Abstract

We investigate frequency-comb generation in normal dispersion silicon microresonators from the near-infrared to mid-infrared wavelength range in the presence of multiphoton absorption and free-carrier effects. It is found that parametric oscillation is inhibited in the telecom wavelength range resulting from strong two-photon absorption. On the contrary, beyond the wavelength of 2200 nm, where three- and four-photon absorption are less detrimental, a comb can be generated with moderate pump power, or free-carriers are swept out by a positive-intrinsic-negative structure. In the temporal domain, the generated combs correspond to flat-top pulses, and the pulse duration can be easily controlled by varying the laser detuning. The reported comb generation process shows a high conversion efficiency compared with anomalous dispersion regime, which can guide and promote comb formation in materials with normal dispersion. As the comb spectra cover the mid-infrared wavelength range, they can find applications in comb-based radiofrequency photonic filters and mid-infrared spectroscopy.

© 2018 Chinese Laser Press

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2017 (5)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, and M. H. Anderson, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

E. Lucas, H. Guo, J. D. Jost, M. Karpov, and T. J. Kippenberg, “Detuning-dependent properties and dispersion-induced instabilities of temporal dissipative Kerr solitons in optical microresonators,” Phys. Rev. A 95, 043822 (2017).
[Crossref]

X. Xue, P. H. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator Kerr frequency combs with high conversion efficiency,” Laser Photon. Rev. 11, 1600276 (2017).
[Crossref]

Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A. Diddams, S. B. Papp, and K. Srinivasan, “Stably accessing octave-spanning microresonator frequency combs in the soliton regime,” Optica 4, 193–203 (2017).
[Crossref]

2016 (5)

A. G. Griffith, M. Yu, Y. Okawachi, J. Cardenas, A. Mohanty, A. L. Gaeta, and M. Lipson, “Coherent mid-infrared frequency combs in silicon-microresonators in the presence of Raman effects,” Opt. Express 24, 13044–13050 (2016).
[Crossref]

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
[Crossref]

A. A. Savchenkov, A. B. Matsko, and L. Maleki, “On frequency combs in monolithic resonators,” Nanophotonics 5, 363–391 (2016).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

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

2015 (9)

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, and C. B. Poitras, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

X. Xue, Y. Xuan, P. H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photon. Rev. 9, L23–L28 (2015).
[Crossref]

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

G. Lihachev, M. L. Gorodetsky, T. J. Kippenberg, and V. E. Lobanov, “Frequency combs and platicons in optical microresonators with normal GVD,” Opt. Express 23, 7713–7721 (2015).
[Crossref]

R. K. W. Lau, M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Effects of multiphoton absorption on parametric comb generation in silicon microresonators,” Opt. Lett. 40, 2778–2781 (2015).
[Crossref]

A. A. Savchenkov, V. S. Ilchenko, F. Di Teodoro, P. M. Belden, W. T. Lotshaw, A. B. Matsko, and L. Maleki, “Generation of Kerr combs centered at 4.5  μm in crystalline microresonators pumped with quantum-cascade lasers,” Opt. Lett. 40, 3468–3471 (2015).
[Crossref]

K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

2014 (6)

W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B. Matsko, and L. Maleki, “Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD,” Opt. Lett. 39, 2920–2923 (2014).
[Crossref]

T. Hansson, D. Modotto, and S. Wabnitz, “Mid-infrared soliton and Raman frequency comb generation in silicon microrings,” Opt. Lett. 39, 6747–6750 (2014).
[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]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

T. Hansson and S. Wabnitz, “Bichromatically pumped microresonator frequency combs,” Phys. Rev. A 90, 013811 (2014).
[Crossref]

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

2013 (4)

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[Crossref]

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[Crossref]

H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013).
[Crossref]

2012 (1)

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, 233901 (2012).
[Crossref]

2011 (2)

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

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. P. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350  nm,” Appl. Phys. Lett. 99, 081102 (2011).
[Crossref]

2009 (2)

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]

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79, 041805 (2009).
[Crossref]

2008 (1)

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300  nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

2007 (1)

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

2006 (1)

2004 (1)

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003).
[Crossref]

1998 (1)

D. C. Harris, “Durable 3-5  μm transmitting infrared window materials,” Infrared Phys. Technol. 39, 185–201 (1998).
[Crossref]

1987 (1)

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

Agha, I. H.

