Abstract

In this Letter, we report phase-matched four-wave mixing separated by over one octave in a dispersion-engineered crystalline microresonator. Experimental and numerical results presented here confirm that primary sidebands were generated with a frequency shift up to 140 THz, and that secondary sidebands formed a localized comb structure, known as a clustered comb in the vicinity of the primary sidebands. A theoretical analysis of the phase-matching condition validated our experimental observations, and our results agree well with numerical simulations. These results offer the potential to realize a frequency-tunable comb cluster generator operating from 1 μm to mid-infrared wavelengths with a single and compact device.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

2017 (4)

C. Bao, H. Taheri, L. Zhang, A. Matsko, Y. Yan, P. Liao, L. Maleki, and A. E. Willner, J. Opt. Soc. Am. B 34, 715 (2017).
[Crossref]

S. Fujii, T. Kato, R. Suzuki, and T. Tanabe, Opt. Lett. 42, 2010 (2017).
[Crossref]

N. L. B. Sayson, K. E. Webb, S. Coen, M. Erkintalo, and S. G. Murdoch, Opt. Lett. 42, 5190 (2017).
[Crossref]

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

2016 (4)

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, Science 354, 600 (2016).
[Crossref]

C. Lecaplain, C. Javerzac-Galy, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Commun. 7, 13383 (2016).
[Crossref]

A. B. Matsko, A. A. Savchenkov, S.-W. Huang, and L. Maleki, Opt. Lett. 41, 5102 (2016).
[Crossref]

2014 (1)

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

2013 (2)

Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
[Crossref]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

2011 (1)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[Crossref]

2009 (1)

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photonics 3, 529 (2009).
[Crossref]

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

2000 (1)

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Amano, H.

S. Fujii, M. Fuchida, H. Amano, R. Suzuki, Y. Kakinuma, and T. Tanabe, Conference on Lasers and Electro-Optics (2019), paper STh4J.

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, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Arcizet, O.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photonics 3, 529 (2009).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Bao, C.

Brasch, V.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Carlson, D. R.

Chembo, Y. K.

Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
[Crossref]

Chen, Z.

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Coen, S.

Del’Haye, P.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photonics 3, 529 (2009).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Diddams, S. A.

Erkintalo, M.

Freude, W.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Fuchida, M.

S. Fujii, M. Fuchida, H. Amano, R. Suzuki, Y. Kakinuma, and T. Tanabe, Conference on Lasers and Electro-Optics (2019), paper STh4J.

Fujii, S.

S. Fujii, T. Kato, R. Suzuki, and T. Tanabe, Opt. Lett. 42, 2010 (2017).
[Crossref]

S. Fujii, M. Fuchida, H. Amano, R. Suzuki, Y. Kakinuma, and T. Tanabe, Conference on Lasers and Electro-Optics (2019), paper STh4J.

Geiselmann, M.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

Gorodetsky, M.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Gorodetsky, M. L.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

C. Lecaplain, C. Javerzac-Galy, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Commun. 7, 13383 (2016).
[Crossref]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photonics 3, 529 (2009).
[Crossref]

Hänsch, T.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Herr, T.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Hickstein, D. D.

Hofer, J.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Holzwarth, R.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[Crossref]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photonics 3, 529 (2009).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Huang, S.-W.

Iga, K.

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Javerzac-Galy, C.

C. Lecaplain, C. Javerzac-Galy, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Commun. 7, 13383 (2016).
[Crossref]

Jost, J.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Kakinuma, Y.

S. Fujii, M. Fuchida, H. Amano, R. Suzuki, Y. Kakinuma, and T. Tanabe, Conference on Lasers and Electro-Optics (2019), paper STh4J.

Karpov, M.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Kato, T.

Kemal, J. N.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Kippenberg, T. J.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

C. Lecaplain, C. Javerzac-Galy, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Commun. 7, 13383 (2016).
[Crossref]

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[Crossref]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photonics 3, 529 (2009).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Kondratiev, N.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Koos, C.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Kordts, A.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Kowligy, A. S.

Koyama, F.

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Lecaplain, C.

C. Lecaplain, C. Javerzac-Galy, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Commun. 7, 13383 (2016).
[Crossref]

Liao, P.

Lihachev, G.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

Lind, A.

Maleki, L.

