Type-Ⅱ micro-comb generation in a filter-driven four wave mixing laser [Invited]
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摘要
We experimentally demonstrate the generation of highly coherent Type-II micro-combs based on a microresonator nested in a fiber cavity loop, known as the filter-driven four wave mixing(FD-FWM) laser scheme.In this system, the frequency spacing of the comb can be adjusted to integer multiples of the free-spectral range(FSR) of the nested micro-resonator by properly tuning the fiber cavity length. Sub-comb lines with single FSR spacing around the primary comb lines can be generated. Such a spectral emission is known as a "Type-II comb".Our system achieves a fully coherent output. This behavior is verified by numerical simulations. This study represents an important step forward in controlling and manipulating the dynamics of an FD-FWM laser.
We experimentally demonstrate the generation of highly coherent Type-II micro-combs based on a microresonator nested in a fiber cavity loop, known as the filter-driven four wave mixing(FD-FWM) laser scheme.In this system, the frequency spacing of the comb can be adjusted to integer multiples of the free-spectral range(FSR) of the nested micro-resonator by properly tuning the fiber cavity length. Sub-comb lines with single FSR spacing around the primary comb lines can be generated. Such a spectral emission is known as a "Type-II comb".Our system achieves a fully coherent output. This behavior is verified by numerical simulations. This study represents an important step forward in controlling and manipulating the dynamics of an FD-FWM laser.
We experimentally demonstrate the generation of highly coherent Type-II micro-combs based on a microresonator nested in a fiber cavity loop, known as the filter-driven four wave mixing(FD-FWM) laser scheme.In this system, the frequency spacing of the comb can be adjusted to integer multiples of the free-spectral range(FSR) of the nested micro-resonator by properly tuning the fiber cavity length. Sub-comb lines with single FSR spacing around the primary comb lines can be generated. Such a spectral emission is known as a "Type-II comb".Our system achieves a fully coherent output. This behavior is verified by numerical simulations. This study represents an important step forward in controlling and manipulating the dynamics of an FD-FWM laser.
引文
1.A.Pasquazi,M.Peccianti,L.Razzari,D.J.Moss,S.Coen,M.Erkintalo,Y.K.Chembo,T.Hansson,S.Wabnitz,P.Del’Haye,X.Xue,A.M.Weiner,and R.Morandotti,“Micro-combs:a novel generation of optical sources,”Phys.Rep.729,1-81(2018).
2.T.J.Kippenberg,R.Holzwarth,and S.Diddams,“Microresonatorbased optical frequency combs,”Science 332,555-559(2011).
3.J.Pfeifle,V.Brasch,M.Lauermann,Y.Yu,D.Wegner,T.Herr,K.Hartinger,P.Schindler,J.Li,D.Hillerkuss,R.Schmogrow,C.Weimann,R.Holzwarth,W.Freude,J.Leuthold,T.Kippenberg,and C.Koos,“Coherent terabit communications with microresonator Kerr frequency combs,”Nat.Photonics 8,375-380(2014).
4.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).
5.P.Marin-Palomo,J.N.Kemal,M.Karpov,A.Kordts,J.Pfeifle,M.H.Pfeiffer,P.Trocha,S.Wolf,V.Brasch,M.H.Anderson,R.Rosenberger,K.Vijayan,W.Freude,T.J.Kippenberg,and C.Koos,“Microresonator-based solitons for massively parallel coherent optical communications,”Nature 546,274-279(2017).
6.M.-G.Suh,Q.-F.Yang,K.Y.Yang,X.Yi,and K.J.Vahala,“Microresonator soliton dual-comb spectroscopy,”Science 354,600-603(2016).
7.S.B.Papp,K.Beha,P.Del’Haye,F.Quinlan,H.Lee,K.J.Vahala,and S.A.Diddams,“Microresonator frequency comb optical clock,”Optica 1,10-14(2014).
8.F.Ferdous,H.Miao,D.E.Leaird,K.Srinivasan,J.Wang,L.Chen,L.T.Varghese,and A.M.Weiner,“Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,”Nat.Photonics 5,770-776(2011).
