Abstract

Optical microresonators are ideal tools for the reduction of the threshold of optical parametric oscillation based on four-wave mixing. Usually, the efficiency and bandwidth of the resonant process are interdependent due to stringent phase matching requirements leading to limitation of the bandwidth of the spectrum generated for a given pump power. We demonstrate a continuous-wave low-threshold resonant optical parametric oscillator with optical spectral span ranging from 0.36 to 1.6 μm. Harmonic generation is observed when a MgF2 microresonator characterized by quality factor approaching 1010 is pumped either at 780 nm, with a standard distributed-feedback semiconductor laser, or at 698 nm, with a reflective amplifier. Pump power does not exceed 25 mW. The nonlinear process is phase matched due to χ(3)-facilitated interaction of different mode families of the resonator. The optical harmonics generated can be used to seed high-power visible lasers, generate correlated photon pairs, and perform spectroscopy measurements.

© 2015 Optical Society of America

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2014 (9)

N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “Phase-matched second harmonic generation at the Dirac point of a 2-D photonic crystal,” Opt. Express 22, 6381–6390 (2014).
[Crossref]

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

C. Godey, I. V. Balakireva, A. Coillet, 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]

W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B. Matsko, 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]

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014).
[Crossref]

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

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

2013 (5)

M. R. E. Lamont, Y. Okawachi, A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38, 3478–3481 (2013).
[Crossref]

T. Hansson, D. Modotto, S. Wabnitz, “Dynamics of the modulational instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
[Crossref]

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, 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. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase mismatch-free nonlinear propagation in optical zero-index materials,” Science 342, 1223–1226 (2013).
[Crossref]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: nonlinear and nonlocal optical properties,” Phys. Rev. B 87, 155140 (2013).
[Crossref]

2012 (4)

2011 (8)

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

G. Kozyreff, J. L. Dominguez-Juarez, J. Martorell, “Nonlinear optics in spheres: from second harmonic scattering to quasi-phase matched generation in whispering gallery modes,” Laser Photon. Rev. 5, 737–749 (2011).
[Crossref]

P. Del-Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, A. L. Gaeta, “Octave spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
[Crossref]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref]

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
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A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
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J. S. Levy, M. A. Foster, A. L. Gaeta, M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19, 11415–11421 (2011).
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2010 (7)

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
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J. U. Furst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett 104, 153901 (2010).
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Y. K. Chembo, 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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H. Tavernier, P. Salzenstein, K. Volyanskiy, Y. K. Chembo, L. Larger, “Magnesium fluoride whispering gallery mode disk-resonators for microwave photonics applications,” IEEE Photon. Technol. Lett. 22, 1629–1631 (2010).

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4, 457–482 (2010).
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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
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2008 (5)

A. Melloni, F. Morichetti, M. Martinelli, “Four-wave mixing and wavelength conversion in coupled resonator optical waveguides,” J. Opt. Soc. Am. B 25, C87–C97 (2008).
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A. C. Turner, M. A. Foster, A. L. Gaeta, M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16, 4881–4887 (2008).
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M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2, 737–740 (2008).
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T. J. Kippenberg, K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
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S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
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2007 (4)

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318, 1118–1121 (2007).
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I. S. Grudinin, L. Maleki, “Ultralow-threshold Raman lasing with CaF2 resonators,” Opt. Lett. 32, 166–168 (2007).
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A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, L. Maleki, “Optical resonators with ten million finesse,” Opt. Express 15, 6768–6773 (2007).
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T. Carmon, K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3, 430–435 (2007).
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2006 (4)

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, L. Maleki, “Ultra-high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
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M. Fujii, C. Koos, C. Poulton, J. Leuthold, W. Freude, “Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP–InP racetrack microresonators,” IEEE Photon. Technol. Lett. 18, 361–363 (2006).
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G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-harmonic generation at angular incidence in a negative-positive index photonic band-gap structure,” Phys. Rev. E 74, 026608 (2006).
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M. L. Gorodetsky, A. E. Fomin, “Geometrical theory of whispering gallery modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006).
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2005 (1)

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
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2004 (5)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004).
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V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92, 043903 (2004).
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T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultra high-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
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A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
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M. Sumetsky, “Whispering-gallery-bottle microcavities: the three-dimensional etalon,” Opt. Lett. 29, 8–10 (2004).
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2003 (1)

D. D. Yavuz, D. R. Walker, M. Y. Shverdin, G. Y. Yin, S. E. Harris, “Quasi-periodic Raman technique for ultrashort pulse generation,” Phys. Rev. Lett. 91, 233602 (2003).
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2001 (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
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2000 (2)

