Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

Godey, Cyril; Balakireva, Irina; Coillet, Aurélien; Chembo, Yanne K.

doi:10.1103/physreva.89.063814

Cited by 405 publications

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“…In this framework a Kerr frequency comb corresponds to the frequency spectrum of a temporal dissipative structure, such as patterns or solitons, circulating inside the cavity [10,11]. While most theoretical studies have focused on the anomalous second-order group velocity dispersion (GVD) regime [12][13][14], where the typical dissipative states are bright solitons, the normal GVD regime has recently attracted interest due to the difficulty of obtaining anomalous GVD in some spectral ranges. In contrast to the anomalous regime, dark solitons are found in the normal GVD regime, i.e., low-intensity dips embedded in a highintensity homogeneous background.…”

Section: Introductionmentioning

confidence: 99%

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

2017

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Using the Lugiato-Lefever model, we analyze the effects of third-order chromatic dispersion on the existence and stability of dark-and bright-soliton Kerr frequency combs in the normal dispersion regime. While in the absence of third-order dispersion only dark solitons exist over an extended parameter range, we find that third-order dispersion allows for stable dark and bright solitons to coexist. Reversibility is broken and the shape of the switching waves connecting the top and bottom homogeneous solutions is modified. Bright solitons come into existence thanks to the generation of oscillations in the switching-wave profiles. Temporal oscillatory instabilities of dark solitons are suppressed in the presence of sufficiently strong third-order dispersion, while bright solitons are never found to oscillate in time. As a result of third-order dispersion both bright and dark solitons are found to move with a velocity that depends on their width.

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Section: Introductionmentioning

confidence: 99%

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

2017

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“…In contrast to "Turing rolls" [18,19] dominating combs in the modulation instability (MI) regime, cavity solitons carry intense peak power and ultrashort duration such that in principle it could excite higher-order nonlinear effects such as the self-steepening effect and Raman scattering. The latter usually exists and is broadband in nature in amorphous oxide and nitride materials such as silica and SiN, which relates to the vibrational material response of the cubic nonlinearity.…”

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confidence: 99%

“…This process has been used to create a photonic chip based (coherent) frequency comb in a SiN microresonator spanning 2/3 of an octave at electronically detectable mode spacing. However, while advances in theoretical simulations of the soliton regime have occured [14,16,17] a key underlying question is what other effects play a role in soliton formation and need to be included into the simulations.In contrast to "Turing rolls" [18,19] dominating combs in the modulation instability (MI) regime, cavity solitons carry intense peak power and ultrashort duration …”

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

et al. 2016

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The formation of temporal dissipative solitons in continuous wave laser driven microresonators enables the generation of coherent, broadband and spectrally smooth optical frequency combs as well as femtosecond pulses with compact form factor. Here we report for the first time on the observation of a Raman-induced soliton self-frequency shift for a microresonator soliton. The Raman effect manifests itself in amorphous SiN microresonator based single soliton states by a spectrum that is hyperbolic secant in shape, but whose center is spectrally red-shifted (i.e. offset) 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 20 fs for amorphous SiN. 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 excellent agreement with numerical simulations based on the Lugiato-Lefever equation (LLE) with a Raman shock term. Our results contribute to the understanding of Kerr frequency combs in the soliton regime, enable to substantially improve the accuracy of modeling and are relevant to the fundamental timing jitter of microresonator solitons.Introduction. -Microresonator based optical frequency combs (Kerr combs) [1, 2] enable optical frequency comb generation from a continuous wave (CW) laser, with repetition rates in the microwave domain (>10 GHz), and broad spectral bandwidth [3][4][5]. Recently, a qualitatively new operation regime has been discovered [6], in which the parametrically generated comb seeds the formation of a temporal dissipative (cavity) soliton [7][8][9]. Such temporal dissipative solitons, first externally induced in fiber cavities [10], have been observed in Kerr frequency comb experiments using crystalline microresonators [6,11] and have recently also been generated in photonic chip based silicon nitride (SiN) integrated resonators [5,12]. Soliton based microresonator frequency combs have several attractive features, in particular being fully coherent, having smooth envelopes and giving access to femtosecond pulses. Indeed, the short duration of temporal solitons in crystalline microresonators have been used for external fiber broadening [6,13] and have allowed to achieve self-referencing (i.e. determination of the comb's carrier envelope frequency) enabling to count the cycles of light [13]. Moreover, taking advantage of dispersion engineering [3,14], the presence of third (and higher) order dispersion allows (coherent) dispersive waves (DWs) to be generated [12] via the effect of soliton induced Cherenkov radiation [15]. This process has been used to create a photonic chip based (coherent) frequency comb in a SiN microresonator spanning 2/3 of an octave at electronically detectable mode spacing. However, while advances in theoretical simulations of the soliton regime have occured [14,16,17] a key underlying question is what ot...

