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

Pimenov, Alexander; Amiranashvili, Shalva; Vladimirov, Andrei G.

doi:10.1051/mmnp/2019054

Cited by 11 publications

(6 citation statements)

References 38 publications

(98 reference statements)

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“…Mode-locked laser models based on DDEs have yet to demonstrate this ability. While DDE-based models can offer a powerful alternative, they hence exhibit a slightly reduced physical accuracy 62 , 63 . We believe a hybrid model therefore offers a valuable complementary modeling technique to DDE-based approaches.…”

Section: Discussionmentioning

confidence: 99%

Hybrid modeling approach for mode-locked laser diodes with cavity dispersion and nonlinearity

Cuyvers

Poelman

Gasse

et al. 2021

Sci Rep

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Semiconductor-based mode-locked lasers, integrated sources enabling the generation of coherent ultra-short optical pulses, are important for a wide range of applications, including datacom, optical ranging and spectroscopy. As their performance remains largely unpredictable due to the lack of commercial design tools and the poorly understood mode-locking dynamics, significant research has focused on their modeling. In recent years, traveling-wave models have been favored because they can efficiently incorporate the rich semiconductor physics of the laser. However, thus far such models struggle to include nonlinear and dispersive effects of an extended passive laser cavity, which can play an important role for the temporal and spectral pulse evolution and stability. To overcome these challenges, we developed a hybrid modeling strategy by unifying the traveling-wave modeling technique for the semiconductor laser sections with a split-step Fourier method for the extended passive laser cavity. This paper presents the hybrid modeling concept and exemplifies for the first time the significance of the third order nonlinearity and dispersion of the extended cavity for a 2.6 GHz III–V-on-Silicon mode-locked laser. This modeling approach allows to include a wide range of physical phenomena with low computational complexity, enabling the exploration of novel operating regimes such as chip-scale soliton mode-locking.

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Section: Discussionmentioning

confidence: 99%

Hybrid modeling approach for mode-locked laser diodes with cavity dispersion and nonlinearity

Cuyvers

Poelman

Gasse

et al. 2021

Sci Rep

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“…This is not only due to their simplicity and availability of well developed tools for analytical and numerical analysis of nonlinear PDEs, but also because of the possibility of straightforward inclusion of the group velocity dispersion into the master equations. On the contrary, the inclusion of the chromatic dispersion into the DDE mode-locking models is not that straightforward, see [31,32]. Another limitation of the PDE Haus model, is that unlike difference-differential Haus equations (1), the development of adequate PDE models of mode-locked class-B lasers require a careful formulation of the equations describing gain dynamics on different time scales.…”

Section: Discussionmentioning

confidence: 99%

A generalized Haus master equation model for mode-locked class-B lasers

Nizette,

Vladimirov

2021

Preprint

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Using an asymptotic technique we develop a generalized version of class-B Haus partial differential equation mode-locking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the conventional class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime, but also the leading edge instability leading to harmonic mode-locked regimes with the increase of the pump power.

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“…In analogy to (and to differentiate from) periodic travelling pulses in spatially-extended systems, which are commonly referred to as (dissipative) solitons in physics [46,48], temporally localised solutions in DDEs are referred to as temporal dissipative solitons (TDSs) [72]. TDSs have been observed experimentally, for example, in semiconductor lasers and optical resonators [18,19,38,49,63], electrically coupled excitable biological cells [67], and various mathematical models of physical processes [33,41,45,50,56,65,66]. Of particular interest in spatially extended systems have been the underlying mechanisms that cause the existence of multi-peak travelling pulses [17,69].…”

Section: Introductionmentioning

confidence: 99%

Pulse-adding of temporal dissipative solitons: resonant homoclinic points and the orbit flip of case B with delay

Giraldo,

Ruschel

2023

Nonlinearity

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We numerically investigate the branching of temporally localised, two-pulse solutions from one-pulse periodic solutions with non-oscillating tails in delay differential equations (DDEs) with large delay. Solutions of this type are commonly referred to as temporal dissipative solitons (TDSs) (Yanchuk et al 2019 Phys. Rev. Lett. 123 53901) in applications, and we adopt this term here. We show by means of a prototypical example that—analogous to travelling pulses in reaction–diffusion partial differential equations (Yanagida 1987 J. Differ. Equ. 66 243–62)—the branching of two-pulse TDSs from one-pulse TDSs with non-oscillating tails is organised by codimension-two homoclinic bifurcation points of a real saddle equilibrium (Homburg and Sandstede 2010 Handbook of Dynamical Systems Elsevier) in a corresponding profile equation. We consider a generalisation of Sandstede’s model (Sandstede 1997 J. Dyn. Differ. Equ. 9 269–88) (a prototypical model for studying codimension-two homoclinic bifurcation points in ordinary differential equations) with an additional time-shift parameter, and use Auto07p (Doedel 1981 Congr. Numer. 30 265–84; Doedel and Oldeman 2010 AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equations Concordia University) and DDE-BIFTOOL (Sieber et al 2014 arXiv:1406.7144) to compute numerically the unfolding of these bifurcation points in the resulting DDE. We then interpret this model as the profile equation for TDSs in a DDE with large delay by exploiting the reappearance of periodic solutions in DDEs (Yanchuk and Perlikowski 2009 Phys. Rev. E 79 046221). In doing so, we identify both the non-orientable resonant homoclinic bifurcation and the orbit flip bifurcation of case B as organising centres for the existence of two-pulse TDSs in the DDE with large delay. We study the bifurcation curves emanating from these codimension-two points beyond a local neighbourhood in parameter space. In this way, we are able to discuss how folds of homoclinic bifurcations in an extended system bound the existence region of TDSs in the DDE with large delay. We also discuss the relation between a reduced multivalued-map (in the limit of infinite delay) and the existence of TDSs.

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

Cited by 11 publications

References 38 publications

Hybrid modeling approach for mode-locked laser diodes with cavity dispersion and nonlinearity

Hybrid modeling approach for mode-locked laser diodes with cavity dispersion and nonlinearity

A generalized Haus master equation model for mode-locked class-B lasers

Pulse-adding of temporal dissipative solitons: resonant homoclinic points and the orbit flip of case B with delay

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