Skip to content
BY-NC-ND 4.0 license Open Access Published by De Gruyter June 17, 2016

On Frequency Combs in Monolithic Resonators

  • A. A. Savchenkov EMAIL logo , A. B. Matsko and L. Maleki
From the journal Nanophotonics

Abstract

Optical frequency combs have become indispensable in astronomical measurements, biological fingerprinting, optical metrology, and radio frequency photonic signal generation. Recently demonstrated microring resonator-based Kerr frequency combs point the way towards chip scale optical frequency comb generator retaining major properties of the lab scale devices. This technique is promising for integrated miniature radiofrequency and microwave sources, atomic clocks, optical references and femtosecond pulse generators. Here we present Kerr frequency comb development in a historical perspective emphasizing its similarities and differences with other physical phenomena. We elucidate fundamental principles and describe practical implementations of Kerr comb oscillators, highlighting associated solved and unsolved problems.

References

[1] Hocker LO, Javan A, Rao DR, Frenkel L, and Sullivan T. Absolute frequency measurement and spectroscopy of gas laser transitions in the far infrared. Appl. Phys. Lett., 10(5):147-149, 1967.10.1063/1.1754887Search in Google Scholar

[2] Evenson KM, Wells JS, Petersen FR, Danielson BL, and Day GW. Accurate frequencies of molecular transitions used in laser stabilization: the 3.39μm transition in CH4 and the 9.33μm and 10.18μm transitions in CO2. Appl. Phys. Lett., 22(4):192-195, 1973.Search in Google Scholar

[3] Jennings DA, Hall JL, Layer HP, Pollock CR, Petersen FR, Drullinger RE, Evenson KM, and Wells JS. Direct frequency measurement of the I2-stabilized He-Ne 473-THz (633-nm) laser. Opt. Lett., 8(3):136-138, Mar 1983.10.1364/OL.8.000136Search in Google Scholar PubMed

[4] F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke. The optical calcium frequency standard. Instrumentation and Measurement, IEEE Transactions on, 48(2):613-617, Apr 1999.10.1109/19.769670Search in Google Scholar

[5] Glauber RJ, Hall JL, and Hänsch TW. Passion for precision. The Nobel Prize in Physics, 2005.Search in Google Scholar

[6] TM Fortier, MS Kirchner, F Quinlan, J Taylor, JC Bergquist, T Rosenband, N Lemke, A Ludlow, Y Jiang, CW Oates, et al. Generation of ultrastable microwaves via optical frequency division. Nature Photonics, 5(7):425-429, 2011.10.1038/nphoton.2011.121Search in Google Scholar

[7] Li CH, Benedick AJ, Fendel P, Glenday AG, Kartner FX, Phillips DF, Sasselov D, Szentgyorgyi A, and Walsworth RL. A laser frequency comb that enables radial velocity measurements with a precision of 1cm s−1. Nature, 452(7187):610 - 612, 2008.10.1038/nature06854Search in Google Scholar PubMed

[8] Levy JS, Gondarenko A, Foster MA, Turner-Foster AC, Gaeta AL, and Lipson M. CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects. Nature Photonic, 4(1):37-40, Jan 2010.10.1038/nphoton.2009.259Search in Google Scholar

[9] Joerg Pfeifle, Victor Brasch, Matthias Lauermann, Yimin Yu, Daniel Wegner, Tobias Herr, Klaus Hartinger, Philipp Schindler, Jingshi Li, David Hillerkuss. Coherent terabit communications with microresonator Kerr frequency combs. Nature Photonics, 8(5):375-380, 2014.10.1038/nphoton.2014.57Search in Google Scholar PubMed PubMed Central

[10] Coddington I, Swann WC, Nenadovic L, and Newbury NR. Rapid and precise absolute distance measurements at long range. Nature Photonics, 3(6):351-356, Jun 2009.10.1038/nphoton.2009.94Search in Google Scholar

[11] DelHaye P, Schliesser A, Arcizet O, Wilken T, Holzwarth R, and Kippenberg TJ. Optical frequency comb generation from a monolithic microresonator. Nature, 450(7173):1214 - 1217, 2007.10.1038/nature06401Search in Google Scholar PubMed

[12] Matsko AB, Savchenkov AA, Strekalov D, Ilchenko VS, and Maleki L. Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion. Phys. Rev. A, 71:033804, Mar 2005.10.1103/PhysRevA.71.033804Search in Google Scholar

[13] Matsko AB and Maleki L. On timing jitter of mode locked Kerr frequency combs. Opt. Express, 21(23):28862-28876, Nov 2013.10.1364/OE.21.028862Search in Google Scholar

[14] Maker PD, Terhune RW, and Savage CM. Intensity-dependent changes in the refractive index of liquids. Phys. Rev. Lett., 12:507-509, May 1964.10.1103/PhysRevLett.12.507Search in Google Scholar

[15] Agrawal GP. Modulation instability induced by cross-phase modulation. Phys. Rev. Lett., 59:880-883, Aug 1987.10.1103/PhysRevLett.59.880Search in Google Scholar

[16] Kaiser W and Garrett GCB. Two-photon excitation in CaF 2 : Eu2+. Phys. Rev. Lett., 7:229-231, 1961.Search in Google Scholar

[17] Woodbury EJ and Ng WK. Ruby laser operation in the near IR. Proc. IRE, 50:2367, 1962.Search in Google Scholar

[18] Maker PD, Terhune RW, and Savage CM. Optical third harmonic generation. Quantum Electronics, pp 1559-1578, 1964.Search in Google Scholar

[19] Maker PD and Terhune RW. Study of optical effects due to an induced polarization third order in the electric field strength. Phys. Rev. A, 137:801-818, 1965.10.1103/PhysRev.137.A801Search in Google Scholar

[20] Bloembergen N. Recent progress in four-wave mixing spectroscopy. Laser Spectroscopy IV, pp 340-348, 1979.10.1007/978-3-540-38950-7_36Search in Google Scholar

[21] Levenson MD and Kano SS. Introduction to Nonlinear Laser Spectroscopy. Academic Press, San Diego, CA, USA, 1988.10.1016/B978-0-12-444722-6.50008-0Search in Google Scholar

[22] Bloembergen N, Lotem H, Lynch RT, and Pure IJ. Study of optical effects due to an induced polarization third order in the electric field strength. Appl. Phys., 16:151, 1978.Search in Google Scholar

[23] Bloembergen N. Conservation laws in nonlinear optics. J. Opt. Soc. Am., 70:1429-1436, 1980.10.1364/JOSA.70.001429Search in Google Scholar

[24] Shen YR. Principles of Nonlinear Optics. Wiley, New York, 1984.Search in Google Scholar

[25] Boyd RW. Nonlinear Optics. Academic Press, Burlington, MA, USA, 2008.Search in Google Scholar

[26] Chang RK and Campillo AJ. Optical Processes in Microresonators, Advanced Series in Applied Physics v.3. World Scientific, Singapore, 1996.10.1142/2828Search in Google Scholar

[27] Fields MH, Popp J, and Chang RK. Nonlinear optics in microspheres. Prog. Opt., 41:1-95, 2000.10.1016/S0079-6638(00)80016-5Search in Google Scholar

[28] Datsyuk VV and Izmailov IA. Optics of microdroplets. Usp. Fiz. Nauk, 171:1117-1129, 2001.10.3367/UFNr.0171.200110m.1117Search in Google Scholar

[29] Oraevsky AN. Whispering-gallery waves. Quant. Electron, 32:377-400, 2002.10.1070/QE2002v032n05ABEH002205Search in Google Scholar

[30] Vahala KJ. Optical microcavities. Nature, 424:839-846, 2003.10.1038/nature01939Search in Google Scholar

[31] Vahala KJ. Optical Microcavities, Advanced Series in Applied Physics. World Scientific, New Jersey, 2004.10.1142/5485Search in Google Scholar

[32] Matsko AB and Ilchenko VS. Optical resonators with whispering gallery modes I: Basics. J. Sel. Top. Quant. Electron., 12:3-14, 2006.Search in Google Scholar

[33] Matsko AB. Practical Applications of Microresonators in Optics and Photonics. CRC Press, 2009.10.1201/9781315218960Search in Google Scholar

[34] Heebner J, Grover R, and Ibrahim T. Photonic Microresonator Research and Applications, Springer Series in Optical Sciences vol. 138. Springer-Verlag, London, 2010.Search in Google Scholar

