Abstract

Universal nonlinear scattering processes such as Brillouin, Raman, and Kerr effects are fundamental light-matter interactions of particular theoretical and experimental importance. They originate from the interaction of a laser field with an optical medium at the lattice, molecular, and electronic scale, respectively. These nonlinear effects are generally observed and analyzed separately, because they do not often occur concomitantly. In this article, we report the simultaneous excitation of these three fundamental interactions in mm-size ultra-high Q whispering gallery mode resonators under continuous wave pumping. Universal nonlinear scattering is demonstrated in barium fluoride and strontium fluoride, separately. We further propose a unified theory based on a spatiotemporal formalism for the understanding of this phenomenology.

© 2016 Optical Society of America

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References

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2016 (1)

Y. K. Chembo, “Quantum dynamics of Kerr optical frequency combs below and above threshold: Spontaneous four-wave mixing, entanglement, and squeezed states of light,” Phys. Rev. A 93, 033820 (2016).
[Crossref]

2015 (10)

C. Milian, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
[Crossref]

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally Coherent Kerr Combs Generated with Crystalline Whispering Gallery Mode Resonators for Ultrahigh Capacity Fiber Communications,” Phys. Rev. Lett. 114, 093902 (2015).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, “Enhancing and inhibiting stimulated Brillouin scattering in photonic integrated circuits,” Nat. Commun. 6, 6396 (2015).
[Crossref]

G. Lin and Y. K. Chembo, “On the dispersion management of fluorite whispering-gallery mode resonators for Kerr optical frequency comb generation in the telecom and mid-infrared range,” Opt. Express 23, 1594–1604 (2015).
[Crossref] [PubMed]

W. Loh, A. A. Green, F. N. Baynes, D. C. Cole, F. J. Quinlan, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Dual-microcavity narrow-linewidth Brillouin laser,” Optica 2, 225–232 (2015).
[Crossref]

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

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 m in crystalline microresonators pumped with quantum-cascade lasers,” Opt. Lett. 40, 3468–3471(2015)
[Crossref] [PubMed]

F. Daniele, B. Andrea, G. C. Righini, C. Gualtiero Nunzi, and S. Silvia, “Generation of hyper-parametric oscillations in silica microbubbles,” Opt. Lett. 40, 4508–4511 (2015).
[Crossref]

C. Guo, K. Che, P. Zhang, J. Wu, Y. Huang, H. Xu, and Z. Cai, “Low-threshold stimulated Brillouin scattering in high-Q whispering gallery mode tellurite microspheres,” Opt. Express 23, 32261–32266 (2015).
[Crossref] [PubMed]

2014 (11)

G. Lin and N. Yu, “Continuous tuning of double resonance-enhanced second harmonic generation in a dispersive dielectric resonator,” Opt. Express 22, 557–562 (2014).
[Crossref] [PubMed]

A. Coillet and Y. K. Chembo, “On the robustness of phase-locking in Kerr optical frequency combs,” Opt. Lett. 39, 1529 (2014).
[Crossref] [PubMed]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor,” Opt. Lett. 39, 6009–6012 (2014).
[Crossref] [PubMed]

W. Liang, A. A. Savchenkov, Z. Xie, J.F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2014).
[Crossref]

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
[Crossref] [PubMed]

G. Lin, S. Diallo, K. Saleh, R. Martinenghi, J.-C. Beugnot, T. Sylvestre, and Y. K. Chembo, “Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators,” Appl. Phys. Lett. 105, 231103 (2014).
[Crossref]

B.-B. Li, W. R. Clements, X.-C. Yu, K. Shi, Q. Gong, and Y.-F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” PNAS 111, 14657–14662 (2014).
[Crossref] [PubMed]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” PNAS 111, E3836–E3844 (2014).
[Crossref] [PubMed]