9.C.Reimer,M.Kues,P.Roztocki,B.Wetzel,F.Grazioso,B.E.Little,S.T.Chu,T.Johnston,Y.Bromberg,L.Caspani,D.J.Moss,and R.Morandotti,“Generation of multiphoton entangled quantum states by means of integrated frequency combs,”Science 351,1176-1180(2016).
10.M.Kues,C.Reimer,P.Roztocki,L.Romero Cortés,S.Sciara,B.Wetzel,Y.Zhang,A.Cino,S.T.Chu,B.E.Little,D.J.Moss,L.Caspani,J.Aza?a,and R.Morandotti,“On-chip generation of highdimensional entangled quantum states and their coherent control,”Nature 546,622-626(2017).
11.P.Del’Haye,A.Schliesser,O.Arcizet,T.Wilken,R.Holzwarth,and T.Kippenberg,“Optical frequency comb generation from a monolithic microresonator,”Nature 450,1214-1217(2007).
12.T.Herr,K.Hartinger,J.Riemensberger,C.Wang,E.Gavartin,R.Holzwarth,M.Gorodetsky,and T.Kippenberg,“Universal formation dynamics and noise of Kerr-frequency combs in microresonators,”Nat.Photonics 6,480-487(2012).
13.T.Herr,V.Brasch,J.D.Jost,C.Y.Wang,N.M.Kondratiev,M.L.Gorodetsky,and T.J.Kippenberg,“Temporal solitons in optical microresonators,”Nat.Photonics 8,145-152(2014).
14.H.Guo,M.Karpov,E.Lucas,A.Kordts,M.H.Pfeiffer,V.Brasch,G.Lihachev,V.E.Lobanov,M.L.Gorodetsky,and T.J.Kippenberg,“Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,”Nat.Phys.13,94-102(2017).
15.M.Karpov,H.Guo,A.Kordts,V.Brasch,M.H.P.Pfeiffer,M.Zervas,M.Geiselmann,and T.J.Kippenberg,“Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,”Phys.Rev.Lett.116,103902(2016).
16.P.Del’Haye,T.Herr,E.Gavartin,M.Gorodetsky,R.Holzwarth,and T.Kippenberg,“Octave spanning tunable frequency comb from a microresonator,”Phys.Rev.Lett.107,063901(2011).
17.J.S.Levy,A.Gondarenko,M.A.Foster,A.C.Turner-Foster,A.L.Gaeta,and M.Lipson,“CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,”Nat.Photonics 4,37-40(2010).
18.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.Photonics 7,597-607(2013).
19.K.Y.Yang,K.Beha,D.C.Cole,X.Yi,P.Del’Haye,H.Lee,J.Li,D.Y.Oh,S.A.Diddams,S.B.Papp,and K.J.Vahala,“Broadband dispersion-engineered microresonator on a chip,”Nat.Photonics10,316-320(2016).
20.P.Del’Haye,A.Coillet,T.Fortier,K.Beha,D.C.Cole,K.Y.Yang,H.Lee,K.J.Vahala,S.B.Papp,and S.A.Diddams,“Phase-coherent microwave-to-optical link with a self-referenced microcomb,”Nat.Photonics 10,516-520(2016).
21.A.B.Matsko,W.Liang,A.A.Savchenkov,and L.Maleki,“Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,”Opt.Lett.38,525-527(2013).
22.C.Bao,J.A.Jaramillo-Villegas,Y.Xuan,D.E.Leaird,M.Qi,and A.M.Weiner,“Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,”Phys.Rev.Lett.117,163901(2016).
23.M.Yu,J.K.Jang,Y.Okawachi,A.G.Griffith,K.Luke,S.A.Miller,X.Ji,M.Lipson,and A.L.Gaeta,“Breather soliton dynamics in microresonators,”Nat.Commun.8,14569(2017).
24.S.-W.Huang,J.Yang,S.-H.Yang,M.Yu,D.-L.Kwong,T.Zelevinsky,M.Jarrahi,and C.W.Wong,“Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,”Phys.Rev.X 7,041002(2017).