[35] Chremmos I, Schwelb O, and Uzunoglu N. Photonic microresonator research and applications, Springer Series in Optical Sciences vol. 156. Springer, New York, 2010.10.1007/978-1-4419-1744-7Search in Google Scholar

[36] Snow JB, Qian SX, and Chang RK. Stimulated Raman scattering from individual water and ethanol droplets at morpholody-dependent resonances. Opt. Lett, 10:37-39, 1985.10.1364/OL.10.000037Search in Google Scholar

[37] Campillo AJ, Eversole JD, and Lin HB. Resonator quantum electrodynamic enhancement of stimulated emission in microdroplets. Phys. Rev. Lett., 67:437-441, 1991.10.1103/PhysRevLett.67.437Search in Google Scholar

[38] Braginsky VB, Gorodetsky ML, and Ilchenko VS. Quality-factor and nonlinear properties of optical whispering-gallery modes. Physics Letters A, 137(7):393 - 397, 1989.10.1016/0375-9601(89)90912-2Search in Google Scholar

[39] Collot L, Lefevre-Seguin V, Brune M, Raimond JM, and Haroshe S. Very high-Q whispering gallery mode resonances observed in fused silica microspheres. Europhys. Lett., 23:327-334, 1993.10.1209/0295-5075/23/5/005Search in Google Scholar

[40] Gorodetsky ML, Savchenkov AA, and Ilchenko VS. Ultimate Q of optical microsphere resonators. Opt. Lett., 21(7):453-455, Apr 1996.10.1364/OL.21.000453Search in Google Scholar PubMed

[41] Vernooy DW, Ilchenko VS, Mabuchi H, Streed EW, and Kimble HJ. High- Q measurements of fused-silica microspheres in the near infrared. Opt. Lett., 23:247-249, 1998.10.1364/OL.23.000247Search in Google Scholar PubMed

[42] Armani DK, Kippenberg TJ, Spillane SM, and Vahala KJ. Ultrahigh- Q toroid microcavity on a chip. Nature, 421:925-928, 2003.10.1038/nature01371Search in Google Scholar PubMed

[43] Gorodetsky ML, Pryamikov AD, and Ilchenko VS. Rayleigh scattering in high-Q microspheres. J. Opt. Soc. Am. B, 17(6):1051-1057, Jun 2000.10.1364/JOSAB.17.001051Search in Google Scholar

[44] Grudinin IS, Matsko AB, Savchenkov AA, Strekalov D, Ilchenko VS, and Maleki L. Ultra-high Q crystalline microcavities. Opt. Commun., 265:33-38, 2006.10.1016/j.optcom.2006.03.028Search in Google Scholar

[45] Savchenkov AA, Matsko AB, Ilchenko VS, and Maleki L. Optical resonators with ten million finesse. Opt. Express, 15(11):6768-6773, May 2007.10.1364/OE.15.006768Search in Google Scholar

[46] Ilchenko VS, Savchenkov AA, Matsko AB, and Maleki L. Nonlinear optics and crystalline whispering gallery mode cavities. Phys. Rev. Lett., 92:043903, 2004.10.1103/PhysRevLett.92.043903Search in Google Scholar PubMed

[47] Yang Z, Chak P, Bristow AD, Driel HM, Iyer R, Aitchison JS, Smirl AL, and Sipe JE. Enhanced second-harmonic generation in AlGaAs microring resonators. Opt. Lett., 32:826-828, 2007.10.1364/OL.32.000826Search in Google Scholar

[48] Kippenberg TJ, Spillane SM, and Vahala KJ. Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity. Phys. Rev. Lett., 93:083904, Aug 2004.10.1103/PhysRevLett.93.083904Search in Google Scholar PubMed

[49] Savchenkov AA, Matsko AB, Strekalov D, Mohageg M, Ilchenko VS, and Maleki L. Low threshold optical oscillations in a whispering gallery mode CaF2 resonator. Phys. Rev. Lett., 93:243905, Dec 2004.10.1103/PhysRevLett.93.243905Search in Google Scholar PubMed

[50] Carmon T and Vahala KJ. Visible continuous emission from a silica microphotonic device by third-harmonic generation. Nature Physics, 3:430-435, Jun 2007.10.1038/nphys601Search in Google Scholar

[51] Kippenberg TJ, Holzwarth R, and Diddams SA. Microresonator-based optical frequency combs. Science, 332:555-559, 2011.10.1126/science.1193968Search in Google Scholar PubMed

[52] Lin HB, Huston AL, Justus BJ, and Campillo AJ. Some characteristics of a droplet whispering-gallery-mode laser. Opt. Lett., 11:614-616, 1986.10.1364/OL.11.000614Search in Google Scholar

[53] Sandoghdar V, Treussart F, Hare J, Lefevre-Seguin V, Raimond JM, and Haroche S. Very low threshold whispering-gallerymode microsphere laser. Phys.Rev. A, 54:R1777-R1780, 1996.10.1103/PhysRevA.54.R1777Search in Google Scholar

[54] Qian SX, Snow JB, and Chang RK. Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets. Opt. Lett., 10:499-501, 1985.10.1364/OL.10.000499Search in Google Scholar

[55] Lin HB and Campillo AJ. cw nonlinear optics in droplet microcavities displaying enhanced gain. Phys. Rev. Lett., 73:2440-2443, 1994.10.1103/PhysRevLett.73.2440Search in Google Scholar PubMed

[56] Spillane SM, Kippenberg TJ, and Vahala KJ. Ultralowthreshold Raman laser using a spherical dielectric microcavity. Nature, 415:621-623, 2002.10.1038/415621aSearch in Google Scholar PubMed

[57] Grudinin IS and Maleki L. Ultralow-threshold Raman lasing with CaF2 resonators. Opt.Lett., 32:166-168, 2007.10.1364/OL.32.000166Search in Google Scholar PubMed

[58] Grudinin IS, Matsko AB, and Maleki L. Brillouin lasing with a CaF2 whispering gallery mode resonator. Phys. Rev. Lett., 102:043902, 2009.10.1103/PhysRevLett.102.043902Search in Google Scholar PubMed

[59] Tomes M and Carmon T. Photonic micro-electromechanical systems vibrating at x-band (11-GHz) rates. Phys. Rev. Lett., 102:113601, 2009.10.1103/PhysRevLett.102.113601Search in Google Scholar PubMed

[60] Carmon T, Rokhsari H, Yang L, Kippenberg TJ, and Vahala KJ. Temporal behavior of radiation pressure-induced vibrations of an optical microcavity phonon mode. Phys. Rev. Lett., 94:223902, 2005.10.1103/PhysRevLett.94.223902Search in Google Scholar PubMed

[61] Kippenberg TJ, Rokhsari H, Carmon T, Scherer A, and Vahala KJ. Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity. Phys. Rev. Lett., 95:033901, Jul 2005.10.1103/PhysRevLett.95.033901Search in Google Scholar PubMed

[62] Wabnitz S. Suppression of interactions in a phase-locked soliton optical memory. Opt. Lett., 18(8):601-603, Apr 1993.10.1364/OL.18.000601Search in Google Scholar PubMed

[63] Leo F, Coen S, Kockaert P, Gorza SP, Emplit P, and Haelterman M. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nature Photonics, 4:471 - 476, May 2010.10.1038/nphoton.2010.120Search in Google Scholar

[64] Akhmediev NN and Ankiewicz A. Dissipative solitons: From optics to biology and medicine. Berlin Heidelberg, Springer, 2008.Search in Google Scholar

[65] Nakazawa M, Suzuki K, and Haus H. The modulational instability laser. I. experiment. Quantum Electronics, IEEE Journal of, 25(9):2036-2044, Sep 1989.10.1109/3.35230Search in Google Scholar

[66] Nakazawa M, Suzuki K, Kubota H, and Haus H. The modulation instability laser. II. theory. Quantum Electronics, IEEE Journal of, 25(9):2045-2052, Sep 1989.10.1109/3.35231Search in Google Scholar

[67] Haelterman M, Trillo S, and Wabnitz S. Additive-modulation-instability ring laser in the normal dispersion regime of a fiber. Opt. Lett., 17(10):745-747, May 1992. 10.1364/OL.17.000745Search in Google Scholar PubMed

[68] Coen S and Haelterman M. Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber. Phys. Rev. Lett., 79:4139-4142, Nov 1997.10.1103/PhysRevLett.79.4139Search in Google Scholar

