Abstract

Anomalous group velocity dispersion is a key parameter for generating bright solitons, and thus wideband Kerr frequency combs. Extension of the frequency combs spectrum to visible wavelengths has been a major challenge because of the strong normal dispersion of conventional photonic materials at these wavelengths. In this paper, we numerically demonstrate a wideband frequency comb extending from near-infrared to visible wavelengths (∼1200 nm to 650 nm). The proposed frequency comb micro-resonator takes advantage of a wideband blue-shifted anomalous dispersion, achieved in an optimized over-etched silicon nitride waveguide and strong power transfer to shorter wavelengths through radiative dispersive waves, achieved by modulating the dispersion in a coupled resonator architecture. We show the possibility of obtaining a close to visible dispersive Cherenkov radiation peak that is only 10 dB below the overall comb peak and can be tuned by adjusting the coupling structure in the coupled resonator architecture.

© 2017 Optical Society of America

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2017 (2)

C. Bao, H. Taheri, L. Zhang, A. Matsko, Y. Yan, P. Liao, L. Maleki, and AE. Willner, ”High-order dispersion in Kerr comb oscillators”, J. Opt. Soc. Am. B 34, 715–725 (2017).
[Crossref]

D. Y. Oh, K. Y. Yang, C. Fredrick, G. Ycas, S. A. Diddams, and K. J. Vahala, “Coherent ultra-violet to near-infrared generation in silica ridge waveguides,” Nat. Commun. 8, 13922 (2017).
[Crossref]

2016 (9)

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

N. Akhmediev and N. Devine, “How Cherenkov radiative losses can improve optical frequency combs,” Science 351, 340–341 (2016).
[Crossref] [PubMed]

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

M. Soltani, A. Matsko, and L. Maleki, “Enabling arbitrary wavelength frequency combs on chip,” Laser Photon. Rev. 10, 158–162 (2016).
[Crossref]

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

X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, and P. Gao, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016).
[Crossref] [PubMed]

P. Zou, T. Steinmetz, A. Falkenburger, Y. Wu, L. Fu, M. Mei, and R. Holzwarth, “Broadband frequency comb for calibration of astronomical spectrographs,” J. of Appl. Math. and Phys. 4, 202 (2016).
[Crossref]

Z. Jafari, L. Zhang, A. M. Agarwal, L. C. Kimerling, J. Michel, and A. Zarifkar, “Parameter space exploration in dispersion engineering of multilayer silicon waveguides from near-infrared to mid-infrared,” J. Lightwave Technol. 34, 3696–3702 (2016).
[Crossref]

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. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
[Crossref]

2015 (5)

2014 (5)

2013 (6)

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).
[Crossref]

Q. Li, A. A. Eftekhar, M. Sodagar, Z. Xia, A. H. Atabaki, and A. Adibi, “Vertical integration of high-Q silicon nitride microresonators into silicon-on-insulator platform,” Opt. Express 21, 18236–18248 (2013).
[Crossref] [PubMed]

L. Zhang, C. Bao, V. Singh, J. Mu, C. Yang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Generation of two-cycle pulses and octave-spanning frequency combs in a dispersion-flattened micro-resonator,” Opt. Lett. 38, 5122–5125 (2013).
[Crossref] [PubMed]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model,” Opt. Lett. 38, 37–39 (2013).
[Crossref] [PubMed]

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

H. Guo, S. Wang, X. Zeng, and M. Bache, “Understanding soliton spectral tunneling as a spectral coupling effect,” IEEE Photonics Technol. Lett. 25, 1928–1931 (2013).
[Crossref]

2012 (6)

2011 (6)

F. De Leonardis and V. Passaro, “Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing,” Adv. OptoElectron. 2011, 751498 (2011).
[Crossref]

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5, 186–188 (2011).
[Crossref]

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

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

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

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[Crossref] [PubMed]

2010 (4)

E. S. Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “Systematic design and fabrication of high-Q single-mode pulley-coupled planar silicon nitride microdisk resonators at visible wavelengths,” Opt. Express 18, 2127–2136 (2010).
[Crossref]

