase mismatch for the FWM process and is given by,
Δk=2kpkski+Δknl,
(1)
where kp, ks, and ki are wavevectors of the pump, signal and idler respectively, and Δknl = γ|Ep|2 is the nonlinear contribution to the phase-mismatch near threshold. To minimize this mismatch, the pump frequency is tuned to the anomalous-GVD regime to compensate for the nonlinear phase mismatch and allow for FWM gain. The cavity geometry results in an additional restriction, such that the pump, signal, and idler each must be resonant with a cavity mode. Additionally, the energy conservation condition 2h̄ωp = h̄ωi + h̄ωs must be satisfied. The signal/idler modes that oscillate at threshold are those that satisfy the phase matching and energy conservation conditions required for FWM [7

7. 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 17, 16209–16215 (2009). [CrossRef] [PubMed]

].

The dispersion is determined by the material and for relatively large ring diameters by the waveguide cross-sectionional geometry, whereas the FSR is determined by the circumference of the microring. Figure 1 shows the simulated dispersion curves for silicon-nitride waveguides with varying cross-sections for the fundamental TE-mode. The curves show that decreasing the width of the waveguides shifts the anomalous dispersion region to lower wavelengths. The peak of the anomalous GVD occurs for a width of 1100 nm and then decreases with further reduction in waveguide widths, which is detrimental for wide bandwidth phase-matching and FWM.

Fig. 1 Simulated dispersion curves for the fundamental TE-mode of a silicon-nitride waveguide with 600-nm height and with widths of 1000, 1100, and 1200 nm.

3. Experiment and discussion

In our experiment, we use a single-frequency continuous wave laser centered at 1064 nm and amplified to 2 W using an Ytterbium-doped fiber amplifier (YDFA). The polarization of the laser is adjusted to quasi-TE and sent into a bus waveguide for coupling into the microring resonator. Both the coupling waveguide and the microring are monolithically fabricated. The bus waveguide and the ring have cross-sections of 600 nm by 1150 nm, which gives a broad region of anomalous GVD, centered at the pump wavelength of 1064 nm. The ring has a 115-μm radius which corresponds to a 230-GHz FSR. The loaded-quality factor Q of the resonator is 200,000. The output light is collected using an objective and sent to an optical spectrum analyzer. Figure 2(a–e) shows the optical spectrum associated with the comb generation dynamics as the pump wavelength is tuned into a cavity resonance. As the power oscillating in the microring increases, the cavity modes that are multiple FSRs away from the pump, experience the maximum FWM gain and oscillate at a threshold power of 80 mW. With further increases in power, cascaded FWM occurs resulting in multiple oscillations and minicomb formation [17

17. T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics of Kerr frequency comb formation in microresonators,” Nature Photon. 6, 480–487 (2012). [CrossRef]

] [Fig. 2(d)]. The density of comb lines increases as the pump frequency is tuned deep in the cavity resonance and adjacent cavity modes are filled through multiple higher-order degenerate and non-degenerate FWM processes [Fig. 2(e)].

Fig. 2 (a–e) Comb generation dynamics (from top to bottom) with a pump laser at 1064 nm. As the power oscillating inside the microring increases and threshold is reached, cavity modes that are maximally phase-matched experience gain and oscillate. When the pump is tuned deeper into resonance and power in the side modes is further increased, cascaded four-wave mixing takes place, leading to multiple cascaded oscillations and development of a wide bandwidth comb. (f) Frequency comb spectrum generated with 2 W of pump power. The comb spans 97.3 THz with a spacing of 230 GHz. (g) A zoomed in spectrum at the longer wavelength end. Comb teeth do not appear at every FSR due to lack of proper phase-matching and power buildup.