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, S. E. Harris, “Raman generation by phased and antiphased molecular states,” Phys. Rev. Lett. 85, 562–565 (2000).
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P. P. Absil, J. H. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554–556 (2000).
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1998 (2)

H. Kawano, Y. Hirakawa, T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34, 260–268 (1998).
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J. A. Hudgings, Y. Lau, “Step-tunable all-optical wavelength conversion using cavity enhanced four-wave mixing,” IEEE J. Quantum Electron. 34, 1349–1355 (1998).
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1997 (3)

S. E. Harris, A. V. Sokolov, “Broadband spectral generation with refractive index control,” Phys. Rev. A 55, R4019–R4022 (1997).
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S. Coen, M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
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1996 (1)

D. Von der Linde, K. Rzazewski, “High-order optical harmonic generation from solid surfaces,” Appl. Phys. B 63, 499–506 (1996).
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1994 (2)

1993 (3)

1992 (3)

1991 (1)

S. Murata, A. Tomita, J. Shimizu, M. Kitamura, A. Suzuki, “Observation of highly nondegenerate four-wave mixing (>1  THz) in an InGaAsP multiple quantum well laser,” Appl. Phys. Lett. 58, 1458–1460 (1991).
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1990 (1)

1989 (2)

P. Bayvel, I. P. Giles, “Frequency generation by four wave mixing in all-fibre single-mode ring resonator,” Electron. Lett. 25, 1178–1180 (1989).
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J. G. Provost, R. Frey, “Cavity enhanced highly nondegenerate four-wave mixing in GaAlAs semiconductor lasers,” Appl. Phys. Lett. 55, 519–521 (1989).
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1988 (1)

L. Hollberg, M. Ohtsu, “Modulatable narrow-linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
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1987 (1)

1974 (1)

H. J. Simon, D. E. Mitchell, J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1534 (1974).
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1973 (1)

C. L. Tang, P. P. Bey, “Phase matching in second-harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. 9, 9–17 (1973).
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1970 (1)

N. Bloembergen, A. J. Sieveres, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
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1969 (1)

J. Falk, J. Murray, “Efficient noncollinear single-cavity parametric oscillator,” IEEE J. Quantum Electron. 5, 356–357 (1969).
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1962 (3)

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Absil, P. P.

Agostini, P.

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Aiello, A.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
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J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
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Andersen, U. L.

J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett. 106, 113901 (2011).
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J. U. Furst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105, 263904 (2010).
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J. U. Furst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, Ch. Marquardt, G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett 104, 153901 (2010).
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Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
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Auge, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
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A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, 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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C. Godey, I. V. Balakireva, A. Coillet, 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).
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P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
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T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106, 143903 (2011).
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F. Couny, F. Benabid, P. J. Roberts, P. S. Light, M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318, 1118–1121 (2007).
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H. Tavernier, N. N. T. Kim, P. Feron, R. Bendoula, P. Salzenstein, E. Rubiola, L. Larger, “Optical disk resonators with micro-wave free spectral range for optoelectronic oscillator,” in Proceedings of the 22nd European Time and Frequency Forum, Toulouse, France, 2008, paper FPE-0179.

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D. Farnesi, A. Barucci, G.-C. Righini, S. Berneschi, S. Soria, G. Nunzi Conti, “Optical frequency conversion in silica-whispering-gallery-mode microspherical resonators,” Phys. Rev. Lett. 112, 093901 (2014).
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C. L. Tang, P. P. Bey, “Phase matching in second-harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. 9, 9–17 (1973).
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N. Bloembergen, A. J. Sieveres, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
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J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
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N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “Phase-matched second harmonic generation at the Dirac point of a 2-D photonic crystal,” Opt. Express 22, 6381–6390 (2014).
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G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-harmonic generation at angular incidence in a negative-positive index photonic band-gap structure,” Phys. Rev. E 74, 026608 (2006).
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C. S. Werner, T. Beckmann, K. Buse, I. Breunig, “Blue-pumped whispering gallery optical parametric oscillator,” Opt. Lett. 37, 4224–4226 (2012).
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T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106, 143903 (2011).
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C. S. Werner, T. Beckmann, K. Buse, I. Breunig, “Blue-pumped whispering gallery optical parametric oscillator,” Opt. Lett. 37, 4224–4226 (2012).
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T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106, 143903 (2011).
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Capolino, F.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: nonlinear and nonlocal optical properties,” Phys. Rev. B 87, 155140 (2013).
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Carmon, T.