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“…theory and simulation [27]- [28], investigating dark solitons experimentally is extremely difficult and no time-domain characterization has ever been reported. The first challenge is spontaneous excitation of dark solitons.…”

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Mode-locked dark pulse Kerr combs in normal-dispersion microresonators

et al. 2015

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Kerr frequency combs from microresonators are now extensively investigated as a potentially portable technology for a variety of applications. Most studies employ anomalous dispersion microresonators that support modulational instability for comb initiation, and mode-locking transitions resulting in coherent bright soliton-like pulse generation have been reported. However, some experiments show comb generation in normal dispersion microresonators; simulations suggest the formation of dark pulse temporal profiles. Excitation of dark pulse solutions is difficult due to the lack of modulational instability in the effective blue-detuned pumping region; an excitation pathway has been demonstrated neither in experiment nor in simulation. Here we report experiments in which dark pulse combs are formed by mode-interaction-aided excitation; for the first time, a mode-locking transition is observed in the normal dispersion regime. The excitation pathway proposed is also supported by simulations.Microresonator-based optical frequency combs, also termed Kerr combs, are generated through conversion of a single pump frequency to a broadband frequency comb inside a high-quality-factor (Q) microresonator via the third-order Kerr nonlinearity [1]- [10]. The advantages of Kerr combs include very compact size, high repetition rate, and capability of generating ultra-broad combs.The dynamics of Kerr comb generation have attracted intense investigations since the first demonstration of the method [11]-[28]. It has been found that Kerr combs are not always coherent [11]-[12] and may be characterized by high intensity noise [13]-[14]; furthermore, lack of coherence and high intensity noise are generally correlated. Experiments have revealed transitions from low coherence, high noise states to highly coherent mode-locked states accompanied by a sudden drop in the comb noise [14]- [18]. It has been found in simulations and experiments that the mode locking of broadband Kerr combs is usually related to soliton formation in the cavity [15], [17]-[28]. These dissipative cavity solitons are localized structures stabilized by a balance between Kerr nonlinearity and dispersion. In time domain they exist as bright or dark pulses, depending on whether the cavity dispersion is anomalous or normal, respectively. Bright microresonator solitons in the anomalous dispersion region have been observed in experiments and well studied through simulations [15], [17]-[27]. Reference [17] reported a method of tuning the pump laser frequency to an effectively red-detuned regime (pump laser wavelength longer than resonant wavelength) which is typically difficult to achieve due to thermal instability [29]. Mode-locking transitions yielding bright solitons were observed after passage through a broadband chaotic state [17]. In contrast, although dark solitons have been predicted in normal dispersion microresonators in 2 / 32 2 / 32 theory and simulation [27]-[28], investigating dark solitons experimentally is extremely difficult and no time-domain char...

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Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

Cited by 405 publications

References 71 publications

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

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

Mode-locked dark pulse Kerr combs in normal-dispersion microresonators

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