25.S.B.Papp,P.Del’Haye,and S.A.Diddams,“Parametric seeding of a microresonator optical frequency comb,”Opt.Express 21,17615-17624(2013).
26.S.-W.Huang,H.Zhou,J.Yang,J.F.Mc Millan,A.Matsko,M.Yu,D.-L.Kwong,L.Maleki,and C.W.Wong,“Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,”Phys.Rev.Lett.114,053901(2015).
27.Y.Liu,Y.Xuan,X.Xue,P.-H.Wang,S.Chen,A.J.Metcalf,J.Wang,D.E.Leaird,M.Qi,and A.M.Weiner,“Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,”Optica 1,137-144(2014).
28.P.Del’Haye,K.Beha,S.B.Papp,and S.A.Diddams,“Self-injection locking and phase-locked states in microresonator-based optical frequency combs,”Phys.Rev.Lett.112,043905(2014).
29.L.Razzari,D.Duchesne,M.Ferrera,R.Morandotti,S.Chu,B.Little,and D.Moss,“CMOS-compatible integrated optical hyper-parametric oscillator,”Nat.Photonics 4,41-45(2010).
30.W.Liang,D.Eliyahu,V.Ilchenko,A.Savchenkov,A.Matsko,D.Seidel,and L.Maleki,“High spectral purity Kerr frequency comb radio frequency photonic oscillator,”Nat.Commun.6,7957(2015).
31.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 351,357-360(2016).
32.C.Y.Wang,T.Herr,P.Del’Haye,A.Schliesser,J.Hofer,R.Holzwarth,T.W.H?nsch,N.Picqué,and T.J.Kippenberg,“Midinfrared optical frequency combs at 2.5μm based on crystalline microresonators,”Nat.Commun.4,1345(2013).
33.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).
34.I.S.Grudinin,L.Baumgartel,and N.Yu,“Frequency comb from a microresonator with engineered spectrum,”Opt.Express 20,6604-6609(2012).
35.I.S.Grudinin,V.S.Ilchenko,and L.Maleki,“Ultrahigh optical Q factors of crystalline resonators in the linear regime,”Phys.Rev.A 74,063806(2006).
36.M.Yu,Y.Okawachi,A.G.Griffith,M.Lipson,and A.L.Gaeta,“Modelocked mid-infrared frequency combs in a silicon microresonator,”Optica 3,854-860(2016).
37..H.Jung,C.Xiong,K.Y.Fong,X.Zhang,and H.X.Tang,“Optical frequency comb generation from aluminum nitride microring resonator,”Opt.Lett.38,2810-2813(2013).
38.M.Pu,L.Ottaviano,E.Semenova,and K.Yvind,“Efficient frequency comb generation in Al Ga As-on-insulator,”Optica 3,823-826(2016).
39.M.Haelterman,S.Trillo,and S.Wabnitz,“Dissipative modulation instability in a nonlinear dispersive ring cavity,”Opt.Commun.91,401-407(1992).
40.F.Leo,S.Coen,P.Kockaert,S.-P.Gorza,P.Emplit,and M.Haelterman,“Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,”Nat.Photonics 4,471-476(2010).
41.S.Coen and M.Erkintalo,“Universal scaling laws of Kerr frequency combs,”Opt.Lett.38,1790-1792(2013).
42.A.Coillet and Y.K.Chembo,“Routes to spatiotemporal chaos in Kerr optical frequency combs,”Chaos 24,013113(2014).
43.C.Bao,P.Liao,A.Kordts,L.Zhang,M.Karpov,M.Pfeiffer,Y.Cao,Y.Yan,A.Almaiman,G.Xie,A.Mohajerin-Ariaei,L.Li,M.Ziyadi,S.Wilkinson,M.Tur,T.Kippenberg,and A.Willner,“Dual-pump generation of high-coherence primary Kerr combs with multiple sub-lines,”Opt.Lett.42,595-598(2017).