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

A. Coillet and Y. K. Chembo, “Routes to spatiotemporal chaos in Kerr optical frequency combs,” Chaos 24, 013313 (2014).
[Crossref]

D. Farnesi, A. Barucci, G. Righini, S. Berneschi, S. Soria, and G. N. Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
[Crossref] [PubMed]

2013 (7)

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett,  103, 181107 (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]

Y. K. Chembo and C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery mode resonators,” Phys. Rev. A 87, 053852 (2013).
[Crossref]

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[PubMed]

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
[Crossref]

I. V. Kabakova, R. Pant, D. Y. Choi, S. Debbarma, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Narrow linewidth Brillouin laser based on chalcogenide photonic chip,” Opt. Lett.,  38, 3208–3211 (2013).
[Crossref] [PubMed]

F. Vanier, M. Rochette, N. Godbout, and Y. A. Peter, “Raman lasing in As2S3 high-Q whispering gallery mode resonators,” Opt. Lett. 38, 4966–4969 (2013).
[Crossref] [PubMed]

2012 (1)

S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, “Dispersion-managed solitons in fibre systems and lasers,” Phys. Reports 521, 135–203 (2012).
[Crossref]

2011 (2)

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

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

2010 (4)

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]

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]

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Phot. Rev. 4, 457–482 (2010).
[Crossref]

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]

2009 (2)

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at x-band (11-ghz) rates,” Phys. Rev. Lett. 102, 113601 (2009).
[Crossref] [PubMed]

2008 (2)

A. A. Kaminskii, H. Rhee, H. J. Eichler, L. Bohaty, P. Becker, and K. Takaichi, “Wide-band Raman stokes and anti-stokes comb lasing in a BaF2 single crystal under picosecond pumping,” Laser Phys. Lett. 5, 304–310 (2008).
[Crossref]

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express 16, 4130–4144 (2008).
[Crossref] [PubMed]

2007 (2)

A. A. Kaminskii, L. Bohaty, P. Becker, H. J. Eichler, and H. Rhee, “Many-wavelength picosecond Raman Stokes and anti-Stokes comb lasing of cubic SrF2 single crystal in the visible and near-IR,” Laser Phys. Lett. 4, 668–673 (2007).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express 15, 6768–6773 (2007).
[Crossref] [PubMed]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

2005 (1)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[Crossref] [PubMed]

2004 (1)

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

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

2002 (1)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref] [PubMed]

1999 (1)

1993 (1)

1983 (1)

M. Laval, M. Moszyński, R. Allemand, E. Cormoreche, P. Guinet, R. Odru, and J. Vacher, “Barium fluoride-inorganic scintillator for subnanosecond timing,” Nucl. Instr. Meth. Phys. Res. 206, 169–176 (1983).
[Crossref]

1964 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2013).

Allemand, R.

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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).
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M. Laval, M. Moszyński, R. Allemand, E. Cormoreche, P. Guinet, R. Odru, and J. Vacher, “Barium fluoride-inorganic scintillator for subnanosecond timing,” Nucl. Instr. Meth. Phys. Res. 206, 169–176 (1983).
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J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
[Crossref] [PubMed]

Lee, H.

Li, B.-B.

B.-B. Li, W. R. Clements, X.-C. Yu, K. Shi, Q. Gong, and Y.-F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” PNAS 111, 14657–14662 (2014).
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J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
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W. Liang, A. A. Savchenkov, Z. Xie, J.F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2014).
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A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photon. 5, 293–296 (2011).
[Crossref]

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

W. Liang, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of Kerr Combs in MgF2 and CaF2 Microresonators,” in Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings (IEEE, 2011), pp. 1–6.

Lin, G.

Lipson, M.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
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H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
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Loh, W.

Long, G. L.

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” PNAS 111, E3836–E3844 (2014).
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Lotshaw, W. T.

Luther-Davies, B.

Madden, S. J.

Maillotte, H.

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
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Maleki, L.

