Raman Self-Frequency Shift of Dissipative Kerr Solitons in an Optical Microresonator

Maxim Karpov, Hairun Guo, Arne Kordts, Victor Brasch, Martin H. P. Pfeiffer, Michail Zervas, Michael Geiselmann, and Tobias J. Kippenberg

Phys. Rev. Lett. 116, 103902 – Published 11 March 2016

Abstract

The formation of temporal dissipative Kerr solitons in microresonators driven by a continuous-wave laser enables the generation of coherent, broadband, and spectrally smooth optical frequency combs as well as femtosecond pulse sources with compact form factors. Here we report the observation of a Raman-induced soliton self-frequency shift for a microresonator dissipative Kerr soliton also referred to as the frequency-locked Raman soliton. In amorphous silicon nitride microresonator-based single soliton states the Raman effect manifests itself by a spectrum that is ${sech}^{2}$ in shape and whose center is spectrally redshifted from the continuous wave pump laser. The shift is theoretically described by the first-order shock term of the material’s Raman response, and we infer a Raman shock time of $\sim 20 fs$ for amorphous silicon nitride. Moreover, we observe that the Raman-induced frequency shift can lead to a cancellation or overcompensation of the soliton recoil caused by the formation of a coherent dispersive wave. The observations are in agreement with numerical simulations based on the Lugiato-Lefever equation with a Raman shock term. Our results contribute to the understanding of Kerr frequency combs in the soliton regime, enable one to substantially improve the accuracy of modeling, and are relevant to the understanding of the fundamental timing jitter of microresonator solitons.

Received 2 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.103902

Physics Subject Headings (PhySH)

Optical solitons Photorefractive & Kerr effects

Solitons

Cavity resonators

Atomic, Molecular & Optical

Authors & Affiliations

Maxim Karpov, Hairun Guo, Arne Kordts, Victor Brasch, Martin H. P. Pfeiffer, Michail Zervas, Michael Geiselmann, and Tobias J. Kippenberg^*

École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

^*tobias.kippenberg@epfl.ch

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Issue

Vol. 116, Iss. 10 — 11 March 2016

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Images

Figure 1
(a) Diagram of the experimental setup: AFG, arbitrary function generator; EDFA, erbium-doped fiber amplifier; OSA, optical spectrum analyzer; OSC, oscilloscope; PD, photodiode. (b) SEM image of ${Si}_{3} N_{4}$ microresonator with a mode spacing of $100 GHz$ . (c) Illustration of the pump laser detuning excitation scheme (reducing the pump frequency). The gray line shows the Kerr-induced cw tilted resonance; the blue line shows the trace of intracavity peak power with an increase of the cavity resonance-pump detuning $2 π δ = ω_{0} - ω_{p}$ ( $ω_{0}$ and $ω_{p}$ are the resonance and pump frequency); the red line shows the single soliton existence range. (d) Illustration of the Raman redshift on the frequency comb spectrum.
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Figure 2
(a),(b) Experimentally generated single soliton combs in a 100-GHz ${Si}_{3} N_{4}$ microresonator shown in linear scale. The envelopes are from numerical simulations. The comb power ( $y$ axis) is normalized to the cw pump power. For soliton comb simulations, we use $D_{2} / 2 π = 2 MHz$ , $D_{3} / 2 π = 4 kHz$ , $κ / 2 π = 350 MHz$ , $δ_{i} = 2.1 GHz$ . (c) Measured soliton combs shown in logarithmic scale, the red comb [same as (a)] has $δ = δ_{i} + 1.0 GHz$ , the green one $δ = δ_{i} + 0.5 GHz$ , and the blue one [same as (b)] $δ = δ_{i}$ . (d) Variation of the comb spectral redshift as a function of the detuning ( $x$ axis: $δ - δ_{i}$ ) at three pump powers: 1.9, 2.3, and 2.7 W. Note that the trend from the simulation is discrete (gray line) as we mark the specific comb line of highest power (the strong pump line excluded). Spacing corresponds to the FSR ( $D_{1} / 2 π$ ). (e) Variation of the spectral 3-dB bandwidth and the (Fourier-limited) pulse duration of single temporal dissipative Kerr soliton with the pump power of 2.7 W.
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Figure 3
(a) Simulation of a single soliton evolution from a breather state to a stable state under the change of detuning ( $δ$ ). The green trace indicates the detuning and is referred to the top axis. (b) Evolution of the frequency comb spectral envelope and the Raman redshift acquired during the detuning change represented in (a). The red trace shows the central frequency of the comb envelope and is referred to the top axis.
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Figure 4
Experimental generation and simulation of single soliton combs with coherent DWs in two different ${Si}_{3} N_{4}$ microresonator geometries (both having a ${Si}_{3} N_{4}$ thickness of $0.8 μ m$ and FSR of $\sim 190 GHz$ ). (a) The sample with the ${Si}_{3} N_{4}$ core width of $1.8 μ m$ (sample taken from Ref. [12]), the comb’s 3-dB bandwidth is $\sim 10 THz$ , $D_{2} / 2 π = 2.2 MHz$ , $D_{3} / 2 π = 18 kHz$ , and the fourth-order dispersion $D_{4} / 2 π = - 350 Hz$ . The pumped resonance is at 1560 nm employing 1 W of power. (b) The sample with ${Si}_{3} N_{4}$ core width of $2.0 μ m$ , the 3-dB bandwith is $\sim 8 THz$ (amplified spontaneous emission (ASE) in the EDFA is not filtered out), $D_{2} / 2 π = 3.2 MHz$ , $D_{3} / 2 π = 26 kHz$ , and $D_{4} / 2 π = - 340 Hz$ . The pumped resonance is at 1554 nm, the power is 1 W. Dispersion and effective mode area are calculated by finite element modeling using COMSOL, while $D_{2} / 2 π$ is also measured [46], showing close agreement to simulations. Blue dashed lines indicate comb envelopes without the Raman contribution.
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