Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays

Abstract

We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed in an external cavity lead to the emission of temporal dissipative solitons. These are vectorial solitons because they appear as localized pulses in the polarized output, but leave the total intensity constant. When the cavity roundtrip time is much longer than the soliton duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solitons coexist together and with the background solution. The experimental results are well described by a theoretical model that can be reduced to a single delayed equation for the polarization orientation, which allows the vectorial solitons to be interpreted as polarization kinks. A Floquet analysis is used to confirm the mutual independence of the observed solitons.T he field of dissipative solitons (DS) in optical systems has been the subject of intensive research during the past 20 years (see, for example, Akhmediev and Ankiewicz 1,2 , Ackemann et al. 3 , Descalzi et al. 4 and Grelu and Akhmediev 5 , and references therein). Optical DS are localized light pulses in time or localized beams in space that appear in nonlinear systems kept out of equilibrium by a continuous flow of energy that counteracts the losses 5 . As a consequence, DS differ substantially from conservative solitons, which originate purely by a compensation between a spreading effect and the nonlinearity.A first important difference concerns the role of the nonlinearity. Although in the beginning DS were envisioned as weakly modified conservative solitons 6 , it was later shown that, for strong dissipation, the scenario that leads to DS formation may be more complex. For instance, bright cavity solitons, which appear in the transverse plane of driven resonators 7-10 , exist even in the presence of defocusing nonlinearities, which favour the spreading effect 11 . Cavity solitons are cellular patterns generated by fronts that connect different coexisting spatial solutions 12 and their existence cannot be reduced to a simple compensation mechanism between nonlinearity and diffraction.Another fundamental difference is that DS are attractors, that is stable solutions towards which the system evolves spontaneously from a wide set of initial conditions 13 . This entails that, at variance with their conservative analogues, DS do not rely on a proper seeding of the initial conditions. This renders them extremely interesting for applications and, in particular, for information processing in which DS are used as bit units. For example, recently all-optical buffers based on cavity solitons have been demonstrated both in spatial and in temporal domains 3,10,14-16 .Temporal DS have been studied largely in mode-locked lasers 5 and, more recently, in Kerr fibre cavities driven by an injected field 14 ; several interesting behaviours have been experimentally demonstrated, as, for example, soliton bound states 17 , molecules 18 , repulsive/attracting forces on an extremely lo...

Features of the Local Dynamics of the Opto-Electronic Oscillator Model with Delay

“…Первоначально такое представление обсуждалось на основе интуитивной интерпретации запазды-вания как размера одной квазипространственной переменной [10]. Метод ПВП ис-пользовался для изучения динамики лазерных систем с несколькими запаздыва-ниями разного масштаба [11], поляризационной динамики VECSEL-лазеров [12], неустойчивости Бенджамина Фейра [13] и других явлений в системах различной природы. В работе [14] ПВП было обосновано на основе локального анализа моде-ли лазерной системы с большим запаздыванием в цепи оптоэлектронной обратной связи.…”

Dispersive Time-Delay Dynamical Systems

“…Time-delay dynamical systems (TDDS) have been successfully used to describe a variety of problems ranging from population and neural dynamics in biological sciences [1][2][3] to short pulse formation and the appearance of instabilities in laser physics [4][5][6][7]. They also appear in control [8], modeling of climate [9], modern computational methods [10,11], and the dynamics of coupled oscillators [12,13].…”

“…The relation (6) gives an expression for the output field from the dispersive delay line. Therefore, in order to account for the effect of dispersion in the model equations we need to replace in these equations the output field Aðt − TÞ from a dispersionless delay line with that calculated in the presence of chromatic dispersion: Aðt − TÞ þ Pðt − TÞ.…”

“…This framework could be used to investigate the impact of dispersion on the dynamics of a broad (8)- (9), (7) for ΔðtÞ ¼ Δ 0 sin ρt at the turning point of the filter transmission sin ρt ¼ −1 (top) in case of (a) normal dispersion Ω ¼ 13 (modulation frequency ρ ¼ 10 class of systems commonly described by DDEs. For example, this approach could be used to understand the effect of linear chromatic dispersion on the characteristics of the mode-locked regime in monolithic multisection lasers and other nonlinear photonic devices [6,7,10,[21][22][23][24][25][26]. In particular, taking chromatic dispersion into consideration is unavoidable when modeling soliton mode-locked lasers frequently used for generation of femtosecond pulses [27], photonic crystal mode-locked lasers [25], as well as many other fiber, solid state, and semiconductor [28] optical systems.…”

Pulsating solitons in mode-locked fibre lasers

“…In this paper, we report on the direct experimental observation of extreme soliton pulsations in a passively mode-locked fibre laser. We capture these kinds of pulsations temporally and spectrally in real time using spatio-temporal intensity dynamics measurements and the dispersive Fourier transformation (DFT) [8,9].The methodology of spatio-temporal dynamics has recently enabled substantial progress in the real-time characterisation of dynamic, non-stationary generation regimes of lasers and soliton interactions in other cavitybased systems [10][11][12] owing to the possibility of identifying and tracking individual features embedded in the radiation that are otherwise hidden in the usual one-dimensional intensity measurements [13]. In this method, the intensity evolution in the laser is traced as it makes round-trip circulations within the laser cavity.…”