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).
[Crossref]

L. Zhang, Y. Yue, R. G. Beausoleil, and A. E. Willner, “Flattened dispersion in silicon slot waveguides,” Opt. Express 18, 20529–20534 (2010).
[Crossref] [PubMed]

Y. K. Chembo, D. V. Strekalov, and N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. 104, 103902 (2010).
[Crossref] [PubMed]

2008 (1)

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

2007 (5)

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref] [PubMed]

M. J. Thorpe, D. D. Hudson, K. D. Moll, J. Lasri, and J. Ye, “Cavity-ringdown molecular spectroscopy based on an optical frequency comb at 1.45–1.65 μm,” Opt. Lett. 32, 307–309 (2007).
[Crossref] [PubMed]

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express 15, 4694–4704 (2007).
[Crossref] [PubMed]

B. Kibler, P.-A. Lacourt, F. Courvoisier, and J. Dudley, “Soliton spectral tunnelling in photonic crystal fibre with sub-wavelength core defect,” Electron. Lett. 43, 967–968 (2007).
[Crossref]

2005 (1)

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Coillet, A.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
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N. Akhmediev and N. Devine, “How Cherenkov radiative losses can improve optical frequency combs,” Science 351, 340–341 (2016).
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Diddams, S.

X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, and P. Gao, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016).
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D.D. Hickstein, H. Jung, D.R. Carlson, A. Lind, I. Coddington, K. Srinivasan, G.G. Ycas, D.C. Cole, A. Kowligy, C. Fredrick, and S. Droste, “Ultrabroadband supercontinuum generation and frequency-comb stabilization using on-chip waveguides with both cubic and quadratic nonlinearities”, arXiv 1704.03908 [physics.optics] (2017).

Dudley, J.

B. Kibler, P.-A. Lacourt, F. Courvoisier, and J. Dudley, “Soliton spectral tunnelling in photonic crystal fibre with sub-wavelength core defect,” Electron. Lett. 43, 967–968 (2007).
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P. Zou, T. Steinmetz, A. Falkenburger, Y. Wu, L. Fu, M. Mei, and R. Holzwarth, “Broadband frequency comb for calibration of astronomical spectrographs,” J. of Appl. Math. and Phys. 4, 202 (2016).
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Gallmann, L.

Gao, P.

X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, and P. Gao, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016).
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Figures (5)

Fig. 1
Fig. 1

Dispersion engineering of a thin over-etched SiN waveguide: a) mode profile and cross section of the over-etched SiN waveguide on SiO2 substrate with air cladding. b) Effect of width (w) and over-etching depth (hp) on group velocity dispersion (GVD) of the waveguide in (a). Red and blue curves show the effect of SiO2 pedestal on GVD parameter for a SiN film with w = 800 nm and w = 1100 nm, respectively. In both cases, symmetric cladding (SiO2 clad with no over-etching), and different over-etching depths from 0 to 150 nm in steps of 50 nm are studied. c) GVD parameter for the proposed waveguide configuration in (a) with different widths and heights of SiN. Green, blue, and red curves are related to w = 780 nm, w = 800 nm, and w = 820 nm waveguide width. Three SiN thicknesses of hf = 400 nm, hf = 417 nm, and hf = 430 nm are studied.

Fig. 2
Fig. 2

Single soliton and soliton-induced Cherenkov radiation in a SiN microring resonator: a) Kerr-comb spectrum of the 40 μm-radius microring resonator formed using the proposed waveguide geometry. The peak in intensity at λ = 741 nm (deep red color wavelength) arose as a result of Cherenkov radiation. The pump wavelength is 900 nm, normalized detuning is α = 3, and normalized power is F2 = 3. The spectral range of the generated Kerr-comb at −70 dB window (i.e., 715 nm – 1070 nm) is shown by dashed lines. b) Time evolution of the signal in the microring resonator, which represents the formation of a soliton. c) Normalized integrated dispersion (2Dintω) in the 40 μm-radius microring resonator formed using the proposed waveguide geometry in Fig. 1(a). d) Soliton amplitude formed in the resonator and its tail, which indicates Cherenkov radiation.