44.M.Peccianti,A.Pasquazi,Y.Park,B.E.Little,S.T.Chu,D.J.Moss,and R.Morandotti,“Demonstration of a stable ultrafast laser based on a nonlinear microcavity,”Nat.Commun.3,765(2012).
45.A.Pasquazi,M.Peccianti,B.E.Little,S.T.Chu,D.J.Moss,and R.Morandotti,“Stable,dual mode,high repetition rate mode-locked laser based on a microring resonator,”Opt.Express 20,27355-27362(2012).
46.A.Pasquazi,L.Caspani,M.Peccianti,M.Clerici,M.Ferrera,L.Razzari,D.Duchesne,B.E.Little,S.T.Chu,D.J.Moss,and R.Morandotti,“Self-locked optical parametric oscillation in a CMOScompatible microring resonator:a route to robust optical frequency comb generation on a chip,”Opt.Express 21,13333-13341(2013).
47.W.Q.Wang,S.T.Chu,B.E.Little,A.Pasquazi,Y.S.Wang,L.R.Wang,W.F.Zhang,L.Wang,X.H.Hu,G.X.Wang,H.Hu,Y.L.Su,F.T.Li,Y.S.Liu,and W.Zhao,“Dual-pump Kerr micro-cavity optical frequency comb with varying FSR spacing,”Sci.Rep.6,28501(2016).
48.W.Q.Wang,W.F.Zhang,S.T.Chu,B.E.Little,Q.H.Yang,L.R.Wang,X.H.Hu,L.Wang,G.X.Wang,Y.H.Wang,and W.Zhao,“Repetition rate multiplication pulsed laser source based on a micro-ring resonator,”ACS Photon.4,1677-1683(2017).
49.L.Di Lauro,J.Li,D.J.Moss,R.Morandotti,S.T.Chu,M.Peccianti,and A.Pasquazi,“Parametric control of thermal self-pulsation in micro-cavities,”Opt.Lett.42,3407-3410(2017).
50.P.Del’Haye,O.Arcizet,M.L.Gorodetsky,R.Holzwarth,and T.J.Kippenberg,“Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,”Nat.Photonics 3,529-533(2009).
51.P.Del’Haye,A.Coillet,W.Loh,K.Beha,S.B.Papp,and S.A.Diddams,“Phase steps and resonator detuning measurements in microresonator frequency combs,”Nat.Commun.6,5668(2015).
52.J.Schr?der,T.D.Vo,and B.J.Eggleton,“Repetition-rate-selective,wavelength-tunable mode-locked laser at up to 640 GHz,”Opt.Lett.34,3902-3904(2009).
53.J.Schr?der,D.Alasia,T.Sylvestre,and S.Coen,“Dynamics of an ultrahigh-repetition-rate passively mode-locked Raman fiber laser,”J.Opt.Soc.Am.B 25,1178-1186(2008).
54.B.E.Little,S.T.Chu,H.A.Haus,J.Foresi,and J.-P.Laine,“Microring resonator channel dropping filters,”J.Lightwave Technol.15,998-1005(1997).
2.T.J.Kippenberg,R.Holzwarth,and S.Diddams,“Microresonatorbased optical frequency combs,”Science 332,555-559(2011).
3.J.Pfeifle,V.Brasch,M.Lauermann,Y.Yu,D.Wegner,T.Herr,K.Hartinger,P.Schindler,J.Li,D.Hillerkuss,R.Schmogrow,C.Weimann,R.Holzwarth,W.Freude,J.Leuthold,T.Kippenberg,and C.Koos,“Coherent terabit communications with microresonator Kerr frequency combs,”Nat.Photonics 8,375-380(2014).
4.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).
5.P.Marin-Palomo,J.N.Kemal,M.Karpov,A.Kordts,J.Pfeifle,M.H.Pfeiffer,P.Trocha,S.Wolf,V.Brasch,M.H.Anderson,R.Rosenberger,K.Vijayan,W.Freude,T.J.Kippenberg,and C.Koos,“Microresonator-based solitons for massively parallel coherent optical communications,”Nature 546,274-279(2017).