[69] Coen S and Haelterman M. Continuous-wave ultrahigh-repetition- rate pulse-train generation through modulational instability in a passive fiber cavity. Opt. Lett., 26(1):39-41, Jan 2001.10.1364/OL.26.000039Search in Google Scholar PubMed

[70] Serkland DK and Kumar P. Tunable fiber-optic parametric oscillator. Opt. Lett., 24(2):92-94, Jan 1999.10.1364/OL.24.000092Search in Google Scholar PubMed

[71] Sharping JE, Fiorentino M, Kumar P, and Windeler RS. Optical parametric oscillator based on four-wave mixing in microstructure fiber. Opt. Lett., 27(19):1675-1677, Oct 2002.10.1364/OL.27.001675Search in Google Scholar

[72] Matos CJS, Taylor JR, and Hansen KP. Continuous-wave, totally fiber integrated optical parametric oscillator using holey fiber. Opt. Lett., 29(9):983-985, May 2004.10.1364/OL.29.000983Search in Google Scholar PubMed

[73] Deng Y, Lin Q, Lu F, Agrawal GP, and Knox WH. Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber. Opt. Lett., 30(10):1234-1236, May 2005.10.1364/OL.30.001234Search in Google Scholar PubMed

[74] Xu YQ, Murdoch SG, Leonhardt R, and Harvey JD. Widely-tunable triply-resonant optical parametric ring oscillator. In IEEE/LEOS Winter Topicals Meeting Series, 2009, pp 264-265, Jan 2009.10.1109/LEOSWT.2009.4771759Search in Google Scholar

[75] Matsko AB, Savchenkov AS, Liang W, Ilchenko VS, Seidel D, and Maleki L. Whispering gallery mode oscillators and optical comb generators. Symp. Frequency Standards and Metrology, 7:539-558, 2009.10.1142/9789812838223_0068Search in Google Scholar

[76] Matsko AB, Savchenkov AA, Liang W, Ilchenko VS, Seidel D, and Maleki L. Mode-locked Kerr frequency combs. Opt. Lett., 36:37-40, 2011.10.1364/OL.36.002845Search in Google Scholar PubMed

[77] Chembo YK and Menyuk CR. Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators. Phys. Rev. A, 87:053852, May 2013.10.1103/PhysRevA.87.053852Search in Google Scholar

[78] Firth WJ and Weiss CO. Cavity and feedback solitons. Opt. Photon. News, 13(2):54-58, Feb 2002.10.1364/OPN.13.2.000054Search in Google Scholar

[79] Firth W. Temporal cavity solitons: Buffering optical data. Nature Photonics, 4(7):415-417, 2010.Search in Google Scholar

[80] Maleki L, Ilchenko VS, Mohageg M, Matsko AB, Savchenkov AA, Seidel D, Wells NP, Camparo JC, and Jaduszliwer B. Alloptical integrated atomic clock. In Frequency Control Symposium (FCS), 2010 IEEE International, pp 119-124, June 2010.10.1109/FREQ.2010.5556362Search in Google Scholar

[81] Maleki L, Savchenkov AA, Ilchenko VS, Liang W, Eliyahu D, Matsko AB, Seidel D, Wells NP, Camparo JC, and Jaduszliwer B. All-optical integrated rubidium atomic clock. In Frequency Control and the European Frequency and Time Forum (FCS), 2011 Joint Conference of the IEEE International, pp 1-5, May 2011.10.1109/FCS.2011.5977304Search in Google Scholar

[82] Savchenkov AA, Eliyahu D, Liang W, Ilchenko VS, Byrd J, Matsko AB, Seidel D, and Maleki L. Stabilization of a Kerr frequency comb oscillator. Opt. Lett., 38(15):2636-2639, Aug 2013.10.1364/OL.38.002636Search in Google Scholar PubMed

[83] Marconi M, Javaloyes J, Balle S, and Giudici M. How lasing localized structures evolve out of passive mode locking. Phys. Rev. Lett., 112:223901, Jun 2014.10.1103/PhysRevLett.112.223901Search in Google Scholar PubMed

[84] Jang JK, Erkintalo M, Coen S, and Murdoch SG. Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons. Nature Communications, 6, 2015.10.1038/ncomms8370Search in Google Scholar PubMed

[85] Jang JK, Erkintalo M, Murdoch SG, and Coen S. Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field. Opt. Lett., 40(20):4755-4758, Oct 2015.10.1364/OL.40.004755Search in Google Scholar PubMed

[86] Herr T, Brasch V, Jost JD, Wang CY, Kondratiev NM, Gorodetsky ML, and Kippenberg TJ. Temporal solitons in optical microresonators. Nature Photonics, 8(2):145-152, 2014.10.1038/nphoton.2013.343Search in Google Scholar

[87] Jang JK, Erkintalo M, Luo K, Oppo GL, Coen S, and Murdoch SG. Controlled merging and annihilation of localized dissipative structures in an AC-driven damped nonlinear Schrodinger system. arXiv preprint arXiv:1504.07231, 2015.Search in Google Scholar

[88] Taheri H, Eftekhar AA, Wiesenfeld K, and Adibi A. Soliton formation in whispering-gallery-mode resonators via input phase modulation. Photonics Journal, IEEE, 7(2):1-9, April 2015.10.1109/JPHOT.2015.2416121Search in Google Scholar

[89] Erkintalo M, Luo K, Jang JK, Coen S, and Murdoch SG. Bunching of temporal cavity solitons via forward Brillouin scattering. New Journal of Physics, 17(11):115009, 2015.10.1088/1367-2630/17/11/115009Search in Google Scholar

[90] Dianov EM, Luchnikov AV, Pilipetskii AN, and Prokhorov AM. Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers. Applied Physics B, 54(2):175-180, 1992.10.1007/BF00331891Search in Google Scholar

[91] Coillet A and Chembo Y. On the robustness of phase locking in Kerr optical frequency combs. Opt. Lett., 39(6):1529-1532, Mar 2014.10.1364/OL.39.001529Search in Google Scholar PubMed

[92] Xue X, Xuan Y, Liu Y, Wang PH, Chen S, Wang J, Leaird DE, Qi M, and Weiner AM. Mode-locked dark pulse Kerr combs in normal-dispersion microresonators. Nature Photonics, 9(9):594-600, 2015.10.1038/nphoton.2015.137Search in Google Scholar

[93] Stolen RH, Bjorkholm JE, and Ashkin A. Phase-matched three-wave mixing in silica fiber optical waveguides. Applied Physics Letters, 24(7):308-310, 1974.10.1063/1.1655195Search in Google Scholar

[94] Stolen RH. Phase-matched-stimulated four-photon mixing in silica-fiber waveguides. Quantum Electronics, IEEE Journal of, 11(3):100-103, 1975.10.1109/JQE.1975.1068571Search in Google Scholar

[95] Hill KO, Johnson DC, Kawasaki BS, and MacDonald RI. cw three-wave mixing in single-mode optical fibers. Journal of Applied Physics, 49(10):5098-5106, 1978.10.1063/1.324456Search in Google Scholar

[96] Liang W, Savchenkov AA, Xie Z, McMillan JF, Burkhart J, Ilchenko VS, Wong CW, Matsko AB, and Maleki L. Miniature multioctave light source based on a monolithic microcavity. Optica, 2(1):40-47, Jan 2015.10.1364/OPTICA.2.000040Search in Google Scholar

[97] Sefler GA and Kitayama K. Frequency comb generation by four-wave mixing and the role of fiber dispersion. J. Lightwave Technol., 16(9):1596, Sep 1998.10.1109/50.712242Search in Google Scholar

[98] Mathlouthi W, Rong H, and Paniccia M. Characterization of eflcient wavelength conversion by four-wave mixing in sub-micron silicon waveguides. Opt. Express, 16(21):16735-16745, Oct 2008.10.1364/OE.16.016735Search in Google Scholar

[99] Melloni A, Morichetti F, and Martinelli M. Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides. J. Opt. Soc. Am. B, 25(12):C87-C97, Dec 2008.10.1364/JOSAB.25.000C87Search in Google Scholar

[100] Strekalov DV and Yu N. Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump. Phys. Rev. A, 79:041805, Apr 2009.10.1103/PhysRevA.79.041805Search in Google Scholar

[101] Papp SB, Del’Haye P, and Diddams SA. Parametric seeding of a microresonator optical frequency comb. Opt. Express, 21(15):17615-17624, Jul 2013.10.1364/OE.21.017615Search in Google Scholar PubMed

