Abstract

Kerr soliton frequency comb generation in monolithic microresonators recently attracted great interests as it enables chip-scale few-cycle pulse generation at microwave rates with smooth octave-spanning spectra for self-referencing. Such versatile platform finds significant applications in dual-comb spectroscopy, low-noise optical frequency synthesis, coherent communication systems, etc. However, it still remains challenging to straightforwardly and deterministically generate and sustain the single-soliton state in microresonators. In this paper, we propose and theoretically demonstrate the excitation of single-soliton Kerr frequency comb by seeding the continuous-wave driven nonlinear microcavity with a pulsed trigger. Unlike the mostly adopted frequency tuning scheme reported so far, we show that an energetic single shot pulse can trigger the single-soliton state deterministically without experiencing any unstable or chaotic states. Neither the pump frequency nor the cavity resonance is required to be tuned. The generated mode-locked single-soliton Kerr comb is robust and insensitive to perturbations. Even when the thermal effect induced by the absorption of the intracavity light is taken into account, the proposed single pulse trigger approach remains valid without requiring any thermal compensation means.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018).
[Crossref] [PubMed]

2017 (6)

Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A. Diddams, S. B. Papp, and K. Srinivasan, “Stably accessing octave-spanning microresonator frequency combs in the soliton regime,” Optica 4(2), 193–203 (2017).
[Crossref] [PubMed]

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. Gorodetsky, and T. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13(1), 94–102 (2017).
[Crossref]

M. H. P. Pfeiffer, C. Herkommer, J. Q. Liu, H. R. Guo, M. Karpov, E. Lucas, M. Zervas, and T. J. Kippenberg, “Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators,” Optica 4(7), 684–691 (2017).
[Crossref]

E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” Nat. Photonics 11(9), 600–607 (2017).
[Crossref]

C. Bao, Y. Xuan, J. A. Jaramillo-Villegas, D. E. Leaird, M. Qi, and A. M. Weiner, “Direct soliton generation in microresonators,” Opt. Lett. 42(13), 2519–2522 (2017).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

2016 (8)

X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, “Thermal tuning of Kerr frequency combs in silicon nitride microring resonators,” Opt. Express 24(1), 687–698 (2016).
[Crossref] [PubMed]

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(16), 163901 (2016).
[Crossref] [PubMed]

F. Li, J. H. Yuan, Z. Kang, Q. Li, and P. K. A. Wai, “Modeling Frequency Comb Sources,” Nanophotonics 5(2), 292–315 (2016).
[Crossref]

X. Yi, Q. F. Yang, K. Youl Yang, and K. Vahala, “Active capture and stabilization of temporal solitons in microresonators,” Opt. Lett. 41(9), 2037–2040 (2016).
[Crossref] [PubMed]

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(6271), 357–360 (2016).
[Crossref] [PubMed]

V. E. Lobanov, G. V. Lihachev, N. G. Pavlov, A. V. Cherenkov, T. J. Kippenberg, and M. L. Gorodetsky, “Harmonization of chaos into a soliton in Kerr frequency combs,” Opt. Express 24(24), 27382–27394 (2016).
[Crossref] [PubMed]

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41(11), 2565–2568 (2016).
[Crossref] [PubMed]

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. Photonics 10(5), 316–320 (2016).
[Crossref]

2015 (6)

2014 (5)

T. Hansson, D. Modotto, and S. Wabnitz, “Mid-infrared soliton and Raman frequency comb generation in silicon microrings,” Opt. Lett. 39(23), 6747–6750 (2014).
[Crossref] [PubMed]

K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4–5), 269–281 (2014).

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(1), 10–14 (2014).
[Crossref]

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. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2014).
[Crossref]

2013 (5)

2012 (2)

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(7), 480–487 (2012).
[Crossref]

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

2011 (2)

2010 (1)

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(7), 471–476 (2010).
[Crossref]

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref] [PubMed]

2004 (1)

2003 (2)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

2002 (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–640 (2000).
[Crossref] [PubMed]

1996 (2)

I. V. Barashenkov and Y. S. Smirnov, “Existence and stability chart for the ac-driven, damped nonlinear Schrödinger solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(5), 5707–5725 (1996).
[Crossref] [PubMed]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76(10), 1623–1626 (1996).
[Crossref] [PubMed]

1993 (1)

1992 (1)

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91(5-6), 401–407 (1992).
[Crossref]

Adibi, A.

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7(2), 2200309 (2015).
[Crossref]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref] [PubMed]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[Crossref] [PubMed]

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Bao, C.

C. Bao, Y. Xuan, J. A. Jaramillo-Villegas, D. E. Leaird, M. Qi, and A. M. Weiner, “Direct soliton generation in microresonators,” Opt. Lett. 42(13), 2519–2522 (2017).
[Crossref] [PubMed]

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(16), 163901 (2016).
[Crossref] [PubMed]

Barashenkov, I. V.

I. V. Barashenkov and Y. S. Smirnov, “Existence and stability chart for the ac-driven, damped nonlinear Schrödinger solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(5), 5707–5725 (1996).
[Crossref] [PubMed]

Barland, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Beha, K.