6.M.-G.Suh,Q.-F.Yang,K.Y.Yang,X.Yi,and K.J.Vahala,“Microresonator soliton dual-comb spectroscopy,”Science 354,600-603(2016).
7.S.B.Papp,K.Beha,P.Del’Haye,F.Quinlan,H.Lee,K.J.Vahala,and S.A.Diddams,“Microresonator frequency comb optical clock,”Optica 1,10-14(2014).
8.F.Ferdous,H.Miao,D.E.Leaird,K.Srinivasan,J.Wang,L.Chen,L.T.Varghese,and A.M.Weiner,“Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,”Nat.Photonics 5,770-776(2011).
9.C.Reimer,M.Kues,P.Roztocki,B.Wetzel,F.Grazioso,B.E.Little,S.T.Chu,T.Johnston,Y.Bromberg,L.Caspani,D.J.Moss,and R.Morandotti,“Generation of multiphoton entangled quantum states by means of integrated frequency combs,”Science 351,1176-1180(2016).
10.M.Kues,C.Reimer,P.Roztocki,L.Romero Cortés,S.Sciara,B.Wetzel,Y.Zhang,A.Cino,S.T.Chu,B.E.Little,D.J.Moss,L.Caspani,J.Aza?a,and R.Morandotti,“On-chip generation of highdimensional entangled quantum states and their coherent control,”Nature 546,622-626(2017).
11.P.Del’Haye,A.Schliesser,O.Arcizet,T.Wilken,R.Holzwarth,and T.Kippenberg,“Optical frequency comb generation from a monolithic microresonator,”Nature 450,1214-1217(2007).
12.T.Herr,K.Hartinger,J.Riemensberger,C.Wang,E.Gavartin,R.Holzwarth,M.Gorodetsky,and T.Kippenberg,“Universal formation dynamics and noise of Kerr-frequency combs in microresonators,”Nat.Photonics 6,480-487(2012).
13.T.Herr,V.Brasch,J.D.Jost,C.Y.Wang,N.M.Kondratiev,M.L.Gorodetsky,and T.J.Kippenberg,“Temporal solitons in optical microresonators,”Nat.Photonics 8,145-152(2014).
14.H.Guo,M.Karpov,E.Lucas,A.Kordts,M.H.Pfeiffer,V.Brasch,G.Lihachev,V.E.Lobanov,M.L.Gorodetsky,and T.J.Kippenberg,“Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,”Nat.Phys.13,94-102(2017).
15.M.Karpov,H.Guo,A.Kordts,V.Brasch,M.H.P.Pfeiffer,M.Zervas,M.Geiselmann,and T.J.Kippenberg,“Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,”Phys.Rev.Lett.116,103902(2016).
16.P.Del’Haye,T.Herr,E.Gavartin,M.Gorodetsky,R.Holzwarth,and T.Kippenberg,“Octave spanning tunable frequency comb from a microresonator,”Phys.Rev.Lett.107,063901(2011).
17.J.S.Levy,A.Gondarenko,M.A.Foster,A.C.Turner-Foster,A.L.Gaeta,and M.Lipson,“CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,”Nat.Photonics 4,37-40(2010).
18.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.Photonics 7,597-607(2013).
19.K.Y.Yang,K.Beha,D.C.Cole,X.Yi,P.Del’Haye,H.Lee,J.Li,D.Y.Oh,S.A.Diddams,S.B.Papp,and K.J.Vahala,“Broadband dispersion-engineered microresonator on a chip,”Nat.Photonics10,316-320(2016).
20.P.Del’Haye,A.Coillet,T.Fortier,K.Beha,D.C.Cole,K.Y.Yang,H.Lee,K.J.Vahala,S.B.Papp,and S.A.Diddams,“Phase-coherent microwave-to-optical link with a self-referenced microcomb,”Nat.Photonics 10,516-520(2016).
21.A.B.Matsko,W.Liang,A.A.Savchenkov,and L.Maleki,“Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,”Opt.Lett.38,525-527(2013).