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 m in crystalline microresonators pumped with quantum-cascade lasers,” Opt. Lett. 40, 3468–3471(2015)
[Crossref] [PubMed]

W. Liang, A. A. Savchenkov, Z. Xie, J.F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2014).
[Crossref]

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

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Passively mode-locked Raman laser,” Phys. Rev. Lett. 105, 143903 (2010).
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I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
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A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express 16, 4130–4144 (2008).
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A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express 15, 6768–6773 (2007).
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W. Liang, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of Kerr Combs in MgF2 and CaF2 Microresonators,” in Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings (IEEE, 2011), pp. 1–6.

Malitson, I. H.

Martinenghi, R.

G. Lin, S. Diallo, K. Saleh, R. Martinenghi, J.-C. Beugnot, T. Sylvestre, and Y. K. Chembo, “Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators,” Appl. Phys. Lett. 105, 231103 (2014).
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Matsko, A. B.

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 m in crystalline microresonators pumped with quantum-cascade lasers,” Opt. Lett. 40, 3468–3471(2015)
[Crossref] [PubMed]

W. Liang, A. A. Savchenkov, Z. Xie, J.F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2014).
[Crossref]

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

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Passively mode-locked Raman laser,” Phys. Rev. Lett. 105, 143903 (2010).
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I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express 16, 4130–4144 (2008).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express 15, 6768–6773 (2007).
[Crossref] [PubMed]

W. Liang, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of Kerr Combs in MgF2 and CaF2 Microresonators,” in Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings (IEEE, 2011), pp. 1–6.

McMillan, J.F.

Menyuk, C. R.

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C. Milian, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” PNAS 111, E3836–E3844 (2014).
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D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
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D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
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M. Laval, M. Moszyński, R. Allemand, E. Cormoreche, P. Guinet, R. Odru, and J. Vacher, “Barium fluoride-inorganic scintillator for subnanosecond timing,” Nucl. Instr. Meth. Phys. Res. 206, 169–176 (1983).
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Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” PNAS 111, E3836–E3844 (2014).
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H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
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Papp, S. B.

Pauliat, G.

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
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Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” PNAS 111, E3836–E3844 (2014).
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Rong, H.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
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Saleh, K.

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally Coherent Kerr Combs Generated with Crystalline Whispering Gallery Mode Resonators for Ultrahigh Capacity Fiber Communications,” Phys. Rev. Lett. 114, 093902 (2015).
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G. Lin, S. Diallo, K. Saleh, R. Martinenghi, J.-C. Beugnot, T. Sylvestre, and Y. K. Chembo, “Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators,” Appl. Phys. Lett. 105, 231103 (2014).
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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).
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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 m in crystalline microresonators pumped with quantum-cascade lasers,” Opt. Lett. 40, 3468–3471(2015)
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W. Liang, A. A. Savchenkov, Z. Xie, J.F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2014).
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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).
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W. Liang, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of Kerr Combs in MgF2 and CaF2 Microresonators,” in Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings (IEEE, 2011), pp. 1–6.

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Schindler, P.

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally Coherent Kerr Combs Generated with Crystalline Whispering Gallery Mode Resonators for Ultrahigh Capacity Fiber Communications,” Phys. Rev. Lett. 114, 093902 (2015).
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A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photon. 5, 293–296 (2011).
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W. Liang, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of Kerr Combs in MgF2 and CaF2 Microresonators,” in Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings (IEEE, 2011), pp. 1–6.

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B.-B. Li, W. R. Clements, X.-C. Yu, K. Shi, Q. Gong, and Y.-F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” PNAS 111, 14657–14662 (2014).
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Skryabin, D. V.

C. Milian, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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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).
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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).
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Yu, X.-C.

B.-B. Li, W. R. Clements, X.-C. Yu, K. Shi, Q. Gong, and Y.-F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” PNAS 111, 14657–14662 (2014).
[Crossref] [PubMed]

Yulin, A. V.