Alic, N.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. P. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350  nm,” Appl. Phys. Lett. 99, 081102 (2011).
[Crossref]

Anderson, M. H.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, and M. H. Anderson, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Baets, R.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[Crossref]

Balakireva, I.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[Crossref]

Belden, P. M.

Bennett, B.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

Borlaug, D.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. P. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350  nm,” Appl. Phys. Lett. 99, 081102 (2011).
[Crossref]

Bowers, J. E.

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

Brasch, V.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, and M. H. Anderson, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Briles, T. C.

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Bulu, I.

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

Campenhout, J.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[Crossref]

Cardenas, J.

A. G. Griffith, M. Yu, Y. Okawachi, J. Cardenas, A. Mohanty, A. L. Gaeta, and M. Lipson, “Coherent mid-infrared frequency combs in silicon-microresonators in the presence of Raman effects,” Opt. Express 24, 13044–13050 (2016).
[Crossref]

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, and C. B. Poitras, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

Chang, L.

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

Chembo, Y. K.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[Crossref]

Chen, S.

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Rotenberg, N.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300  nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Saleh, K.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[Crossref]

Savchenkov, A. A.

Schliesser, A.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

Schmidt, B. S.

Seidel, D.

Sharping, J. E.

Shen, B.

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

Simic, A.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. P. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350  nm,” Appl. Phys. Lett. 99, 081102 (2011).
[Crossref]

Soref, R.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

Srinivasan, K.

Stoll, R.

Stone, J. R.

Strekalov, D. V.

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79, 041805 (2009).
[Crossref]

Suh, M.-G.

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

Tang, H. X.

Trocha, P.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, and M. H. Anderson, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Turner, A. C.

Vahala, K.

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

Vahala, K. J.

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[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, 233901 (2012).
[Crossref]

van Driel, H. M.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300  nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Venkataraman, V.

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

Verheyen, P.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[Crossref]

Volet, N.

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

Wabnitz, S.

T. Hansson and S. Wabnitz, “Bichromatically pumped microresonator frequency combs,” Phys. Rev. A 90, 013811 (2014).
[Crossref]

T. Hansson, D. Modotto, and S. Wabnitz, “Mid-infrared soliton and Raman frequency comb generation in silicon microrings,” Opt. Lett. 39, 6747–6750 (2014).
[Crossref]

Wang, C. Y.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

Wang, H.

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

Wang, J.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Wang, L.

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

Wang, P. H.

X. Xue, P. H. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator Kerr frequency combs with high conversion efficiency,” Laser Photon. Rev. 11, 1600276 (2017).
[Crossref]

X. Xue, Y. Xuan, P. H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photon. Rev. 9, L23–L28 (2015).
[Crossref]

Wang, P.-H.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Weiner, A. M.

X. Xue, P. H. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator Kerr frequency combs with high conversion efficiency,” Laser Photon. Rev. 11, 1600276 (2017).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P. H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photon. Rev. 9, L23–L28 (2015).
[Crossref]

Westly, D. A.

Wolf, S.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, and M. H. Anderson, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Wong, C. W.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Xiong, C.

Xuan, Y.

X. Xue, P. H. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator Kerr frequency combs with high conversion efficiency,” Laser Photon. Rev. 11, 1600276 (2017).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P. H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photon. Rev. 9, L23–L28 (2015).
[Crossref]

Xue, X.

X. Xue, P. H. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator Kerr frequency combs with high conversion efficiency,” Laser Photon. Rev. 11, 1600276 (2017).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P. H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photon. Rev. 9, L23–L28 (2015).
[Crossref]

Yang, J.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Yang, K. Y.

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

Yang, Q.-F.

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

Yi, X.

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

Yu, M.

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
[Crossref]

A. G. Griffith, M. Yu, Y. Okawachi, J. Cardenas, A. Mohanty, A. L. Gaeta, and M. Lipson, “Coherent mid-infrared frequency combs in silicon-microresonators in the presence of Raman effects,” Opt. Express 24, 13044–13050 (2016).
[Crossref]

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, and C. B. Poitras, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Yu, N.

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79, 041805 (2009).
[Crossref]

Yu, Y.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[Crossref]

Zervas, M.

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

Zhang, X.

