Multistability and coexisting soliton combs in ring resonators: the Lugiato-Lefever approach

Kartashov, Yaroslav V.; Alexander, Orbett T.; Skryabin, Dmitry V.

doi:10.1364/oe.25.011550

Cited by 29 publications

(23 citation statements)

References 19 publications

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“…Despite the coexistence of the Ψ ± families at δ > 0, the Ψ − family is found to be unstable for δ > 0, hence no stable coexistence (as in Refs. [17][18][19][20][21] ) was observed to occur. Figures 4 and 5 show the existence and stability domains for the Ψ ± families vs pump.…”

Section: Ocis Codesmentioning

confidence: 99%

Cavity solitons in a microring dimer with gain and loss

Milián¹,

Kartashov²,

Skryabin³

et al. 2018

Opt. Lett.

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We address a pair of vertically coupled microring resonators with gain and loss pumped by a single-frequency field. Coupling between microrings results in a twofold splitting of the single microring resonance that increases when gain and losses decrease, giving rise to two cavity soliton (CS) families. We show that the existence regions of CSs are tunable and that both CS families can be stable in the presence of an imbalance between gain and losses in the two microrings. These findings enable experimental realization of frequency combs in configurations with active microrings and contribute toward the realization of compact multisoliton comb sources.

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Section: Ocis Codesmentioning

confidence: 99%

Cavity solitons in a microring dimer with gain and loss

Milián¹,

Kartashov²,

Skryabin³

et al. 2018

Opt. Lett.

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“…The complete and exact dynamical scenario can be reproduced by the famous Ikeda map [9], but this model does not give any reasonable physical insight owing to its complex mathematical structure. A model sharing the accuracy of the Ikeda map and the simplicity of LLE will be of paramount importance in the design of the next-generation of resonators [10]. A reliable model capable to reproduce quantitatively the results of the Ikeda map and the latest experiments [8] is still missing.…”

mentioning

confidence: 99%

“…A conceptually different model was derived very recently following a single-equation approach [10], but crucially it is not based on the exact Ikeda map and it is still far too complicated to allow a deep physical understanding (e.g. stationary solutions like CSs cannot be found even numerically).…”

mentioning

confidence: 99%

Multi-resonant Lugiato–Lefever model

Conforti

Biancalana

2017

Opt. Lett.

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We introduce a new model describing multiple resonances in Kerr optical cavities. It perfectly agrees quantitatively with the Ikeda map and predicts complex phenomena such as super cavity solitons and coexistence of multiple nonlinear states.Optical resonators featuring Kerr media display a wealth of phenomena, encompassing frequency combs [1], cavity solitons [2,3] and instabilities [4], which are being intensively studied in view of their high impact applications [1]. Given the complexity and the diversity of the physical phenomena, deriving simple, accurate and efficient models is of paramount importance. The workhorse for the description of nonlinear cavity dynamics is the celebrated Lugiato-Lefever equation (LLE) [5,6], which allows for deep theoretical insight and fast and accurate numerical modelling. Despite the fact that the LLE holds valid well beyond the mean-field approximation under which it has been historically derived, it is not capable of modelling all the phenomena of interest. Indeed, LLE can model the evolution of only one Fabry-Pérot mode, that corresponds to a single resonance. Phenomena not captured by LLE range from "super cavity solitons" (SCSs) [7] to the coexistence of stable modulational instability (MI) patterns and solitons, observed in Ref.[8]. The complete and exact dynamical scenario can be reproduced by the famous Ikeda map [9], but this model does not give any reasonable physical insight owing to its complex mathematical structure. A model sharing the accuracy of the Ikeda map and the simplicity of LLE will be of paramount importance in the design of the next-generation of resonators [10]. A reliable model capable to reproduce quantitatively the results of the Ikeda map and the latest experiments [8] is still missing. In this Memorandum, we derive rigorously a multi-resonant LLE system, which agrees quantitatively with the Ikeda map. Each Fabry-Pérot resonance is described by an LLE-type equation, which is coupled to the others in a nontrivial way. An arbitrary number of resonances can be treated, making the model highly flexible and scalable to any situation of experimental interest. For definiteness, we consider a fiber ring cavity, but the method can be of course straightforwardly applied to micro-resonators.We start from the Ikeda map in dimensional units:i ∂EE (n) is the electric field envelope at the n-th round-trip (measured in √ W ), P in = |E in | 2 is the input pump power, ρ 2 , θ 2 are respectively the power reflection and transmission coefficients of the coupler, and φ 0 = β 0 L is the linear cavity round-trip phase shift. For simplicity we lump all the losses in the boundary condition, with 1 − ρ 2 describing the total power lost per roundtrip. Z measures the propagation distance inside the fiber of length L, and T is time in a reference frame traveling at the group velocity of the pulse. To proceed, we note that the map above can be replaced -without loss of generality -with a single equation where the boundary conditions are explicitly incorporated in an NLSEtype...

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“…Similarly to the solitons of nonlinear Schrödinger equation [40], dissipative optical localised structures known also as temporal cavity solitons (TCSs) are localised in time and in longitudinal direction. They can be studied by direct numerical simulations of complex Ginzburg-Landau-type equations [8,11] or alternatively as stationary solutions of properly constructed ordinary differential equations in the co-moving reference frame [30,34,35]. Although this approach allows for a detailed bifurcation analysis of TCSs, complex Ginzburg-Landau models are hardly applicable to account accurately for some important physical effects in realistic laser devices, such as those containing intracavity semiconductor medium [19,33].…”

Section: Introductionmentioning

confidence: 99%

“…For example, the LLE fails to describe the bistability between two TCS branches corresponding to neighbouring longitudinal cavity modes [9], which requires large detunings. On the other hand, this bistability is well captured in the framework of the travelling wave equation approach [11]. Similarly to the travelling wave equations DDE models are free from the small detuning approximation.…”

Section: Introductionmentioning

confidence: 99%

Temporal cavity solitons in a delayed model of a dispersive cavity ring laser

Pimenov

Amiranashvili

Vladimirov

2020

Math. Model. Nat. Phenom.

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Nonlinear localised structures appear as solitary states in systems with multistability and hysteresis. In particular, localised structures of light known as temporal cavity solitons were observed recently experimentally in driven Kerr-cavities operating in the anomalous dispersion regime when one of the two bistable spatially homogeneous steady states exhibits a modulational instability. We use a distributed delay system to study theoretically the formation of temporal cavity solitons in an optically injected ring semiconductor-based fiber laser, and propose an approach to derive reduced delay-differential equation models taking into account the dispersion of the intracavity fiber delay line. Using these equations we perform the stability and bifurcation analysis of injection-locked continuous wave (CW) states and temporal cavity solitons.

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Multistability and coexisting soliton combs in ring resonators: the Lugiato-Lefever approach

Cited by 29 publications

References 19 publications

Cavity solitons in a microring dimer with gain and loss

Cavity solitons in a microring dimer with gain and loss

Multi-resonant Lugiato–Lefever model

Temporal cavity solitons in a delayed model of a dispersive cavity ring laser

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