C. Milian, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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Zhang, P.

Zhu, J.

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” PNAS 111, E3836–E3844 (2014).
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G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett,  103, 181107 (2013).
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G. Lin, S. Diallo, K. Saleh, R. Martinenghi, J.-C. Beugnot, T. Sylvestre, and Y. K. Chembo, “Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators,” Appl. Phys. Lett. 105, 231103 (2014).
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R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
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B.-B. Li, W. R. Clements, X.-C. Yu, K. Shi, Q. Gong, and Y.-F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” PNAS 111, 14657–14662 (2014).
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Figures (9)

Fig. 1
Fig. 1 Universal scattering behavior. (a) Simplified energy level scheme for Brillouin, Raman, and Kerr scattering. The excited states are virtual energy states. (b) The ultra-high Q resonator features a long photon lifetime (∼ 1 μs) which increases the probability of occurrence for nonlinear interactions. Above a certain pump power threshold, these scattering effects become stimulated and can be steadily observed.
Fig. 2
Fig. 2 Schematic illustration of the multi-resonant nonlinear optical frequency conversion and the experimental setup. (a) Schematic drawing of multi-resonant Raman, Brillouin, and Kerr combs in a monolithic optical cavity. FSR: free spectral range; Gray solid curves: cavity modes; Blue dashed curve: Raman gain; Green dashed curve: Brillouin gain; Red line: pump laser; Green solid line: Brillouin lasing; Blue solid lines: Raman lasing; Violet lines: Kerr comb. Note the overmoded nature of the WGM resonances allowed by the multiplicity of transverse mode families. (b) Scheme of the experimental setup. PC: fiber polarization controller; FC: fiber coupler; L1, L2: GRIN lenses; VOA: variable fiber optical attenuator; OSA1, OSA2: optical spectrum analyzers with 12.5 GHz and 0.1 GHz resolution, respectively; PD1, PD2: InGaAs photodetectors; FG: function generator; OSC: digital oscilloscope; HVA: high voltage amplifier. Inset: photo of the BaF2 disk coupled by a prism.
Fig. 3
Fig. 3 Experimental optical spectra of Raman, Brillouin lasing and Kerr comb simultaneously observed in BaF2. (a) Raman laser spectrum in the forward direction covering both the pump and Raman lasers in OSA1. The resolution is 0.1 nm. The measured Raman shift ΩR/2π is equivalent to 240 cm−1. (b,d) High resolution spectra in the forward and backward direction centered at the pump wavelength (λc = 1548.7 nm) in OSA2. The resolution is set at 0.1 GHz. The measured Brillouin shift ΩB/2π is 8.3 GHz and the frequency spacing of the Kerr comb is 5.5 GHz. (c,e) High resolution spectra centered at the Raman wavelength (λc = 1608.6 nm) in OSA2. The frequency spacing of the Raman comb is 5.5 GHz.
Fig. 4
Fig. 4 Experimental Brillouin spectra with FWM peaks in BaF2. No odd order anti-Stokes peaks were observed in both forward and backward direction. The measured frequency spacing between the even order Stokes is 16.5 GHz, matching the triple FSR value.
Fig. 5
Fig. 5 Experimental optical spectra of Raman, Brillouin lasing and Kerr comb simultaneously observed in BaF2 with PDH locking implemented. Note: time scale is shown in wavelength.. (a) Full spectrum covering both the pump and Raman signals. (b,c) The corresponding zoom-in spectra.
Fig. 6
Fig. 6 Beatnote spectra for Raman and Brillouin lasing. (a) Brillouin lasing. The beatnote has the Brillouin shift frequency (8.223 GHz). (b) Raman lasing. The beatnote has the FSR frequency (5.466 GHz).
Fig. 7
Fig. 7 Observation of a mode transition related to the FWM between the pump and the Raman comb. (a), (b) Red curves: transmission of the pump light through the prism coupling setup. Green curves: detected signal in the backward direction in PD2. The coupling strength is increased in (b) by decreasing the coupling gap between the prism and the cavity. Gray regime highlights a transition regime which is accompanied with the observation of a FWM comb. (c) Typical FWM comb spectrum.
Fig. 8
Fig. 8 Experimental optical spectra of Raman, Brillouin lasing and FWM comb simultaneously observed in SrF2. (a) Raman laser spectrum in the forward direction covering both the pump and Raman lasers in OSA1. The resolution is 0.2 nm. The Raman laser occurs at 1619.7 nm, outside the measurable range of OSA2. The measured Raman shift ΩR/2π is 283 cm−1. (b) High resolution spectra in the forward direction centered at the pump wavelength (λc = 1548.7 nm) in OSA2. The resolution is set at 0.1 GHz. The measured Brillouin shift ΩB/2π is 9.8 GHz and the frequency spacing of the PRFWM comb FSR is 6.1 GHz. (c) High resolution spectra in the backward direction centered at the pump wavelength (λc = 1548.7 nm) in OSA2. The measured frequency spacing of two BRFWM combs is 6.1 GHz.
Fig. 9
Fig. 9 Numerical simulations for a BaF2 disk-resonator. The parameters are set to γ = 1 W−1km−1, and κ/2π = 1.2 MHz, κext/2π = 0.8 MHz. (a) Brillouin power spectrum around the pump. Note that the intermodal spacing corresponds to the Brillouin frequency shift. (b) Corresponding spectro-temporal dynamics. (c) Kerr-induced four-wave mixing around the pump. (d) Corresponding spectro-temporal dynamics. (e) Power spectrum around the first Raman Stokes line. (f) Corresponding spectro-temporal dynamics.