Zhou, H.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Zlatanovic, S.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. P. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350  nm,” Appl. Phys. Lett. 99, 081102 (2011).
[Crossref]

Appl. Phys. Lett. (4)

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300  nm,” Appl. Phys. Lett. 93, 131102 (2008).
[Crossref]

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. P. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350  nm,” Appl. Phys. Lett. 99, 081102 (2011).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003).
[Crossref]

IEEE J. Quantum Electron. (1)

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

IEEE Photon. J. (1)

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[Crossref]

Infrared Phys. Technol. (1)

D. C. Harris, “Durable 3-5  μm transmitting infrared window materials,” Infrared Phys. Technol. 39, 185–201 (1998).
[Crossref]

Laser Photon. Rev. (4)

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[Crossref]

X. Xue, Y. Xuan, P. H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photon. Rev. 9, L23–L28 (2015).
[Crossref]

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

X. Xue, P. H. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator Kerr frequency combs with high conversion efficiency,” Laser Photon. Rev. 11, 1600276 (2017).
[Crossref]

Nanophotonics (1)

A. A. Savchenkov, A. B. Matsko, and L. Maleki, “On frequency combs in monolithic resonators,” Nanophotonics 5, 363–391 (2016).
[Crossref]

Nat. Commun. (3)

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

S. H. Lee, D. Y. Oh, Q.-F. Yang, B. Shen, H. Wang, K. Y. Yang, Y. H. Lai, X. Yi, and K. Vahala, “Towards visible soliton microcomb generation,” Nat. Commun. 8, 1295 (2017).
[Crossref]

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, and C. B. Poitras, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

Nat. Photonics (3)

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Nature (1)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, and M. H. Anderson, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Opt. Express (5)

Opt. Lett. (6)

Optica (4)

Phys. Rev. A (3)

E. Lucas, H. Guo, J. D. Jost, M. Karpov, and T. J. Kippenberg, “Detuning-dependent properties and dispersion-induced instabilities of temporal dissipative Kerr solitons in optical microresonators,” Phys. Rev. A 95, 043822 (2017).
[Crossref]

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79, 041805 (2009).
[Crossref]

T. Hansson and S. Wabnitz, “Bichromatically pumped microresonator frequency combs,” Phys. Rev. A 90, 013811 (2014).
[Crossref]

Phys. Rev. Lett. (2)

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[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, 233901 (2012).
[Crossref]

Science (2)

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

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

Other (1)

M. Karpov, M. H. P. Pfeiffer, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” arXiv: 1706.06445 (2017).

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Figures (6)

Fig. 1.
Fig. 1. (a) Frequency-comb spectra in the absence (blue) and presence (red) of two-photon absorption. (b) The corresponding temporal evolution of (a) (blue curve). (c) The final stable flat top pulse in (b).
Fig. 2.
Fig. 2. (a) Spectra are generated in the presence of 3PA and FC effects (red), in the presence of 3PA without FC effects (blue), and in the absence of 3PA (green). (b) Temporal evolution of comb [blue curve in (a)] in the presence of 3PA without FC effects.
Fig. 3.
Fig. 3. (a) Spectra are generated in the presence of 4PA without FC effects (blue) and with FC effects (red). (b) Corresponding temporal profiles.
Fig. 4.
Fig. 4. (a) Spectra generated in the presence of 3PA and FC effects with different frequency separations of pumps. (b) Corresponding temporal evolution of blue curve in (a). (c) The final stable pulse of (b).
Fig. 5.
Fig. 5. (a) Spectrum generated in the presence of 4PA and FC effects. (b) Corresponding temporal evolution. (c) The final stable pulse of (b).
Fig. 6.
Fig. 6. (a)–(c) Spectra and (d)–(f) temporal profiles correspond to locations a, b, and c in temporal evolution of (g) with detuning of 0.05, 0.11, and 0.12, respectively.

Equations (3)

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

TRE(t,τ)t={α2κ2iδ0+iLβ22!(iτ)2+(1+iω0τ)×[iγL|E(t,τ)|2β2PAL2Aeff|E(t,τ)|2β3PAL3Aeff2|E(t,τ)|4β4PAL4Aeff3|E(t,τ)|6]σL2(1+iμ)Nc(t,τ)}E(t,τ)+κEin,
Ein=Pin1+Pin2exp(i2πfτ),
dNc(t)dt=β2PA2ω|E|4Aeff2+β3PA3ω|E|6Aeff3+β4PA4ω|E|8Aeff4Nc(t)τeff,

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