[102] Kaup DJ and Newell AC. Theory of nonlinear oscillating dipolar excitations in one-dimensional condensates. Phys. Rev. B, 18:5162, 1978.10.1103/PhysRevB.18.5162Search in Google Scholar

[103] Lugiato LA and Lefever R. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett., 58:2209, 1987. 10.1103/PhysRevLett.58.2209Search in Google Scholar PubMed

[104] T. Ackemann, W. J. Firth, and G.-L. Oppo. Fundamentals and applications of spatial dissipative solitons in photonic devices. Advances in Atomic, Molecular, and Optical Physics, 57:323-421, 2009.10.1016/S1049-250X(09)57006-1Search in Google Scholar

[105] Lomdahl PS and Samuelson MR. Persistent breather excitations in an ac-driven sine-Gordon system with loss. Phys. Rev. A, 34:664, 1986.10.1103/PhysRevA.34.664Search in Google Scholar

[106] Wysin G and Bishop AR. Chaos and coherence in classical one-dimensional magnets. J. Magnetism and Magnet. Materials, 54-57:1132, 1986.10.1016/0304-8853(86)90750-XSearch in Google Scholar

[107] Maugin GA and Miled A. Solitary waves in elastic ferromagnets. Phys. Rev. B, 33:4830, 1986.10.1103/PhysRevB.33.4830Search in Google Scholar

[108] Nozaki K and Bekki N. Low-dimensional chaos in a driven damped nonlinear Schrödinger equation. Physica (Amsterdam), 21D:381, 1986.10.1016/0167-2789(86)90012-6Search in Google Scholar

[109] Walls DF and Milburn GJ. Quantum Optics. Springer, New York, 1994.10.1007/978-3-642-79504-6Search in Google Scholar

[110] Maleki L, Ilchenko VS, Savchenkov AA, and Matsko AB. Crystalline Whispering Gallery Mode Resonators in Optics and Photonics, Chapter 3. CRC Press, 2009.10.1364/FIO.2009.FThC1Search in Google Scholar

[111] S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala. Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics. Phys. Rev. Lett., 91:043902, Jul 2003.10.1103/PhysRevLett.91.043902Search in Google Scholar PubMed

[112] Gorodetsky ML and Ilchenko VS. Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes. J. Opt. Soc. Am. B, 16:147-154, 1999.Search in Google Scholar

[113] Yariv A. Critical coupling and its control in optical waveguidering resonator systems. IEEE Photon. Tech. Lett., 14:483-485, 2002.10.1109/68.992585Search in Google Scholar

[114] Savchenkov AA, Rubiola E, Matsko AB, Ilchenko VS, and Maleki L. Phase noise of whispering gallery photonic hyperparametric microwave oscillators. Opt. Express, 16(6):4130-4144, Mar 2008.10.1364/OE.16.004130Search in Google Scholar

[115] Chembo YK and Yu N. Modal expansion approach to opticalfrequency- comb generation with monolithic whisperinggallery- mode resonators. Phys. Rev. A, 82:033801, Sep 2010.10.1103/PhysRevA.82.033801Search in Google Scholar

[116] Chembo YK, Strekalov D, and Yu N. Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators. Phys. Rev. Lett., 104:103902, Mar 2010.10.1103/PhysRevLett.104.103902Search in Google Scholar PubMed

[117] Chembo YK and Yu N. On the generation of octave-spanning optical frequency combs using monolithic whispering-gallery-mode microresonators. Opt. Lett., 35(16):2696-2698, Aug 2010.10.1364/OL.35.002696Search in Google Scholar PubMed

[118] Matsko AB, Savchenkov AA, and Maleki L. Normal groupvelocity dispersion Kerr frequency comb. Opt. Lett., 37(1):43-45, Jan 2012.10.1364/OL.37.000043Search in Google Scholar PubMed

[119] Matsko AB, Savchenkov AA, Ilchenko VS, Seidel D, and Maleki L. Hard and soft excitation regimes of Kerr frequency combs. Phys. Rev. A, 85:023830, Feb 2012.10.1103/PhysRevA.85.023830Search in Google Scholar

[120] Savchenkov AA, Matsko AB, Liang W, Ilchenko VS, Seidel D, and Maleki L. Kerr frequency comb generation in overmoded resonators. Opt. Express, 20(24):27290-27298, Nov 2012.10.1364/OE.20.027290Search in Google Scholar PubMed

[121] Matsko AB, Savchenkov AA, and Maleki Li. On excitation of breather solitons in an optical microresonator. Opt. Lett., 37:4856-4858, 2012.10.1364/OL.37.004856Search in Google Scholar PubMed

[122] Savchenkov AA, Matsko AB, Liang W, Ilchenko VS, Seidel D, and Maleki L. Transient regime of Kerr-frequency-comb formation. Phys. Rev. A, 86:013838, Jul 2012.10.1103/PhysRevA.86.013838Search in Google Scholar

[123] Hansson T, Modotto D, and Wabnitz S. On the numerical simulation of Kerr frequency combs using coupled mode equations. Optics Communications, 312:134-136, 2014.10.1016/j.optcom.2013.09.017Search in Google Scholar

[124] Park QH and Shin HJ. Parametric control of soliton light traffic by cw traflc light. Phys. Rev. Lett., 82:4432-4435, May 1999.10.1103/PhysRevLett.82.4432Search in Google Scholar

[125] Li S, Li L, Li Z, and Zhou G. Properties of soliton solutions on a cw background in optical fibers with higher-order effects. J. Opt. Soc. Am. B, 21(12):2089-2094, Dec 2004.10.1364/JOSAB.21.002089Search in Google Scholar

[126] Coillet A, Dudley J, Genty G, Larger L, and Chembo YK. Optical rogue waves in whispering-gallery-mode resonators. Physical Review A, 89:013835, 2014.10.1103/PhysRevA.89.013835Search in Google Scholar

[127] Blow KJ and Doran NJ. Global and local chaos in the pumped nonlinear Schrödinger equation. Phys. Rev. Lett., 52:526-529, Feb 1984.10.1103/PhysRevLett.52.526Search in Google Scholar

[128] Ghidaglia JM. Finite dimensional behavior for weakly damped driven Schrödinger equations. In Annales de l’IHP Analyse non linéaire, v 5, pp 365-405, 1988.10.1016/s0294-1449(16)30343-2Search in Google Scholar

[129] Barashenkov IV and Smirnov YS. Existence and stability chart for the ac-driven, damped nonlinear Schrödinger solitons. Phys. Rev. E, 54:5707-5725, Nov 1996.10.1103/PhysRevE.54.5707Search in Google Scholar PubMed

[130] Afanasjev VV, Malomed BA, and Chu PL. Stability of bound states of pulses in the Ginzburg-Landau equations. Phys. Rev. E, 56:6020-6025, Nov 1997.10.1103/PhysRevE.56.6020Search in Google Scholar

[131] Coen S and Erkintalo M. Universal scaling laws of Kerr frequency combs. Opt. Lett., 38(11):1790-1792, Jun 2013.10.1364/OL.38.001790Search in Google Scholar PubMed

[132] Matsko AB and Maleki L. Noise conversion in Kerr comb RF photonic oscillators. J. Opt. Soc. Am. B, 32(2):232-240, Feb 2015.10.1364/JOSAB.32.000232Search in Google Scholar

[133] Matsko AB and Maleki L. Feshbach resonances in Kerr frequency combs. Phys. Rev. A, 91:013831, Jan 2015.10.1103/PhysRevA.91.013831Search in Google Scholar

[134] Zhang L, Bao C, Singh V, Mu J, Yang C, Agarwal AM, Kimerling LC, and Michel J. Generation of two-cycle pulses and octavespanning frequency combs in a dispersion-flattened microresonator. Opt. Lett., 38(23):5122-5125, Dec 2013.10.1364/OL.38.005122Search in Google Scholar PubMed

[135] Coen D, Randle HG, Sylvestre T, and Erkintalo M. Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model. Opt. Lett., 38(1):37-39, Jan 2013.10.1364/OL.38.000037Search in Google Scholar PubMed

[136] Lamont MRE, Okawachi Y, and Gaeta AL. Route to stabilized ultrabroadband microresonator-based frequency combs. Opt. Lett., 38(18):3478-3481, Sep 2013.10.1364/OL.38.003478Search in Google Scholar PubMed