Tables (1)

Tables Icon

Table 1 Coefficents of the Sellmeier equation n 2 ( λ ) = 1 + i = 1 3 A i λ 2 / ( λ 2 / λ i 2 ) for barium and strontium fluoride, with λ in units of μm [51, 53].

Equations (12)

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( θ , t ) = l = N N l ( t ) e i l θ
( θ , t ) = l = N 0 3 ( l 1 2 ) ( t ) e i 3 ( l 1 2 ) θ
𝒮 ( θ , t ) = 𝒬 ( t ) e i 3 2 θ + * ( t ) e i 3 2 θ
t = κ + i σ e + i v g D ^ θ + 2 κ ext / T FSR P L + i v g γ f R [ ( θ , t ) π π h R ( θ / Ω FSR ) | ( θ θ , t ) | 2 d θ ] + i v g γ ( 1 f R ) [ | | 2 + 2 | | 2 ] + i v g η 𝒮
t = κ + i σ b + i v g γ [ | | 2 + 2 | | 2 ] + i v g η 𝒮 *
𝒮 t = μ 𝒮 + i μ { e i 3 2 θ | e i 3 2 θ + | e i 3 2 θ e i 3 2 θ } .
D ^ θ k = 2 + ( i Ω FSR ) k ( β k / k ! ) θ k ,
| 𝒩 = 1 2 π π + π * 𝒩 d θ .
D ˜ chr ( ω ) = 1 c [ ω n ( ω ) ω L n ( ω L ) ] β 1 , chr ( ω ω L ) ,
D ˜ geo ( ω ) = ξ q 2 1 / 3 a { ( ω Ω FSR ) 1 / 3 ( ω L Ω FSR ) 1 / 3 1 3 ( ω L Ω FSR ) 1 / 3 ( ω ω L ) ω L }
h R ( t ) = H ( t ) τ 1 2 + τ 2 2 τ 1 τ 2 2 e t / τ 2 sin ( t / τ 1 )
f R = c π ω L n 2 ( ω L ) 0 + d t 0 + d Ω g ( Ω ) sin ( Ω t ) ,

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