22.C.Bao,J.A.Jaramillo-Villegas,Y.Xuan,D.E.Leaird,M.Qi,and A.M.Weiner,“Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,”Phys.Rev.Lett.117,163901(2016).
23.M.Yu,J.K.Jang,Y.Okawachi,A.G.Griffith,K.Luke,S.A.Miller,X.Ji,M.Lipson,and A.L.Gaeta,“Breather soliton dynamics in microresonators,”Nat.Commun.8,14569(2017).
24.S.-W.Huang,J.Yang,S.-H.Yang,M.Yu,D.-L.Kwong,T.Zelevinsky,M.Jarrahi,and C.W.Wong,“Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,”Phys.Rev.X 7,041002(2017).
25.S.B.Papp,P.Del’Haye,and S.A.Diddams,“Parametric seeding of a microresonator optical frequency comb,”Opt.Express 21,17615-17624(2013).
26.S.-W.Huang,H.Zhou,J.Yang,J.F.Mc Millan,A.Matsko,M.Yu,D.-L.Kwong,L.Maleki,and C.W.Wong,“Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,”Phys.Rev.Lett.114,053901(2015).
27.Y.Liu,Y.Xuan,X.Xue,P.-H.Wang,S.Chen,A.J.Metcalf,J.Wang,D.E.Leaird,M.Qi,and A.M.Weiner,“Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,”Optica 1,137-144(2014).
28.P.Del’Haye,K.Beha,S.B.Papp,and S.A.Diddams,“Self-injection locking and phase-locked states in microresonator-based optical frequency combs,”Phys.Rev.Lett.112,043905(2014).
29.L.Razzari,D.Duchesne,M.Ferrera,R.Morandotti,S.Chu,B.Little,and D.Moss,“CMOS-compatible integrated optical hyper-parametric oscillator,”Nat.Photonics 4,41-45(2010).
30.W.Liang,D.Eliyahu,V.Ilchenko,A.Savchenkov,A.Matsko,D.Seidel,and L.Maleki,“High spectral purity Kerr frequency comb radio frequency photonic oscillator,”Nat.Commun.6,7957(2015).
31.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 351,357-360(2016).
32.C.Y.Wang,T.Herr,P.Del’Haye,A.Schliesser,J.Hofer,R.Holzwarth,T.W.H?nsch,N.Picqué,and T.J.Kippenberg,“Midinfrared optical frequency combs at 2.5μm based on crystalline microresonators,”Nat.Commun.4,1345(2013).
33.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).
34.I.S.Grudinin,L.Baumgartel,and N.Yu,“Frequency comb from a microresonator with engineered spectrum,”Opt.Express 20,6604-6609(2012).
35.I.S.Grudinin,V.S.Ilchenko,and L.Maleki,“Ultrahigh optical Q factors of crystalline resonators in the linear regime,”Phys.Rev.A 74,063806(2006).
36.M.Yu,Y.Okawachi,A.G.Griffith,M.Lipson,and A.L.Gaeta,“Modelocked mid-infrared frequency combs in a silicon microresonator,”Optica 3,854-860(2016).
37..H.Jung,C.Xiong,K.Y.Fong,X.Zhang,and H.X.Tang,“Optical frequency comb generation from aluminum nitride microring resonator,”Opt.Lett.38,2810-2813(2013).
38.M.Pu,L.Ottaviano,E.Semenova,and K.Yvind,“Efficient frequency comb generation in Al Ga As-on-insulator,”Optica 3,823-826(2016).
39.M.Haelterman,S.Trillo,and S.Wabnitz,“Dissipative modulation instability in a nonlinear dispersive ring cavity,”Opt.Commun.91,401-407(1992).
40.F.Leo,S.Coen,P.Kockaert,S.-P.Gorza,P.Emplit,and M.Haelterman,“Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,”Nat.Photonics 4,471-476(2010).
41.S.Coen and M.Erkintalo,“Universal scaling laws of Kerr frequency combs,”Opt.Lett.38,1790-1792(2013).
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