The optical spectrum of the fully formed comb is shown in Fig. 2(f). The 230-GHz-spaced comb lines are generated over a wavelength span of 406 nm which corresponds to 97.3 THz. Figure 2(g) shows the zoomed-in optical spectrum of the higher wavelength side of the frequency comb. We observe that the comb teeth are not formed at every FSR, which can be explained by considering the phase-matching relations for FWM. The relatively low anomalous dispersion of the microring resonator leads to improper phase-matching for wavelengths farther detuned from the original pump wavelength, which is due to the fact that the low anomalous dispersion cannot compensate for the non-linear contribution to the phase mismatch from self- and cross-phase modulation [7

7. 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 17, 16209–16215 (2009). [CrossRef] [PubMed]

]. This results in small FWM mixing gain and insufficient buildup of signal/idler pairs which ultimately must act as pump modes for further frequency generation, thus preventing further comb line formation. To investigate this issue further, we dispersion engineer and fabricate devices with larger anomalous dispersion.

Fig. 3 (a) Simulated dispersion curves for the fundamental TE-mode (dashed yellow) and TM-mode (solid red) of a silicon-nitride waveguide with a 725-nm height and 1000-nm width. (b) Broadband frequency comb at 1 μm spanning 55 THz and 230-GHz comb spacing. (c–d) Zoomed in spectra of the low and high wavelength regions of the frequency comb showing fully developed comb lines at every cavity mode.

Recently there have been multiple investigations directed towards testing the coherence properties of frequency combs [12

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

,17

17. T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics of Kerr frequency comb formation in microresonators,” Nature Photon. 6, 480–487 (2012). [CrossRef]

,29

29. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line shaping of on-chip microring resonator frequency combs,” Nature Photon. 5, 770–776 (2011). [CrossRef]

31

31. 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,” arXiv:1210.2994.

]. We have recently characterized spectral and temporal properties of the microresonator-based combs at 1.5-μm and have observed mode-locking and ultrashort pulse generation [32

32. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, M. A. Foster, M. Lipson, and A. L. Gaeta, “On-chip high repetition rate femtosecond source,” CTu3G.3, CLEO: Science and Innovations (2012).

]. As we use the same silicon-nitride microresonator platform, and observe that the spectral dynamics of the comb generated in the 1-μm region is similar to that of the 1.5-μm comb, we expect to observe similar temporal and coherence properties as well. We are currently working on characterizing the phase noise and temporal dynamics of the frequency comb generated in the 1-μm region.

4. Conclusion

In conclusion, we demonstrate broadband frequency comb generation in a monolithically integrated silicon-nitride microring resonator using a single-frequency laser at 1064 nm. We achieve a 55-THz comb bandwidth with a FSR of 230 GHz. Dispersion engineering a wider anomalous region around 1064-nm, in a microresonator with higher Q-factor will allow for generation of an octave spanning comb for comb stabilization using existing frequency stabilization equipment and techniques. Our results illustrate how the microring geometry in silicon nitride can be readily extended to broadband comb generation over a wide range of wavelengths, which could have significant applications in spectroscopy, metrology, high-speed communications, and on-chip optical clocks.

Acknowledgments

We acknowledge support from Defense Advanced Research Projects Agency (DARPA), the Air-Force Office of Scientific Research and the Center for Nanoscale Systems, supported by the National Science Foundation and the New York State Foundation for Science, Technology, and Innovation (NYSTAR). This work was performed in part at the Cornell Nano-Scale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (NSF) (grant ECS-0335765). K. S. and Y. O. contributed equally to this work.

References and links

1.

Th. Udem, R. Holzwart, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). [CrossRef] [PubMed]

2.

S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Science 3, 825–828 (2001). [CrossRef]

3.

M. J. Thorpe and J. Ye, “Cavity enhanced direct frequency comb spctroscopy,” Appl. Phys. B 91, 397–414 (2008). [CrossRef]

4.

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

5.

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]

6.

I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF2 resonator,” Opt. Lett. 45, 878–880 (2009). [CrossRef]

7.

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 17, 16209–16215 (2009). [CrossRef] [PubMed]

8.

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett. 102, 193902 (2009).

9.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010). [CrossRef]

10.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple wavelength oscillator for on-chip optical interconnects,” Nature Photon. 4, 37–40 (2010). [CrossRef]

11.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nature Photon. 6, 369–373 (2012). [CrossRef]

12.

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

13.

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011). [CrossRef] [PubMed]

14.

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, 3398–3400 (2011). [CrossRef] [PubMed]

15.

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]

16.

