Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory

Gärtner, Janina; Trocha, P.; Mandel, Rainer; Koos, C.; Jahnke, Tobias; Reichel, Wolfgang

doi:10.1103/physreva.100.033819

Cited by 16 publications

(9 citation statements)

References 39 publications

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“…The formation of LSs in the normal regime has been addressed in a number of theoretical works (Godey et al, 2014b;Lobanov et al, 2015;Parra-Rivas et al, 2016a,b;Gärtner et al, 2019), and their existence has been confirmed experimentally in microresonators (Xue et al, 2015;Nazemosadat et al, 2019) and pulse-pumped fiber cavities (Garbin et al, 2017). In this section we present the main results regarding the origin and bifurcation structure of dark LSs in this regime of operation.…”

Section: Localized Structures In the Normal Regime: Collapsed Snakingmentioning

confidence: 78%

See 1 more Smart Citation

Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

Parra-Rivas¹,

Knobloch²,

Gelens³

et al. 2020

Preprint

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Localized coherent structures can form in externally-driven dispersive optical cavities with a Kerr-type nonlinearity. Such systems are described by the Lugiato-Lefever equation, which supports a large variety of dynamical solutions. Here, we review our current knowledge on the formation, stability and bifurcation structure of localized structures in the one-dimensional Lugiato-Lefever equation. We do so by focusing on two main regimes of operation: anomalous and normal second-order dispersion. In the anomalous regime, localized patterns are organized in a homoclinic snaking scenario, which is eventually destroyed, leading to a foliated snaking bifurcation structure. In the normal regime, however, localized structures undergo a different type of bifurcation structure, known as collapsed snaking.

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Section: Localized Structures In the Normal Regime: Collapsed Snakingmentioning

confidence: 78%

“…Unlike HH the subsidiary primary bifurcations cannot be characterized in terms of spatial dynamics. However, as recently shown by Gärtner et al, they can be determined analytically in terms of transversality conditions (Gärtner et al, 2019).…”

Section: Bifurcation Structure Of the Periodic Turing Patternsmentioning

confidence: 88%

Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

Parra-Rivas¹,

Knobloch²,

Gelens³

et al. 2020

Preprint

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“…For ε = 0 there is a plethora of non-trivial (non-constant) stationary solutions, cf. [8,21]. We start with such a solution under the assumption of its nondegeneracy according to the following definition.…”

Section: Resultsmentioning

confidence: 99%

“…Existence and bifurcation behavior of solutions of (1.1) have been studied quite well, cf. [8,9,12,13,21,23,24,25,26] and their stability properties have been investigated in [3,4,14,15,16,28,30]. Analytical and numerical investigations of (1.2) have recently been reported [10,11].…”

Section: Introductionmentioning

confidence: 99%

Pinning in the Extended Lugiato–Lefever Equation

Bengel,

Pelinovsky,

Reichel

2024

SIAM J. Math. Anal.

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We consider a variant of the Lugiato-Lefever equation (LLE), which is a nonlinear Schrödinger equation on a one-dimensional torus with forcing and damping, to which we add a first-order derivative term with a potential εV(x). The potential breaks the translation invariance of LLE. Depending on the existence of zeroes of the effective potential V eff , which is a suitably weighted and integrated version of V, we show that stationary solutions from ε = 0 can be continued locally into the range ε = 0. Moreover, the extremal points of the ε-continued solutions are located near zeros of V eff . We therefore call this phenomenon pinning of stationary solutions. If we assume additionally that the starting stationary solution at ε = 0 is spectrally stable with the simple zero eigenvalue due to translation invariance being the only eigenvalue on the imaginary axis, we can prove asymptotic stability or instability of its ε-continuation depending on the sign of V eff at the zero of V eff and the sign of ε. The variant of the LLE arises in the description of optical frequency combs in a Kerr nonlinear ring-shaped microresonator which is pumped by two different continuous monochromatic light sources of different frequencies and different powers. Our analytical findings are illustrated by numerical simulations.

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“…However recent, studies showed that it is possible to reach the values of 20-40% 16,17 even without any special schemes, showing that this problem has not been fully investigated and no fundamental limit of the conversion efficiency has been clearly defined. Although previous studies concerned the dependence of the pump conversion efficiency on the Free Spectral Range (FSR) of the microresonator, 17 the input power and the coupling rate, 18,19 those dependencies were usually treated independently and only general trends were shown. In reality both FSR and coupling influence the threshold power -the former through the mode volume, and the latter through the loaded quality factor.…”

Section: Introductionmentioning

confidence: 99%

Kerr soliton comb generation efficiency in microresonators and microresonator coupling rate

Kondratiev¹,

Lobanov

Cordette

et al. 2023

Quantum and Nonlinear Optics IX

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Compact microresonator-based frequency comb sources are perspective elements of modern photonic technologies. They attract even more interest after the integrated device was demonstrated. The main disadvantage of the Kerr frequency combs is said to be the comparatively low generation power. However, this problem is not studied quite well. Previous studies concerned its dependence on the microresonator FSR, input power and coupling separately, expecting pump-to-comb efficiencies no more than five percents. Usually it is stated that the threshold power should be reduced to provide lower necessary pump and larger soliton existence range. However, the problem is quite complex as coupling also induce the changes into the loaded quality factor, threshold power and even the number of comb lines. Also more than 20% efficiency was demonstrated recently in the self-injection locking regime. Here we present the more comprehensive analysis of the comb generation efficiency optimization and show the theoretical way to reach the limit of 100%.

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Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory

Cited by 16 publications

References 39 publications

Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

Pinning in the Extended Lugiato–Lefever Equation

Kerr soliton comb generation efficiency in microresonators and microresonator coupling rate

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