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Parametrically driven pure-Kerr temporal solitons in a chip-integrated microcavity

Nature Photonics (2024)Cite this article

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Abstract

The discovery that externally driven nonlinear optical resonators can sustain ultrashort pulses (solitons) corresponding to coherent optical frequency combs has enabled landmark advances in applications from telecommunications to sensing. Most previous research has focused on resonators with purely cubic (Kerr-type) nonlinearity that are externally driven with a monochromatic continuous-wave laser—in such systems, the solitons manifest themselves as unique attractors whose carrier frequency coincides with that of the external driving field. Recent experiments have, however, shown that a qualitatively different type of temporal soliton can arise via parametric downconversion in resonators with simultaneous quadratic and cubic nonlinearity. In contrast to conventional solitons in pure-Kerr resonators, these parametrically driven solitons come in two different flavours with opposite phases, and they are spectrally centred at half of the frequency of the driving field. Here we theoretically predict and experimentally demonstrate that parametrically driven solitons can also arise in resonators with pure-Kerr nonlinearity under conditions of bichromatic driving. In this case, the solitons arise through four-wave-mixing-mediated phase-sensitive amplification, come with two distinct phases and have a carrier frequency in between the two external driving fields. Our experiments are performed in an integrated silicon nitride microcavity, and we observe frequency comb spectra in remarkable agreement with theoretical predictions. In addition to representing the discovery of a new type of temporal dissipative soliton, our results constitute an unequivocal realization of parametrically driven soliton frequency combs in a microcavity platform that is compatible with foundry-ready mass fabrication.

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Fig. 1: Comparison of platforms and schematic illustration of parametrically driven cavity soliton (PDCS) generation in Kerr resonators.
Fig. 2: Illustrative simulations of PDCSs in dispersive Kerr resonators.
Fig. 3: Experimental observation of pure-Kerr temporal PDCSs in an on-chip microcavity.
Fig. 4: Observations of multi-soliton interference.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

M.E. aknowledges financial support from the Marsden Fund of the Royal Society of New Zealand Te Apārangi. G.M. and K.S. acknowledge support from the NIST-on-a-chip programme. J.F. acknowledges the CNRS (IRP WALL-IN project).

Author information

Authors and Affiliations

  1. Joint Quantum Institute, NIST/University of Maryland, College Park, MD, USA

    Grégory Moille & Kartik Srinivasan

  2. Microsystems and Nanotechnology Division, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Grégory Moille & Kartik Srinivasan

  3. Department of Physics, University of Auckland, Auckland, New Zealand

    Miriam Leonhardt, David Paligora & Miro Erkintalo

  4. The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand

    Miriam Leonhardt, David Paligora & Miro Erkintalo

  5. Service OPERA-Photonique, Université libre de Bruxelles (U.L.B.), Brussels, Belgium

    Nicolas Englebert & François Leo

  6. Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS Université de Bourgogne, Dijon, France

    Julien Fatome

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  1. Grégory Moille
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Contributions

G.M. performed all of the experiments and assisted in the interpretation of the results. M.L. and D.P. contributed to the theoretical development of the scheme and performed initial simulations to confirm the fundamental viability of the scheme. N.E. and F.L. provided guidance on parametrically driven soliton theory. J.F. assisted in the interpretation of Kerr cavity physics. K.S. supervised and obtained funding for the experiments. M.E. developed the theory, performed the simulations and wrote the manuscript with input from all authors.

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Correspondence to Miro Erkintalo.

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Nature Photonics thanks Xu Yi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Extended visualization of numerical simulation results shown in Fig. 2c.

(a) Snapshot of the total temporal intensity profile at the simulation output over the entire simulation time window (corresponding to one resonator round trip time). Inset shows a zoom around the two solitons. (b) Temporal intensity profiles of fields centred around the pump frequencies ω± (orange and green curves) and the degenerate FWM frequency ω0 = (ω+ + ω−)/2 (blue curve). Inset shows a zoom around the two solitons. The intensity traces in (b) were obtained from the full simulated field envelope by spectrally isolating the relevant frequency components via numerical filtering.

Extended Data Fig. 2 Linear phase-matching of nonlinear Bragg scattering.

Two strong pumps with angular frequencies ω± (with ω+ > ω−) can spectrally translate a low-power signal wave at ωS to a new idler frequency ωI via the process of nonlinear Bragg scattering four-wave-mixing: ωI = ωS + ω+ − ω−. The blue solid curve shows the linear phase-mismatch of the Bragg scattering FWM for parameters relevant to our experiment (for example resonator dispersion, pump frequencies): Δϕ = β(ωI) + β(ω−) − β(ω+) − β(ωS), where β(ω) is the propagation constant of the resonator mode. The phase-mismatch crosses zero at a signal frequency of about 232.5 THz, corresponding to an idler frequency of about 354.5 THz. This phase-matching suggests that the spectral features around 350 THz observed in the experimentally measured spectrum shown in Fig. 3(e) originate from Bragg scattering translation of soliton components at about 232 THz.

Supplementary information

Supplementary Information

Supplementary Notes 1–7 and Figs. 1–4.

Supplementary Video 1

Animation corresponding to the temporal dynamics shown in Fig. 2b. The animation shows numerical simulation results, illustrating the evolution of the total intensity profile from an initial condition consisting of two hyperbolic secant pulses to a steady-state configuration of two PDCSs. The intensity profile exhibits rapid oscillations due to the beating between the quasi-CW intracavity fields at the pump frequencies.

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Moille, G., Leonhardt, M., Paligora, D. et al. Parametrically driven pure-Kerr temporal solitons in a chip-integrated microcavity. Nat. Photon. (2024). https://doi.org/10.1038/s41566-024-01401-6

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