Temporal solitons in optical microresonators

Journal name:
Nature Photonics
Volume:
8,
Pages:
145–152
Year published:
DOI:
doi:10.1038/nphoton.2013.343
Received
Accepted
Published online

Abstract

Temporal dissipative solitons in a continuous-wave laser-driven nonlinear optical microresonator were observed. The solitons were generated spontaneously when the laser frequency was tuned through the effective zero detuning point of a high-Q resonance, which led to an effective red-detuned pumping. Transition to soliton states were characterized by discontinuous steps in the resonator transmission. The solitons were stable in the long term and their number could be controlled via pump-laser detuning. These observations are in agreement with numerical simulations and soliton theory. Operating in the single-soliton regime allows the continuous output coupling of a femtosecond pulse train directly from the microresonator. This approach enables ultrashort pulse syntheses in spectral regimes in which broadband laser-gain media and saturable absorbers are not available. In the frequency domain the single-soliton states correspond to low-noise optical frequency combs with smooth spectral envelopes, critical to applications in broadband spectroscopy, telecommunications, astronomy and low noise microwave generation.

At a glance

Figures

  1. MgF2 microresonator, dispersion and bistability.
    Figure 1: MgF2 microresonator, dispersion and bistability.

    a, MgF2 crystal carrying two whispering-gallery-mode microresonators of different size (the smaller one with an FSR of 35.2 GHz was used). An optical whispering-gallery-mode propagates along the circumference of the resonator. The smaller panels show a magnified view of the resonator and the simulated optical mode profile. b, Anomalous dispersion (FSR increases with mode number) of the microresonator with 35.2 GHz FSR shown as the deviation of the measured resonance frequencies (blue dots), , from an equidistant frequency grid ω0 + μD1 (horizontal grey line), where μ denotes the relative mode number and D1 corresponds to the FSR at the frequency ω0. The resonator's anomalous dispersion is described accurately by D2/2π  16 kHz (red dashed line) while higher order terms are negligible. The grey vertical lines mark spectral intervals of width 25 nm (μ = 0 corresponds to 1,553 nm). c, Bistable intracavity power as a function of laser detuning for a linear (blue) and a nonlinear resonator (orange). The dashed line marks an unstable regime. The effectively blue-detuned and the effectively red-detuned regimes are indicated. In FWM combs the phases of the comb lines are constant but random, which leads to a periodic but not pulsed intracavity waveform. The left inset shows the optical spectrum resulting from cascaded FWM and illustrates how the superposition of comb frequencies (blue waves) with arbitrary phase (black arrows) results in a periodic intracavity power (red). The presence of a soliton implies synchronized phases and a pulsed intracavity power (right inset). a.u., arbitrary units.

  2. Transmission and beatnote.
    Figure 2: Transmission and beatnote.

    a, Transmission observed when scanning a laser over a resonance of a high-Q Kerr-nonlinear MgF2 microresonator (coupled pump power 5 mW). The transmission signal follows the expected triangular resonance shape (see inset) with deviations in the form of discrete steps (green shading). b, Evolution of the optical power spectrum for three different positions in the scan; spectrum II and, in particular, the mesa-shaped spectrum III exhibit a high-noise RF beat signal. c, Down-mixed RF beat signal. d, Main experimental set-up composed of pump laser and resonator followed by an optical spectrum analyser (OSA), an oscilloscope to record the transmission and to sample the down-mixed beatnote (via the third harmonic of a local oscillator (LO) at 11.7 GHz), and an electrical spectrum analyser (ESA) to monitor the beatnote. Before beatnote detection the pump was filtered out by a narrow FBG in transmission (circulator and reflected beam dump not shown). FPC, fibre polarization controller; PD, photodetector; EDFA, erbium-doped fibre amplifier. e, Transmission and PDH error signal. Effective blue and red detunings are shaded blue and red, respectively.

  3. Numerical simulations of soliton formation in a microresonator.
    Figure 3: Numerical simulations of soliton formation in a microresonator.

    a, Average intracavity power (blue, corresponding to the transmission signal in Fig. 2a when mirrored horizontally) during a simulated laser scan (101 simulated modes) over a resonance in a MgF2 resonator. The step features are well reproduced. The orange lines trace out all possible evolutions of the system during the scan. The dashed lines show an analytical description of the steps. The green area corresponds to the area in which solitons can exist, the yellow area allows for breather solitons with a time-variable envelope; solitons cannot exist in the red area. b,c, Optical spectra and intracavity powers for the different positions I–XI in the laser scan. d, Optical spectrum obtained when simulating 501 modes and stopping the simulated laser scan in the soliton regime. e, Intracavity power for the state in d with five solitons (TR round-trip time). f, Enlargement of one of the solitons that shows the numerical results for the field real (red) and imaginary (dark blue) parts. The respective analytical soliton solutions are shown as light blue and orange lines.

  4. Experimental demonstration of stable temporal solitons in an optical microresonator.
    Figure 4: Experimental demonstration of stable temporal solitons in an optical microresonator.

    a, Optical spectra of three selected states with one, two and five solitons, respectively. The insets show the RF beatnote, which is resolution-bandwidth limited to a 1 kHz width in all cases. The dashed red line in the optical spectrum of the one-pulse state shows the spectral sech2 envelope expected for solitons with a 3 dB bandwidth of 1.6 THz. b, FROG traces of the states in a that display the signal of the single and multiple pulses. (The FROG set-up is shown in Fig. 5b.)

  5. Temporal characterization of ultrashort pulses.
    Figure 5: Temporal characterization of ultrashort pulses.

    a, Higher-resolution experimental FROG trace of a one-soliton pulse (left colour scale same as in Fig. 4b). The reconstruction (middle) converges to a FROG error of ε  1.7%, in good agreement with the experimental trace. The reconstruction (right) of power and phase yields an estimated pulse duration of 200 fs (FWHM), time (ps). b, Set-up of the FROG experiment. c, Sampled optical power of the microresonator output over a duration of 40 ps. The three measurements (frames 1, 2 and 3) are separated from one another by a duration of 4 ns, which corresponds to ~140 round-trip times of 28.4 ps. The smaller trailing peaks can be attributed to ringing in the photodetection circuit. d. Set-up of the power sampling experiment, including the PicoLuz LLC temporal magnifier and a 4 GHz sampling oscilloscope. FBG is in transmission (circulator and reflected beam dump not shown). FLC, fibre laser comb (250 MHz repetition rate); HWP, half-wave plate; QWP, quarter-wave plate; DCF, dispersion-compensating fibre.

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Author information

Affiliations

  1. École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

    • T. Herr,
    • V. Brasch,
    • J. D. Jost,
    • C. Y. Wang &
    • T. J. Kippenberg
  2. Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia

    • N. M. Kondratiev &
    • M. L. Gorodetsky
  3. Russian Quantum Center, Skolkovo 143025, Russia

    • M. L. Gorodetsky

Contributions

T.H. designed and performed the experiments and analysed the data. M.L.G. and T.H. performed the numerical simulations, M.L.G. developed the analytic description, V.B. assisted in the experiments, J.D.J. assisted in the temporal magnifier experiment, T.H. and M.L.G. fabricated the sample, C.Y.W. assisted in sample fabrication and N.M.K. assisted in developing the analytic description. T.H., M.L.G. and T.J.K. wrote the manuscript. T.J.K. supervised the project.

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The authors declare no competing financial interests.

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