[137] Bao C, Zhang L, Matsko AB, Yan Y, Zhao Z, Xie G, Agarwal AM, Kimerling LC, Michel J, Maleki L, and Willner AE. Nonlinear conversion efficiency in Kerr frequency comb generation. Opt. Lett., 39(21):6126-6129, Nov 2014.10.1364/OL.39.006126Search in Google Scholar PubMed

[138] Bao C, Zhang L, Kimerling LC, Michel Y, and Yang. Soliton breathing induced by stimulated Raman scattering and selfsteepening in octave-spanning Kerr frequency comb generation. Opt. Express, 23(14):18665-18670, Jul 2015.10.1364/OE.23.018665Search in Google Scholar PubMed

[139] Hansson T and Wabnitz S. Frequency comb generation beyond the Lugiato-Lefever equation: multi-stability and super cavity solitons. J. Opt. Soc. Am. B, 32(7):1259-1266, Jul 2015.10.1364/JOSAB.32.001259Search in Google Scholar

[140] P. Chýlek, H.-B. Lin, J. D. Eversole, and A. J. Campillo. Absorption effects on microdroplet resonant emissionstructure. Opt. Lett., 16(22):1723-1725, Nov 1991.10.1364/OL.16.001723Search in Google Scholar PubMed

[141] Absil PP, Hryniewicz JV, Little BE, Cho PS, Wilson RA, Joneckis LG, and Ho PT. Wavelength conversion in GaAs micro-ring resonators. Opt. Lett., 25(8):554-556, Apr 2000.10.1364/OL.25.000554Search in Google Scholar PubMed

[142] Fülöp A, Krückel CJ, Castelló-Lurbe D, Silvestre E, and Torres- Company V. Triply resonant coherent four-wave mixing in silicon nitride microresonators. Opt. Lett., 40(17):4006-4009, Sep 2015.10.1364/OL.40.004006Search in Google Scholar PubMed

[143] Kourogi M, Nakagawa K, and Ohtsu M. Wide-span optical frequency comb generator for accurate optical frequency difference measurement. IEEE Quantum Electronics, 29(10):2693-2701, Oct 1993.10.1109/3.250392Search in Google Scholar

[144] Brothers LR, Lee D, and Wong NC. Terahertz optical frequency comb generation and phase locking of an optical parametric oscillator at 665 GHz. Opt. Lett., 19(4):245-247, Feb 1994.10.1364/OL.19.000245Search in Google Scholar

[145] Kourogi M, Widiyatomoko B, Takeuchi Y, and Ohtsu M. Limit of optical-frequency comb generation due to material dispersion. IEEE Journal of Quantum Electronics, 31(12):2120-2126, Dec 1995.10.1109/3.477736Search in Google Scholar

[146] Macfarlane GM, Bell AS, Riis E, and Ferguson AI. Optical comb generator as an eflcient short-pulse source. Opt. Lett., 21(7):534-536, Apr 1996.10.1364/OL.21.000534Search in Google Scholar PubMed

[147] Ilchenko VS, Savchenkov AA, Matsko AB, and Maleki L. Whispering-gallery-mode electro-optic modulator and photonic microwave receiver. J. Opt. Soc. Am. B, 20(2):333-342, Feb 2003.10.1364/JOSAB.20.000333Search in Google Scholar

[148] Huang YP, Velev V, and Kumar P. Quantum frequency conversion in nonlinear microcavities. Opt. Lett., 38(12):2119-2121, Jun 2013.10.1364/OL.38.002119Search in Google Scholar PubMed

[149] Li Q, Davanco M, and Srinivasan K. Eflcient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics. arXiv preprint arXiv:1510.02527, 2015.Search in Google Scholar

[150] Hansson T and Wabnitz S. Bichromatically pumped microresonator frequency combs. Phys. Rev. A, 90:013811, Jul 2014.10.1103/PhysRevA.90.013811Search in Google Scholar

[151] Hu X, Liu Y, Xu X, Feng Y, Zhang W, Wang W, Song J, Wang Y, and Zhao W. Spatiotemporal evolution of a cosine-modulated stationary field and Kerr frequency comb generation in a microresonator. Appl. Opt., 54(29):8751-8757, Oct 2015.10.1364/AO.54.008751Search in Google Scholar PubMed

[152] Lobanov VE, Lihachev G, and Gorodetsky ML. Generation of platicons and frequency combs in optical microresonators with normal GVD by modulated pump. Europhysics Letters, 112(5):54008, 2015.10.1209/0295-5075/112/54008Search in Google Scholar

[153] V.E. Lobanov, G. Lihachev, T. J. Kippenberg, and M.L. Gorodetsky. Frequency combs and platicons in optical microresonators with normal gvd. Opt. Express, 23(6):7713-7721, Mar 2015.10.1364/OE.23.007713Search in Google Scholar PubMed

[154] Lin G, Martinenghi R, Diallo S, Saleh K, Coillet A, and Chembo YK. Spectro-temporal dynamics of Kerr combs with parametric seeding. Appl. Opt., 54(9):2407-2412, Mar 2015.10.1364/AO.54.002407Search in Google Scholar PubMed

[155] V.S. Ilchenko, J. Byrd, A.A. Savchenkov, D. Eliyahu, Wei Liang, A.B. Matsko, D. Seidel, and L. Maleki. Kerr frequency combbased Ka-band RF photonic oscillator. In 2013 Joint European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), pp 29-32, July 2013.10.1109/EFTF-IFC.2013.6702050Search in Google Scholar

[156] Ferdous F, Miao H, Leaird DE, Srinivasan K, Wang J, Chen L, Varghese LT, and Weiner AM. Spectral line-by-line pulse shaping of on-chip microresonator frequency combs. Nature Photonics, 5(12):770-776, 2011.10.1038/nphoton.2011.255Search in Google Scholar

[157] Turing A. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B, 237:37-72, 1952.10.1098/rstb.1952.0012Search in Google Scholar

[158] Klyshko DN. Photons and Nonlinear Optics. Taylor and Francis, New York, New York, USA, 1988.Search in Google Scholar

[159] Foster MA, Turner AC, Sharping JE, Schmidt BS, Lipson M, and Gaeta AL. Broad-band optical parametric gain on a silicon photonic chip. Nature, 441(7096):960-963, 2006.10.1038/nature04932Search in Google Scholar PubMed

[160] Savchenkov AA, Matsko AB, Wei Liang, Vladimir S Ilchenko, David Seidel, and Lute Maleki. Transient regime of Kerr frequency comb formation. arXiv preprint arXiv:1111.3922, 2011.10.1103/PhysRevA.86.013838Search in Google Scholar

[161] A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki. Transient regime of kerr-frequency-comb formation. Phys. Rev. A, 86:013838, Jul 2012.10.1103/PhysRevA.86.013838Search in Google Scholar

[162] Hasegawa A and Brinkman W. Tunable coherent IR and FIR sources utilizing modulational instability. Quantum Electronics, IEEE Journal of, 16(7):694-697, Jul 1980.10.1109/JQE.1980.1070554Search in Google Scholar

[163] Hasegawa A. Soliton-based optical communications: an overview. Selected Topics in Quantum Electronics, IEEE Journal of, 6(6):1161-1172, Nov 2000.10.1109/2944.902164Search in Google Scholar

[164] Agrawal GP. Nonlinear fiber optics. Academic Press, San Diego, California, USA, 2001.Search in Google Scholar

[165] Savchenkov AA, Matsko AB, Ilchenko VS, Solomatine I, Seidel D, and Maleki L. Tunable optical frequency comb with a crystalline whispering gallery mode resonator. Physical Review Letters, 101(9):093902, 2008.10.1103/PhysRevLett.101.093902Search in Google Scholar PubMed

[166] T Herr, K Hartinger, J Riemensberger, CY Wang, E Gavartin, R Holzwarth, ML Gorodetsky, and TJ Kippenberg. Universal formation dynamics and noise of Kerr-frequency combs in microresonators. Nature Photonics, 6(7):480-487, 2012.10.1038/nphoton.2012.127Search in Google Scholar

[167] Matsko AB, Liang W, Savchenkov AA, and Maleki L. Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators. Opt. Lett., 38(4):525-527, Feb 2013.10.1364/OL.38.000525Search in Google Scholar PubMed

[168] Andrey B. Matsko and Lute Maleki. Partially coherent Kerr frequency combs. In Nonlinear Optics, page NTu2B.2. Optical Society of America, 2013.10.1364/NLO.2013.NTu2B.2Search in Google Scholar