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

17.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics of Kerr frequency comb formation in microresonators,” Nature Photon. 6, 480–487 (2012). [CrossRef]

18.

S. B. Papp, P. Del’Haye, and S. A. Diddams,“Mechanical control of a microrod-resonator optical frequency comb,” arXiv:1205.4272v1.

19.

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

20.

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

21.

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011). [CrossRef] [PubMed]

22.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Transient regime of Kerr frequency comb formation,” arXiv:1111.3922v1.

23.

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]

24.

F. Quinlan, G. Ycas, S. Osterman, and S. A Diddams, “A 12.5 GHz-spaced optical frequency comb spanning ¿400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum. 81, 063105 (2010). [CrossRef] [PubMed]

25.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Nature Photon. 5, 293–296 (2011). [CrossRef]

26.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hansch, N. Picque, and T. J. Kippenberg, “Mid-Infrared optical frequency combs based on crystalline microresonators,” arXiv:119.2716v1.

27.

J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, and T. J. Kippenberg, “Dispersion engineered high-Q silicon nitride ring-resonators via atomic layer deposition,” arXiv:1207.3841v1.

28.

A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lipson, and A. L. Gaeta, “Chip-based frequency combs with sub-100 GHz repetition rates,” Opt. Lett. 37, 875–877 (2012). [CrossRef] [PubMed]

29.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line shaping of on-chip microring resonator frequency combs,” Nature Photon. 5, 770–776 (2011). [CrossRef]

30.

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] [PubMed]

31.

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,” arXiv:1210.2994.

32.

K. Saha, Y. Okawachi, B. Shim, J. S. Levy, M. A. Foster, M. Lipson, and A. L. Gaeta, “On-chip high repetition rate femtosecond source,” CTu3G.3, CLEO: Science and Innovations (2012).

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

ToC Category:
Frequency Comb Generation

History
Original Manuscript: September 13, 2012
Revised Manuscript: October 18, 2012
Manuscript Accepted: November 1, 2012
Published: November 14, 2012

Citation
Kasturi Saha, Yoshitomo Okawachi, Jacob S. Levy, Ryan K. W. Lau, Kevin Luke, Mark A. Foster, Michal Lipson, and Alexander L. Gaeta, "Broadband parametric frequency comb generation with a 1-μm pump source," Opt. Express 20, 26935-26941 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-26935


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References

  1. Th. Udem, R. Holzwart, and T. W. Hänsch, “Optical frequency metrology,” Nature416, 233–237 (2002). [CrossRef] [PubMed]
  2. S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Science3, 825–828 (2001). [CrossRef]
  3. M. J. Thorpe and J. Ye, “Cavity enhanced direct frequency comb spctroscopy,” Appl. Phys. B91, 397–414 (2008). [CrossRef]
  4. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator based optical frequency combs,” Science332, 555–559 (2011). [CrossRef] [PubMed]
  5. 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]
  6. I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF2 resonator,” Opt. Lett.45, 878–880 (2009). [CrossRef]
  7. 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]
  8. D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett.102, 193902 (2009).
  9. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010). [CrossRef]
  10. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple wavelength oscillator for on-chip optical interconnects,” Nature Photon.4, 37–40 (2010). [CrossRef]
  11. H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nature Photon.6, 369–373 (2012). [CrossRef]
  12. Scott B. Papp and Scott A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A84, 053833 (2011). [CrossRef]
  13. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express19, 14233–14239 (2011). [CrossRef] [PubMed]
  14. 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, 3398–3400 (2011). [CrossRef] [PubMed]
  15. 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]
  16. I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express20, 6604–6609 (2012). [CrossRef] [PubMed]
  17. T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics of Kerr frequency comb formation in microresonators,” Nature Photon.6, 480–487 (2012). [CrossRef]
  18. S. B. Papp, P. Del’Haye, and S. A. Diddams,“Mechanical control of a microrod-resonator optical frequency comb,” arXiv:1205.4272v1.
  19. A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal group-velocity dispersion Kerr frequency comb,” Opt. Lett.37, 43–45 (2012). [CrossRef] [PubMed]
  20. Y. K. Chembo and Nan Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A82, 033801 (2010). [CrossRef]
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