T. Carmon, K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3, 430–435 (2007).
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C. Godey, I. V. Balakireva, A. Coillet, 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).
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A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, 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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H. Tavernier, P. Salzenstein, K. Volyanskiy, Y. K. Chembo, L. Larger, “Magnesium fluoride whispering gallery mode disk-resonators for microwave photonics applications,” IEEE Photon. Technol. Lett. 22, 1629–1631 (2010).

Y. K. Chembo, 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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Chen, S.

Chiasera, A.

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

Choo, H. R.

Christov, I. P.

I. P. Christov, M. M. Murnane, H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the “single-cycle” regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
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Chu, S.

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

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2, 737–740 (2008).
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S. Coen, M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
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Coillet, A.

C. Godey, I. V. Balakireva, A. Coillet, 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, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, 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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F. Couny, F. Benabid, P. J. Roberts, P. S. Light, M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318, 1118–1121 (2007).
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D’Aguanno, G.

N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “Phase-matched second harmonic generation at the Dirac point of a 2-D photonic crystal,” Opt. Express 22, 6381–6390 (2014).
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G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-harmonic generation at angular incidence in a negative-positive index photonic band-gap structure,” Phys. Rev. E 74, 026608 (2006).
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Drullinger, R.

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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2, 737–740 (2008).
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J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
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Dudley, J. M.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, 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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Dumeige, Y.

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

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup. The inset shows a drawing of the packaged MgF2 resonator used in the experiments. The 7 mm diameter resonator was inserted into an enclosure. The enclosure was used for the protection of the open resonator from dust particles as well as for stabilizing the air gap between the surface of the resonator and the coupling prism.

Fig. 2.
Fig. 2.

(a) Demonstration of OPO including two pairs of frequency sidebands only. The resonator is pumped with 20 mW of 780 nm light. The intensity nonuniformity of the harmonic sidebands arises from the wavelength-dependent coupling efficiency. (b) Optical spectrum of the light leaving the resonator when pumped with 25 mW of optical power. The optical harmonics generated in the resonator result from a pair of OPO processes (52.4 THz, line 1, and 74.5 THz, line 2, from the carrier). The Stokes sideband generated in the vicinity of the carrier (12.3 THz away to the red side, line 3) results from the SRS process. All visible lines of the spectrum can be explained by FWM of the harmonics generated in the processes 1, 2, and 3.

Fig. 3.
Fig. 3.

Frequency spectrum of the oscillation signal for the case where optical pumping exceeds the threshold by approximately two orders of magnitude (50 mW of pumping). The spectrum is taken using two different OSAs. The closest line to the carrier on the red side is the first-order SRS Stokes line. The spectrum covers more than two octaves.

Fig. 4.
Fig. 4.

Light emitted by the WGMR pumped with 780 nm light observed on a screen placed after a diffraction grating. (a)–(c) are obtained by injection locking the laser to different modes of the resonator at different pump powers, and different resonator temperatures. The spot due to the pump light is to the far left of each plot. The spot is elongated along the horizontal direction due to the elliptical shape of the laser beam itself. The spots on the right, corresponding to the harmonics generated, can be single or (more frequently, but not always) have two lobes. Colors from red to blue are visible.

Fig. 5.
Fig. 5.

Schematic of the setup of the OPO involving a reflective amplifier. The inset shows the RF signal produced by the 698 nm laser mixed with an optical local oscillator on a fast photodiode. The linewidth measured is limited by the accuracy of the measurement and is less than 25 kHz.

Fig. 6.
Fig. 6.

Emission spectra of the resonator pumped at 698 nm taken with (a) a CCD spectrometer and (b) an OSA.

Fig. 7.
Fig. 7.

Demonstration of parametric frequency conversion in the resonator pumped with 698 nm light. The pump laser, located to the left side of the picture, is glowing red, whereas the pumped resonator glows green.

Fig. 8.
Fig. 8.

Frequency difference among resonator mode triplets as a function of sideband–carrier frequency separation. The triplets involve an optically pumped mode characterized by frequency ν0 corresponding to a wavelength of 780 nm (azimuthal index l0=36,340) and sideband modes, characterized by frequencies ν+ and ν (azimuthal indices l0+Δl and l0Δl, respectively). The frequency separation between the sideband and the carrier modes is determined by Δl. Inset: GVD parameter 2νlνl+1νl1 versus pump wavelength.

Equations (2)

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νl,qc2πn0(νl,q)R[l+αq(l2)1/3n0(νl,q)2n0(νl,q)21],
2ν0(l,q,p=0)ν+(l+Δl,q,p)ν(lΔl,q,p)Dc2πn0(νl,q)R2(Rr)rp,

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