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. Photonics 10(5), 316–320 (2016).
[Crossref]

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(1), 10–14 (2014).
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F. Li, J. H. Yuan, Z. Kang, Q. Li, and P. K. A. Wai, “Modeling Frequency Comb Sources,” Nanophotonics 5(2), 292–315 (2016).
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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(7), 480–487 (2012).
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T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2014).
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D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013).
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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagram of the proposed single-soliton Kerr comb generation. (b) Schematic diagram of the spectral profiles of a trigger pulse train at three different pulse period T (i) T = 1/FSR, where FSR is the free spectral range of the microresonator, (ii) T = K/FSR, where K is a positive integer, and (iii) T = ∞ (single shot trigger pulse). (c) and (d) are the illustrative diagrams of the variation of averaged intracavity power versus pump-resonance detuning in the Kerr comb excitation process when (c) only Kerr effect, and (d) both Kerr and thermal effects are considered. The blue solid curves show the possible intracavity power evolution to approach a single-soliton state in conventional pump frequency tuning scheme. The black dashed curves indicate the states with different number of intracavity solitons [14,18]. The lower red solid curve indicates the stable cold state with CW field only in the cavity. The evolution path to the single-soliton state utilizing the pump frequency tuning scheme (A→B→C→D) and the proposed trigger scheme (F→E→D) are indicated by the red and blue dashed arrows, respectively. Different colored regions indicate different intracavity states. MI stands for modulation instability. λp is the pump wavelength, and λ0 is the closest cold-cavity resonant wavelength. λa and λb mark the wavelength detuning region where the SCS state exists as indicated in (c) and (d).
Fig. 2
Fig. 2 (a)-(c) Temporal and (d)-(f) spectral evolutions of the intracavity field and the instantaneous profiles at the final and 3084-th roundtrips, respectively, when a single shot pulse trigger with a peak power of 520 W and an FWHM of 1.5 ps is injected. (g) Pt_min versus τt at different Δf. (h) Different operation regions within the parameter space of Pt and δ0 with τt = 1.5 ps and Δf = 6·FSR. Other parameters: |ψcw|2 = 1 W, β2 = −59 ps2/km, γ = 1 W−1/m, α0L = 0.012. Dispersion parameters up to 7-th order are included to properly describe the broadband dispersion characteristics of the resonator.
Fig. 3
Fig. 3 (a)-(b) Temporal and (c)-(d) spectral evolutions of the intracavity field and the instantaneous profiles at the final roundtrip. (e) The intracavity energy at each roundtrip. (f) Instantaneous temporal profile at the 8000-th roundtrip of the pump frequency tuning approach. 1,000 simulation results using (g) the pump frequency tuning and (h) the proposed trigger approaches, respectively. The counts of different soliton states of the 1,000 simulations using (i) the pump frequency tuning and (j) the trigger approaches, respectively.
Fig. 4
Fig. 4 (a) Stabilized δ1 at the end of CW stage starting from a cold cavity as a function of initial detuning δ0 under different propagation loss and pump power. Other parameters: γ = 1.4 W−1/m, L = 628 μm, θ = 0.0025, tR = 4.425 ps. (b) S-curves with the border detuning values δ1_lower and δ1_upper for the pump power of 0.5 W when α0L are 0.005 and 0.01, respectively.
Fig. 5
Fig. 5 The green regions are the possible CS excitation regions (bistable regions) bounded by the detuning δ1_upper and δ1_lower. Blue dashed curves with dots show the minimum δ1 that can be thermally stabilized in the red-detuned side. Hatched regions indicate the valid regions for SCS excitation with thermal effect. The loss α0L is (a) 0.0012, (b) 0.004, (c) 0.008, and (d) 0.012, respectively. The inset in (a) shows the zoom-in view of the pump power ranging from 0 to 0.2 W.
Fig. 6
Fig. 6 (a) Temporal evolution and final instantaneous temporal profiles (b) spectral evolution and final instantaneous spectral profiles in the CW and CS stages. (c) Evolution of intracavity average power. Inset I and II show the zoom-in views in [0, 400] roundtrips of the CW stage and [0, 3000] roundtrips of the CS stage, respectively. (d) Evolution of δ0 + δtherm.

Equations (8)

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ψ (m+1) (z=0,τ)= θ ψ in (m) (τ)+ 1θ e i δ 0 ψ (m) (z=L,τ),
ψ (m) (z,τ) z = α 0 2 ψ (m) +i k2 i k β k k! k ψ (m) τ k +iγ(1+i τ s τ ) | ψ (m) | 2 ψ (m) .
ψ in (m) (τ)= ψ cw + P t exp[ iΔΩ(τ+m t R ) ]sech[ (τ+m t R δt)/ τ t ].
t R ψ t = θ ψ in α 0 L+θ 2 ψi( δ 0 + δ therm )ψ+iL k2 i k β k k! k ψ τ k +iγL(1+i τ s τ ) | ψ | 2 ψ,
d δ therm dt = δ therm τ 0 + ξ t R 0 t R | ψ | 2 dτ .
Y= γ 2 L 2 θ X 3 2 δ 1 γL θ X 2 + ( δ 1 2 + α 2 ) θ X.
3 γ 2 L 2 X 2 4 δ 1 γLX+( δ 1 2 + α 2 )=0.
X 1,2 = 2 δ 1 ± δ 1 2 3 α 2 3γL .

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