Marin-Palomo, P.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Maser, D. L.

Matsko, A.

Matsko, A. B.

Matsutani, A.

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Menyuk, C. R.

Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
[Crossref]

Miyamoto, T.

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Murdoch, S. G.

Nader, N.

Ng, V.

Papp, S. B.

Pfeiffer, M. H.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

Pfeiffer, M. H. P.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Pfeifle, J.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Pham, H.

Picqué, N.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Rosenberger, R.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Sakaguchi, T.

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Savchenkov, A. A.

Sayson, N. L. B.

Schlenker, D.

F. Koyama, D. Schlenker, T. Miyamoto, Z. Chen, A. Matsutani, T. Sakaguchi, and K. Iga, IEEE Photon. Technol. Lett. 12, 125 (2000).
[Crossref]

Schliesser, A.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Schwefel, H. G. L.

Srinivasan, K.

Suh, M.-G.

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, Science 354, 600 (2016).
[Crossref]

Suzuki, R.

S. Fujii, T. Kato, R. Suzuki, and T. Tanabe, Opt. Lett. 42, 2010 (2017).
[Crossref]

S. Fujii, M. Fuchida, H. Amano, R. Suzuki, Y. Kakinuma, and T. Tanabe, Conference on Lasers and Electro-Optics (2019), paper STh4J.

Taheri, H.

Tanabe, T.

S. Fujii, T. Kato, R. Suzuki, and T. Tanabe, Opt. Lett. 42, 2010 (2017).
[Crossref]

S. Fujii, M. Fuchida, H. Amano, R. Suzuki, Y. Kakinuma, and T. Tanabe, Conference on Lasers and Electro-Optics (2019), paper STh4J.

Timmers, H.

Trainor, L. S.

Trocha, P.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Vahala, K. J.

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, Science 354, 600 (2016).
[Crossref]

Vijayan, K.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017).
[Crossref]

Wang, C.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Wang, C. Y.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Webb, K. E.

Westly, D.

Wilken, T.

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Figures (5)

Fig. 1.
Fig. 1. Kerr comb spectrum and corresponding integrated dispersion (solid red line). Dissipative Kerr solitons dominated by D 2 (a), with a single peak (b) and double peaks (c) affected by D 3 and D 4 , respectively. Clustered comb formed in a normal dispersion regime from the balance between D 2 and D 4 . The green solid line shows phase-matching points.
Fig. 2.
Fig. 2. (a) Transmission spectrum of fabricated MgF 2 microresonator. Red circles indicate resonances belonging to same mode family that we used as pump mode in the comb experiment. (b) Experimentally observed mode structure, where dots show the position of resonances, in a wavelength from 1530 nm to 1590 nm, limited by bandwidth of fiber comb source. (c) Calculated dispersion and measured result of 55 resonances for fundamental TE mode. Inset shows picture of experimental setup for tapered fiber coupling.
Fig. 3.
Fig. 3. (a) Calculated integrated dispersion D int (solid red line) and frequency difference value ω 0 + μ + ω 0 μ 2 ω 0 ) (solid green line) of fundamental TE mode. The points at which the green line crosses black reference line predict the phase-matched wavelength. (b) Simulation results with increasing pump detuning. The parameters are as follows: Q int = 1 × 10 8 , Q ext = 4 × 10 8 , g = 0.004 , and P in = 300 mW .
Fig. 4.
Fig. 4. (a) Experimentally observed spectrum at a pump mode μ = 0 when using different OSAs (depicted in different colors). Inset shows the experimental setup. MIR fiber was used above a 2.4 μm wavelength to avoid unwanted attenuation. (b) Detailed spectra of interest, which show a clustered comb formation in the vicinity of 1140 nm and the pump wavelength, and also confirm the signal wavelength at 2425 nm. (c) Observed spectra when pumping in an adjacent mode μ = 1 , indicating an FWM pair of 1137 nm and 2433 nm.
Fig. 5.
Fig. 5. Phase-matched wavelength of fundamental mode as a function of the pump wavelength in MgF 2 used in this work. Experimental plots are shown as blue and red circles.

Equations (1)

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A ( ϕ , t ) t = ( κ tot 2 + i δ 0 ) A + i k = 2 D k k ! ( i ϕ ) k A + i g | A | 2 A + κ ext A in ,