Dissipative Solitons for Mode-locked Fiber Lasers

Ph. Grelu(1), S. Chouli(1), J.M. Soto-Crespo(2), W. Chang(3), A. Ankiewicz(4), N. Akhmediev(4) (1) Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 5209 CNRS

Université de Bourgogne – 9 avenue Savary 21000 Dijon France (2) Instituto de Óptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain

(3) Max-Planck Institute for the Science of Light, Guenther-Scharowsky Str. 1/24, D-91058 Erlangen, Germany (4) Optical Sciences Group, Research School of Physics and Engineering,

The Australian National University, Canberra, ACT 0200, Australia

Abstract- The concept of a dissipative optical soliton is applied to interpret various pulse dynamics either predicted numerically or observed experimentally in passively mode-locked fiber lasers. The recently discovered “dissipative soliton resonance” phenomenon and “soliton rain” dynamics are highlighted as prominent examples.

I. INTRODUCTION

For the past few years, the use of the dissipative soliton terminology has been rapidly expanding in many fields of nonlinear optics [1]. In particular, it has become widely used to interpret a variety of mode-locked fiber laser dynamics [2]. In contrast to conventional solitons that manifest in conservative systems, such as in passive nonlinear transmission lines, dissipative solitons are robust, fixed-shaped pulse solutions in general. Since their pulse shape is dictated by the parameter set of the optical system, dissipative solitons provide an interesting framework for numerous applications where gain and loss mechanisms apply, such as mode-locked fiber lasers and optical regeneration. The concept of a dissipative soliton can be applied to explain or reinterpret a variety of pulse dynamics that have been observed experimentally in mode-locked fiber lasers, such as the existence of stable bright pulses in the normal dispersion regime [3,4], and the formation of stable soliton molecules or bound states [5-7]. The situation of large sets of interacting solitons inside the laser cavity, which often goes beyond the capacity of existing numerical models, can also be addressed qualitatively [8-10]. Complex and remarkable multi-soliton dynamics can be illustrated by the recently discovered soliton rain dynamics in a fiber laser experiment [11,12]. On the side of single-pulse dynamics, the dissipative soliton resonance phenomenon has attracted much attention over the past couple of years, providing an alternative theoretical framework for the quest of the highest-energy pulses produced out of mode-locked laser oscillators [13-18].

II. SOLITON RAINS

The soliton rain dynamics is a striking illustration of self-organization among large numbers of solitons and radiation. We have observed it in a fiber laser operated in a highly pumped but weakly mode-locked regime, when both soliton pulses and cw background coexist [11,12]. Soliton rains are obviously a manifestation of dissipative nonlinear dynamics. It is characterized by the interactions among three main field

components. The first component is a condensed soliton phase of several tens of jittering bound solitons that seems analogous to a liquid thermodynamical phase. Just as a liquid would evaporate, the condensed phase emits a large amount of radiation, which is also superimposed on other preexisting cw modes, producing a noisy, inhomogeneous background, the second field component. When fluctuations exceed a certain level, a new soliton is formed, like a droplet formed from a vapor cloud, which then drifts back to the condensed phase at a nearly constant relative velocity – third field component. The whole scenario repeats in a quasi-stationary fashion. In addition to interesting analogies with the cycle of water, the soliton rain dynamics addresses the largely unexplored field of nonlinear dissipative dynamics in the case of large soliton manifolds, brings useful information in the context of mode-locking dynamics, and illustrates the diversity of operating regimes accessible in fiber lasers mode-locked through nonlinear polarization evolution.

III. DISSIPATIVE SOLITON RESONANCES

There is an intense experimental research activity in developing high-energy single-pulse oscillators within passively mode-locked fiber laser technology. In essence, the current trend corresponds to incorporating the well-established concept of chirped-pulsed amplification inside the laser oscillator [19]. However, laser cavity design is not an obvious task since, unlike the use of an external amplifier, the input field at the amplifier section is not known in advance but results from a global dynamical balance of the various physical effects at play. Hence, it is useful to map the possible dynamics that can be found out of simple master equations for mode-locked lasers. Owing to its applicability to various mode-locked lasers schemes, the complex cubic-quintic Ginzburg-Landau equation (CGLE) is a master equation of choice [1-3,20].

During numerical explorations of dissipative soliton solutions in the parameter space of the CGLE, a certain region of the equation parameters was found where the energy of single pulses increased indefinitely whenever the equation parameter converged to this given region [13]. A set of parameters where the soliton energy diverges to infinity was called a Dissipative Soliton Resonance (DSR) [14]. We have extended numerical studies in the parameter space of the CGLE, in order to clearly demonstrate the existence of DSRs for both signs of chromatic dispersion

over a wide range of parameters [18]. The general pulse features in the vicinity of a DSR, which are common to both dispersion regimes and to all numerical observations of DSR reported so far, are summarized as follows: (i) the pulse energy diverges to infinity, (ii) the pulse shape becomes flat-topped due to the saturation of pulse amplitude, (iii) consequently, the pulse width diverges to infinity, and finally, (iv) in order for DSR to be distinct from a mere transition to a continuous wave, the spectral width remains finite and the pulse coherence remains.

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