[169] Liang W, Matsko AB, Savchenkov AA, Ilchenko VS, Seidel D, and Maleki L. Generation of Kerr combs in MgF2 and CaF2 microresonators. In Frequency Control and the European Frequency and Time Forum (FCS), 2011 Joint Conference of the IEEE International, pp 1-6, May 2011.10.1109/FCS.2011.5977756Search in Google Scholar

[170] Liang W, Savchenkov AA, Matsko AB, Ilchenko VS, Seidel D, and Maleki L. Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator. Opt. Lett., 36(12):2290-2292, Jun 2011.10.1364/OL.36.002290Search in Google Scholar PubMed

[171] Liu Y, Xuan Y, Xue X, Wang PH, Chen S, Metcalf AJ, Wang J, Leaird DE, Qi M, and Weiner AM. Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation. Optica, 1(3):137-144, Sep 2014.10.1364/OPTICA.1.000137Search in Google Scholar

[172] Lin G, Saleh K, Henriet R, Diallo S, Martinenghi R, Coillet A, and Chembo YK. Wide-range tunability, thermal locking, and mode-crossing effects in Kerr optical frequency combs. Optical Engineering, 53(12):122602, 2014.10.1117/1.OE.53.12.122602Search in Google Scholar

[173] Farnesi D, Barucci A, Righini GC, Conti GN, and Soria S. Generation of hyper-parametric oscillations in silica microbubbles. Opt. Lett., 40(19):4508-4511, Oct 2015.10.1364/OL.40.004508Search in Google Scholar PubMed

[174] Ramelow S, Farsi A, Clemmen S, Levy JS, Johnson AR, Okawachi Y, Lamont MRE, Lipson M, and Gaeta AL. Strong polarization mode coupling in microresonators. Opt. Lett., 39(17):5134-5137, Sep 2014.10.1364/OL.39.005134Search in Google Scholar PubMed

[175] Herr T, Brasch V, Jost JD, Mirgorodskiy I, Lihachev G, Gorodetsky ML, and Kippenberg TJ. Mode spectrum and temporal soliton formation in optical microresonators. Phys. Rev. Lett., 113:123901, Sep 2014. 10.1103/PhysRevLett.113.123901Search in Google Scholar PubMed

[176] Huang SW, Yang J, Zhou H, Yu M, Kwong DL, and Wong CW. A low-phase-noise 18 GHz Kerr frequency microcomb phaselocked over 65 THz. Scientific Reports, 5:13355, 2015.10.1038/srep13355Search in Google Scholar PubMed PubMed Central

[177] Del’Haye P, Beha K, Papp SB, and Diddams SA. Self-injection locking and phase-locked states in microresonator-based optical frequency combs. Phys. Rev. Lett., 112:043905, Jan 2014.10.1103/PhysRevLett.112.043905Search in Google Scholar PubMed

[178] Del’Haye P, Coillet A, Loh W, Beha K, Papp SB, and Diddams SA. Phase steps and resonator detuning measurements in microresonator frequency combs. Nature communications, v6, 2015.10.1038/ncomms6668Search in Google Scholar PubMed

[179] Saha K, Okawachi Y, Shim B, Levy JS, Salem R, Johnson AR, Foster MA, Lamont MRE, Lipson M, and Gaeta AL. Modelocking and femtosecond pulse generation in chip-based frequency combs. Opt. Express, 21(1):1335-1343, Jan 2013.10.1364/OE.21.001335Search in Google Scholar PubMed

[180] Matsko AB, Savchenkov AS, Liang W, Ilchenko VS, Seidel D, and Maleki L. Group velocity dispersion and stability of resonant hyper-parametric oscillations. In Nonlinear Optics, page NWD2. Optical Society of America, 2011.10.1364/NLO.2011.NWD2Search in Google Scholar

[181] V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg. Photonic chip-based optical frequency comb using soliton Cherenkov radiation. Science, 351(6271):357-360, 2016.10.1126/science.aad4811Search in Google Scholar PubMed

[182] Xu Yi, Qi-Fan Yang, Ki Youl Yang, Myoung-Gyun Suh, and Kerry Vahala. Soliton frequency comb at microwave rates in a high-Q silica microresonator. Optica, 2(12):1078-1085, Dec 2015.10.1364/OPTICA.2.001078Search in Google Scholar

[183] Jose A. Jaramillo-Villegas, Xiaoxiao Xue, Pei-Hsun Wang, Daniel E. Leaird, and Andrew M. Weiner. Deterministic single soliton generation and compression in microring resonators avoiding the chaotic region. Opt. Express, 23(8):9618-9626, Apr 2015.10.1364/OE.23.009618Search in Google Scholar PubMed

[184] Hansson T, Modotto D, and Wabnitz S. Dynamics of the modulational instability in microresonator frequency combs. Phys. Rev. A, 88:023819, Aug 2013.10.1103/PhysRevA.88.023819Search in Google Scholar

[185] Mollenauer LF, Gordon JP, and Islam MN. Soliton propagation in long fibers with periodically compensated loss. Quantum Electronics, IEEE Journal of, 22(1):157-173, Jan 1986.10.1109/JQE.1986.1072858Search in Google Scholar

[186] Haus HA, Tamura K, Nelson LE, and Ippen EP. Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment. Quantum Electronics, IEEE Journal of, 31(3):591-598, Mar 1995.10.1109/3.364417Search in Google Scholar

[187] Becker M, Kuizenga Dirk J, and Siegman A. Harmonic mode locking of the Nd: YAG laser. Quantum Electronics, IEEE Journal of, 8(8):687-693, August 1972.10.1109/JQE.1972.1077271Search in Google Scholar

[188] Sato K, Wakita K, Kotaka I, Kondo Y, Yamamoto M, and Takada A. Monolithic strained InGaAsP multiple quantum well lasers with integrated electroabsorption modulators for active mode locking. Applied Physics Letters, 65(1):1-3, 1994.10.1063/1.113059Search in Google Scholar

[189] Arahira S and Ogawa Y. 480-GHz subharmonic synchronous mode locking in a short-cavity colliding-pulse mode-locked laser diode. Photonics Technology Letters, IEEE, 14(4):537-539, April 2002.10.1109/68.992603Search in Google Scholar

[190] Harvey GT and Mollenauer LF. Harmonically mode-locked fiber ring laser with an internal Fabry-Perot stabilizer for soliton transmission. Opt. Lett., 18(2):107-109, Jan 1993.10.1364/OL.18.000107Search in Google Scholar PubMed

[191] DePriest CM, Yilmaz T, Etamad S, Braun A, Abeles J, and Delfyett PJ. Ultra low noise and supermode suppression in an actively modelocked external-cavity semiconductor diode ring laser. In Optical Fiber Communication Conference and Exhibit, 2002. OFC 2002, pp 589-590, Mar 2002.Search in Google Scholar

[192] Chowdhury DQ, Hill SC, and Barber PW. Time dependence of internal intensity of a dielectric sphere on and near resonance. J. Opt. Soc. Am. A, 9(8):1364-1373, Aug 1992.10.1364/JOSAA.9.001364Search in Google Scholar

[193] Khaled EEM, Chowdhury DQ, Hill SC, and Barber PW. Internal and scattered time-dependent intensity of a dielectric sphere illuminated with a pulsed gaussian beam. J. Opt. Soc. Am. A, 11(7):2065-2071, Jul 1994.10.1364/JOSAA.11.002065Search in Google Scholar

[194] Frolov SV, Shkunov M, Vardeny ZV, and Yoshino K. Ring microlasers from conducting polymers. Phys. Rev. B, 56:R4363-R4366, Aug 1997.10.1103/PhysRevB.56.R4363Search in Google Scholar

[195] Heebner JE, Boyd RW, and Park QH. Scissor solitons and other novel propagation effects in microresonator-modified waveguides. J. Opt. Soc. Am. B, 19(4):722-731, Apr 2002.10.1364/JOSAB.19.000722Search in Google Scholar

[196] Whitten WB, Barnes MD, and Ramsey JM. Propagation of short optical pulses in a dielectric sphere. J. Opt. Soc. Am. B, 14(12):3424-3429, Dec 1997.10.1364/JOSAB.14.003424Search in Google Scholar

[197] Shaw RW, Whitten WB, Barnes MD, and Ramsey JM. Timedomain observation of optical pulse propagation in whispering-gallery modes of glass spheres. Opt. Lett., 23(16):1301-1303, Aug 1998.10.1364/OL.23.001301Search in Google Scholar