Fig. 3
Fig. 3

Adjusting soliton Cherenkov radiation using a coupled-racetrack resonator: a) schematic of a coupled-resonator structure formed by coupling two identical racetrack resonators (based on the proposed waveguide) with the coupling gap of dc = 100 nm and a coupling length (l1) varying between 0 and 44 μm. b) Normalized integrated dispersion (2Dintω) of the odd resonant eigenmode of the coupled-racetrack resonator in (a) for different effective coupling lengths (l1) between resonators, ranging from zero (no coupling, i.e., single resonator case, far right) to 44 μm (far left) in steps of 4 μm. c) Generated Kerr-comb in the coupled-racetrack resonator structures in (a) for different coupling lengths (l1) with normalized detuning of α = 3 and normalized power of F2 = 3.

Fig. 4
Fig. 4

Coupled racetrack resonators to increase both the dispersive wave amplitude, and the bandwidth of the generated Kerr-comb: a) schematic of a three-segment coupled racetrack resonator with coupling lengths l1, l3, and phase adjustment segment with length Δl2 in one arm. b) Normalized integrated dispersion (2Dintω), and c) Kerr-comb spectrum of the three-segment coupled resonator (solid green curve, with lengths l1 = 19 μm, l2 = 1 μm, l3 = 1 μm, and Δl2 = 10 μm), one segment coupled (dashed red, with coupling length l1 = 20 μm), and single resonator (Fig. 2(a), dashed-dotted blue). Total length of all resonators are identical (i.e., 2π.40 μm). Peak at Cherenkov radiation is increased for the coupled resonator, due to higher power density of fundamental soliton at resonance wavelength, when compared with a single resonator.

Fig. 5
Fig. 5

Increasing peak associated with Cherenkov radiation in a multi-soliton state inside the coupled resonator structure in Fig. 4(a) with coupling lengths l1 = 18 μm, l2 = 1 μm, l3 = 1 μm, phase adjusting segment with length Δl2 = 11 μm, normalized detuning α = 3 and normalized input power F2 = 5: a) amplitude of the generated solitons. b) Time evolution of solitons in the multi-soliton state. c) Generated Kerr-comb in the coupled racetrack resonator.

Equations (11)

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P th = κ 2 n 0 2 V eff 8 η c ω 0 n 2 ,
d ψ d τ = ( 1 + i α ) ψ + ( n = 2 ( i ) n 1 n ! ( 2 D n Δ ω ) d n ψ d θ n ) + i | ψ | 2 ψ + F
A 2 2 = 2 D int Δ ω α ,
( t m j k m j k m * t m * ) = exp ( ( j β 1 j K m j K m j β 2 ) l m ) ,
( a f b f ) = ( t f j k f j k f * t f * ) m = 1 ( e j β 1 ( l 2 m + δ l 2 m ) 0 0 e j β 2 l 2 m ) ( t 2 m 1 j k 2 m 1 j k 2 m 1 * t 2 m 1 * ) ( a i b i ) .
( a i b i ) = ( e j β 1 l r 1 0 0 e j β 2 l r 2 ) ( a f b f ) ,
l r 1 = l t m = 1 l m + δ l m ,
l r 2 = l t m = 1 l m
( t j k j k ˜ t ˜ ) = ( e j β 1 l t 0 0 e j β 2 l t ) ( e j β 1 l r 1 0 0 e j β 2 l r 2 ) ( t f j k f j k f * t f * ) m = 1 ( e j β 1 ( l 2 m + δ l 2 m ) 0 0 e j β 2 l 2 m ) ( t 2 m 1 j k 2 m 1 j k 2 m 1 * t 2 m 1 * )
ω ˜ = ω 0 ± c n l t cos 1 ( t + t ˜ 2 ) ,
( λ ) = inf + A λ 2 λ 2 B 2 E λ 2