Abstract
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 states and temporal cavity solitons.
Highlights
Temporal localised structures of light propagating along the axial direction in nonlinear cavities attracted significant theoretical and experimental attention in the last decade due to their potential applications for optical data storage and transmission [7, 12, 13, 15, 16]
In the framework of time delay models, we propose another way to study moving CSs in optical resonators with the help of differential equations involving nonlinear delay terms that complements the existing studies of the effect of feedback loop described by linear delay term in form of Pyragas control [27], which can be applied to the models of broad-area lasers [18, 28, 31], as well as to nonlinear optical cavities such as fiber resonators or disk microresonators subjected to delayed optical feedback, where a Lugiato-Lefever equation (LLE) with time delay can be used to study the drift of temporal cavity solitons (TCSs) [29]
We have proposed for the first time an efficient methodological approach for numerical bifurcation analysis of periodic TCSs in dispersive time-delay systems that was previously available only for envelope PDEs
Summary
Temporal localised structures of light propagating along the axial direction in nonlinear cavities attracted significant theoretical and experimental attention in the last decade due to their potential applications for optical data storage and transmission [7, 12, 13, 15, 16]. To the solitons of nonlinear Schrodinger equation [40], dissipative optical localised structures known 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]. 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]. We find a narrow region of multistability between TCSs of different width
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