[198] Zhang J and Grischkowsky D. Whispering-gallery mode terahertz pulses. Opt. Lett., 27(8):661-662, Apr 2002.10.1364/OL.27.000661Search in Google Scholar PubMed

[199] Mees L, Gouesbet G, and Grehan G. Numerical predictions of microcavity internal fields created by femtosecond pulses, with emphasis on whispering gallery modes. Journal of Optics A: Pure and Applied Optics, 4(5):S150, 2002.10.1088/1464-4258/4/5/363Search in Google Scholar

[200] Maleki L, Savchenkov AA, Ilchenko VS, and Matsko AB. Whispering gallery mode lithium niobate microresonators for photonics applications. volume 5104, pp 1-13, 2003.10.1117/12.488253Search in Google Scholar

[201] Huang SW, Zhou H, Yang J, McMillan JF, Matsko AB, Yu M, Kwong DL, Maleki L, and Wong CW. Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators. Phys. Rev. Lett., 114:053901, Feb 2015.10.1103/PhysRevLett.114.053901Search in Google Scholar PubMed

[202] Brasch V, Geiselmann M, Herr T, Lihachev G, Pfeiffer M, Gorodetsky ML, and Kippenberg K. Photonic chip based optical frequency comb using soliton induced Cherenkov radiation. In CLEO: 2015, page STh4N.1. Optical Society of America, 2015.10.1364/CLEO_SI.2015.STh4N.1Search in Google Scholar

[203] Grudinin IS and Yu N. Towards eflcient octave-spanning comb with micro-structured crystalline resonator. Proc. SPIE, 9343, pp 93430F-93430F-9, 2015.10.1117/12.2085420Search in Google Scholar

[204] Liang W, Eliyahu D, Ilchenko VS, Savchenkov AA, Matsko AB, Seidel D, and Maleki L. High spectral purity Kerr frequency comb radio frequency photonic oscillator. Nature Communications, v6, 2015.10.1038/ncomms8957Search in Google Scholar PubMed PubMed Central

[205] Liang W, Savchenkov AA, Ilchenko VS, Eliyahu D, Seidel D, Matsko AB, and Maleki L. Generation of a coherent nearinfrared Kerr frequency comb in a monolithic microresonator with normal GVD. Opt. Lett., 39(10):2920-2923, May 2014.10.1364/OL.39.002920Search in Google Scholar PubMed

[206] Godey C, Balakireva IV, Coillet A, and Chembo YK. Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes. Physical Review A, 89:063814, 2014.10.1103/PhysRevA.89.063814Search in Google Scholar

[207] Coillet A, Balakireva I, Henriet R, Saleh K, Larger L, Dudley JM, Menyuk CR, and Chembo YK. Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators. Photonics Journal, IEEE, 5(4):6100409-6100409, Aug 2013. 10.1109/JPHOT.2013.2277882Search in Google Scholar

[208] Henriet R, Lin G, Coillet A, Jacquot M, Furfaro L, Larger L, and Chembo YK. Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor. Opt. Lett., 40(7):1567-1570, Apr 2015.10.1364/OL.40.001567Search in Google Scholar PubMed

[209] Soltani M, Matsko AB, and Maleki L. Enabling arbitrary wavelength frequency combs on chip. Laser and Photonics Reviews, 10(1):158-162, 2016.10.1002/lpor.201500226Search in Google Scholar

[210] NN Rosanov, VA Smirnov, and NV Vyssotina. Numerical simulations of interaction of bright spatial solitons in medium with saturable nonlinearity. Chaos, Solitons & Fractals, 4(8):1767-1782, 1994.10.1016/0960-0779(94)90110-4Search in Google Scholar

[211] S. Coen, M. Tlidi, Ph. Emplit, and M. Haelterman. Convection versus dispersion in optical bistability. Phys. Rev. Lett., 83:2328-2331, Sep 1999.10.1103/PhysRevLett.83.2328Search in Google Scholar

[212] P Parra-Rivas, D Gomila, E Knobloch, S Coen, and L Gelens. Origin and stability of dark pulse Kerr combs in normal dispersion resonators. arXiv preprint arXiv:1602.07068, 2016.Search in Google Scholar

[213] Savchenkov AA, Ilchenko VS, Teodoro F, Belden PM, Lotshaw WT, Matsko AB, and Maleki L. Generation of Kerr combs centered at 4.5um in crystalline microresonators pumped with quantum-cascade lasers. Opt. Lett., 40(15):3468-3471, Aug 2015.10.1364/OL.40.003468Search in Google Scholar PubMed

[214] Lecaplain C, Javerzac-Galy C, Lucas E, Jost JD, and Kippenberg T. Quantum cascade laser-based Kerr frequency comb generation. In CLEO: 2015, page SW4F.2. Optical Society of America, 2015.10.1364/CLEO_SI.2015.SW4F.2Search in Google Scholar

[215] Kuznetsov E. Solitons in a parametrically unstable plasma. Sov. Phys. Dokl., 22:507-508, 1977.Search in Google Scholar

[216] Ma YC. The perturbed plane-wave solutions of the cubic Schrodinger equation. Stud. Appl. Math., 60:43-58, 1979.10.1002/sapm197960143Search in Google Scholar

[217] Kibler B, Fatome J, Finot C, Millot G, Genty G, Wetzel B, Akhmediev N, Dias F, and Dudley JM. Observation of Kuznetsov-Ma soliton dynamics in optical fibre. Sci. Rep., 2:463, 2012.10.1038/srep00463Search in Google Scholar PubMed PubMed Central

[218] Akhmediev N and Korneev VI. Modulation instability and periodic solutions of the nonlinear Schrodinger equation. Theor. Math. Phys., 69:1089-1093, 1986.10.1007/BF01037866Search in Google Scholar

[219] Dudley JM, Genty G, Dias F, Kibler B, and Akhmediev N. Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation. Opt. Express, 17:21497-21508, 2009.10.1364/OE.17.021497Search in Google Scholar PubMed

[220] Nozaki K and Bekki N. Chaotic solitons in a plasma driven by an RF field. J. Phys. Soc. Jpn., 54:2363-2366, 1985.10.1143/JPSJ.54.2363Search in Google Scholar

[221] Turaev D, Vladimirov AG, and Zelik S. Long-range interaction and synchronization of oscillating dissipative solitons. Phys. Rev. Lett., 108:263906, 2012.10.1103/PhysRevLett.108.263906Search in Google Scholar PubMed

[222] Fermi E, Pasta J, and Ulam S. Studies of nonlinear problems I. Los Alamos report LA-1940, 1955, reprinted E. Fermi, Collected Papers, II:978, 1965.10.2172/4376203Search in Google Scholar

[223] Simaeys GV, Emplit Ph, and Haelterman M. Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave. Phys. Rev. Lett., 87:033902, 2001.10.1103/PhysRevLett.87.033902Search in Google Scholar PubMed

[224] Akhmediev N. Nonlinear physics: Deja vu in optics. Nature, 413:267-268, 2001.Search in Google Scholar

[225] Leo F, Gelens L, Emplit P, Haelterman M, and Coen S. Dynamics of one-dimensional Kerr cavity solitons. Opt. Express, 21:9180-9191, 2013.10.1364/OE.21.009180Search in Google Scholar PubMed

[226] Del’Haye P, Herr T, Gavartin E, Gorodetsky ML, Holzwarth R, and Kippenberg TJ. Octave spanning tunable frequency comb from a microresonator. Phys. Rev. Lett., 107:063901, Aug 2011.10.1103/PhysRevLett.107.063901Search in Google Scholar PubMed

[227] Kippenberg TJ, Spillane SM, and Vahala KJ. Modal coupling in traveling-wave resonators. Opt. Lett., 27(19):1669-1671, Oct 2002.10.1364/OL.27.001669Search in Google Scholar PubMed

[228] Savchenkov AA, Matsko AB, Strekalov D, Ilchenko VS, and Maleki L. Enhancement of photorefraction in whispering gallery mode resonators. Phys. Rev. B, 74:245119, Dec 2006.10.1103/PhysRevB.74.245119Search in Google Scholar

[229] Savchenkov AA, Liang W, Matsko AB, Ilchenko VS, Seidel D, and Maleki L. Tunable optical single-sideband modulator with complete sideband suppression. Opt. Lett., 34(9):1300-1302, May 2009.10.1364/OL.34.001300Search in Google Scholar PubMed

[230] Savchenkov AA, Matsko AB, Ilchenko VS, Strekalov D, and Maleki L. Direct visualization of stationary interference patterns of several running whispering gallery modes. In Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, page QTuG6. Optical Society of America, 2007.10.1109/QELS.2007.4431749Search in Google Scholar

[231] Carmon T, Schwefel HGL, Yang L, Oxborrow M, Stone AD, and Vahala KJ. Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities. Phys. Rev. Lett., 100:103905, Mar 2008.10.1103/PhysRevLett.100.103905Search in Google Scholar PubMed

[232] Grudinin IS, Baumgartel L, and Yu N. Impact of cavity spectrum on span in microresonator frequency combs. Opt. Express, 21(22):26929-26935, Nov 2013.10.1364/OE.21.026929Search in Google Scholar PubMed

[233] Matsko AB, Wei L, Ilchenko VS, Savchenkov AA, Byrd J, Seidel D, and Maleki L. Control of Kerr optical frequency comb generation with temperature dependent group velocity dispersion. In Photonics Conference (IPC), 2014 IEEE, pp 108-109, Oct 2014.10.1109/IPCon.2014.6995235Search in Google Scholar

[234] Xue X, Xuan Y, Wang PH, Liu Y, Leaird DE, Qi M, and Weiner AM. Normal-dispersion microcombs enabled by controllable mode interactions. Laser and Photonics Reviews, 9(4):L23- L28, 2015.10.1002/lpor.201500107Search in Google Scholar

[235] Maleki L, Ilchenko VS, Savchenkov AA, Liang W, Seidel D., and Matsko AB. High performance, miniature hyperparametric microwave photonic oscillator. In Frequency Control Symposium (FCS), 2010 IEEE International, pp 558-563, June 2010.10.1109/FREQ.2010.5556265Search in Google Scholar

[236] Birks TA, Wadsworth WJ, and Russell PSJ. Supercontinuum generation in tapered fibers. Opt. Lett., 25(19):1415-1417, Oct 2000.10.1364/OL.25.001415Search in Google Scholar PubMed

[237] Cordeiro CMB, Wadsworth WJ, Birks TA, and Russell PSJ. Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser. Opt. Lett., 30(15):1980-1982, Aug 2005.10.1364/OL.30.001980Search in Google Scholar

[238] Ilchenko VS, Gorodetsky ML, Yao XS, and Maleki L. Microtorus: a high-finesse microcavity with whispering-gallery modes. Opt. Lett., 26(5):256-258, Mar 2001.10.1364/OL.26.000256Search in Google Scholar

[239] Savchenkov AA, Grudinin IS, Matsko AB, Strekalov D, Mohageg M, Ilchenko VS, and Maleki L. Morphology-dependent photonic circuit elements. Opt. Lett., 31(9):1313-1315, May 2006.10.1364/OL.31.001313Search in Google Scholar PubMed

[240] Ferdous F, Demchenko AA, Vyatchanin SP, Matsko AB, and Maleki L. Microcavity morphology optimization. Phys. Rev. A, 90:033826, Sep 2014.10.1103/PhysRevA.90.033826Search in Google Scholar

[241] Savchenkov AA, Matsko AB, Liang W, Ilchenko VS, Seidel D, and Maleki L. Kerr combs with selectable central frequency. Nature Photonics, 5(5):293-296, 2011. 10.1038/nphoton.2011.50Search in Google Scholar

[242] Lin G and Chembo YK. 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(2):1594-1604, Jan 2015.10.1364/OE.23.001594Search in Google Scholar PubMed

[243] Demchenko YA and Gorodetsky ML. Analytical estimates of eigenfrequencies, dispersion, and field distribution in whispering gallery resonators. J. Opt. Soc. Am. B, 30(11):3056-3063, Nov 2013.10.1364/JOSAB.30.003056Search in Google Scholar

[244] Sumetsky M. Whispering-gallery-bottle microcavities: the three-dimensional etalon. Opt. Lett., 29(1):8-10, Jan 2004.10.1364/OL.29.000008Search in Google Scholar PubMed

[245] Agha IH, Okawachi Y, Foster MA, Sharping JE, and Gaeta AL. Four-wave-mixing parametric oscillations in dispersioncompensated high-Q silica microspheres. Phys. Rev. A, 76:043837, Oct 2007.10.1103/PhysRevA.76.043837Search in Google Scholar

[246] Matsko AB, Savchenkov AA, Liang W, Ilchenko VS, Seidel D, and Maleki L. Spectrum engineering in whispering gallery mode resonators. volume 7913, pp 79130Q-79130Q-10, 2011.10.1117/12.873991Search in Google Scholar

[247] Grudinin IS, Baumgartel L, and Yu N. Frequency comb from a microresonator with engineered spectrum. Opt. Express, 20(6):6604-6609, Mar 2012.10.1364/OE.20.006604Search in Google Scholar PubMed

[248] Benisty H and Piskunov N. Mastered dispersion of material resonators: Broad corrugated waveguides working under the Littrow regime. Applied Physics Letters, 102(15), 2013.10.1063/1.4802253Search in Google Scholar

[249] Li M, Wu X, Liu L, and Xu L. Kerr parametric oscillations and frequency comb generation from dispersion compensated silica micro-bubble resonators. Opt. Express, 21(14):16908-16913, Jul 2013.10.1364/OE.21.016908Search in Google Scholar PubMed

[250] Moss DJ, Morandotti R, Gaeta AL, and Lipson M. New CMOScompatible platforms based on silicon nitride and hydex for nonlinear optics. Nature Photonics, 7(8):597-607, 2013.10.1038/nphoton.2013.183Search in Google Scholar

[251] Grudinin IS and Yu N. Dispersion engineering of crystalline resonators via microstructuring. Optica, 2(3):221-224, Mar 2015.10.1364/OPTICA.2.000221Search in Google Scholar

[252] Yang KY, Beha K, Cole DC, Yi X, Del’Haye P, Lee H, Li J, Oh DY, Diddams SA, Papp SB, et al. Broadband dispersion engineered microresonator on-a-chip. arXiv preprint arXiv:1506.07157, 2015.Search in Google Scholar

[253] Ilchenko VS, Savchenkov AA, Matsko AB, and Maleki L. Dispersion compensation in whispering-gallery modes. J. Opt. Soc. Am. A, 20(1):157-162, Jan 2003.10.1364/JOSAA.20.000157Search in Google Scholar

[254] Zhang L, Yue Y, Beausoleil RG, and Willner AE. Flattened dispersion in silicon slot waveguides. Opt. Express, 18(19):20529-20534, Sep 2010.10.1364/OE.18.020529Search in Google Scholar PubMed

[255] Riemensberger J, Hartinger K, Herr T, Brasch V, Holzwarth R, and Kippenberg TJ. Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition. Opt. Express, 20(25):27661-27669, Dec 2012.10.1364/OE.20.027661Search in Google Scholar PubMed

[256] Jiang WC, Zhang J, Usechak NG, and Lin Q. Dispersion engineering of high-Q silicon microresonators via thermal oxidation. Applied Physics Letters, 105(3):-, 2014.10.1063/1.4890986Search in Google Scholar

[257] Bao C, Yan Y, Zhang L, Yue Y, Ahmed N, Agarwal AM, Kimerling LC, Michel J, and Willner AE. Increased bandwidth with flattened and low dispersion in a horizontal double-slot silicon waveguide. J. Opt. Soc. Am. B, 32(1):26-30, Jan 2015.10.1364/JOSAB.32.000026Search in Google Scholar

[258] Liang W, Ilchenko VS, Savchenkov AA, Matsko AB, Seidel D, and Maleki L. Passively mode-locked Raman laser. Phys. Rev. Lett., 105:143903, Sep 2010.10.1103/PhysRevLett.105.143903Search in Google Scholar PubMed

[259] Chembo YK, Grudinin IS, and Yu N. Spatiotemporal dynamics of Kerr-Raman optical frequency combs. Phys. Rev. A, 92:043818, Oct 2015.10.1103/PhysRevA.92.043818Search in Google Scholar

Received: 2015-11-12
Accepted: 2016-3-4
Published Online: 2016-6-17
Published in Print: 2016-6-1

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Downloaded on 21.3.2023 from https://www.degruyter.com/document/doi/10.1515/nanoph-2016-0031/html
Scroll Up Arrow