Ultra-long mode-locked Er-droped fibre lasers

The development of ultra-long (UL) cavity (hundreds of meters to several kilometres) mode-locked fibre lasers for the generation of high-energy light pulses with relatively low (sub-megahertz) repetition rates has emerged as a new rapidly advancing area of laser physics. The first demonstration of high pulse energy laser of this type was followed by a number of publications from many research groups on long-cavity Ytterbium and Erbium lasers featuring a variety of configurations with rather different mode-locked operations. The substantial interest to this new approach is stimulated both by non-trivial underlying physics and by the potential of high pulse energy laser sources with unique parameters for a range of applications in industry, bio-medicine, metrology and telecommunications. It is well known, that pulse generation regimes in mode-locked fibre lasers are determined by the intra-cavity balance between the effects of dispersion and non-linearity, and the processes of energy attenuation and amplification. The highest per-pulse energy has been achieved in normal-dispersion UL fibre lasers mode-locked through nonlinear polarization evolution (NPE) for self-modelocking operation. In such lasers are generated the so-called dissipative optical solitons. The uncompensated net normal dispersion in long-cavity resonatorsusually leads to very high chirp and, consequently, to a relatively long duration of generated pulses. This thesis presents the results of research Er-doped ultra-long (more than 1 km cavity length) fibre lasers mode-locked based on NPE. The self-mode-locked erbium-based 3.5-km-long all-fiber laser with the 1.7 µJ pulse energy at a wavelength of 1.55 µm was developed as a part of this research. It has resulted in direct generation of short laser pulses with an ultralow repetition rate of 35.1 kHz. The laser cavity has net normal-dispersion and has been fabricated from commercially-available telecom fibers and optical-fiber elements. Its unconventional linear-ring design with compensation for polarization instability ensures high reliability of the self-mode-locking operation, despite the use of a non polarization-maintaining fibers. The single pulse generation regime in all-fibre erbium mode-locking laser based on NPE with a record cavity length of 25 km was demonstrated. Modelocked lasers with such a long cavity have never been studied before. Our result shows a feasibility of stable mode-locked operation even for an ultra-long cavity length. A new design of fibre laser cavity – “y-configuration”, that offers a range of new functionalities for optimization and stabilization of mode-locked lasing regimes was proposed. This novel cavity configuration has been successfully implemented into a long-cavity normal-dispersion self-mode-locked Er-fibre laser. In particular, it features compensation for polarization instability, suppression of ASE, reduction of pulse duration, prevention of in-cavity wave breaking, and stabilization of the lasing wavelength. This laser along with a specially designed double-pass EDFA have allowed us to demonstrate anenvironmentally stable all-fibre laser system able to deliver sub-nanosecond high-energy pulses with low level of ASE noise.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Dispersion and nonlinearity-management in mode-locked fibre lasers

In this work we extend theory of dispersion-managed (DM) solitons to dissipative systems with the main focus on applications in mode-locked lasers. In general, pulses in mode-locked fibre lasers experience both nonlinear and dispersion management per cavity round trip. In stretched-pulse lasers, this concept was utilized to obtain high energy pulses. Here we model the pulse propagation in a mode-locked fibre laser with a distributed nonlinear and DM Ginzburg-Landau type equation. We extend existing results on DM solitons and investigate the impact on soliton properties of dissipative perturbations that occur due to the effects of gain amplification, saturable absorption, and loss. In conclusion, in contrast to standard DM solitons in Hamiltonian systems, dissipative DM solitons do exist at high map strengths, thus opening a way for the generation of stable, short pulses with high energy.

Picosecond soliton propagation using nonlinear optical loop mirrors as intensity filters

The authors show that by inserting nonlinear optical loop mirrors into an optical fibre transmission line, 1.5 ps solitons may be transmitted over at least 750 km, with amplifiers spaced at 15 km intervals.

Dispersion-modified actively mode-locked erbium fibre laser using a chirped fibre grating

The authors describe the operation of an actively modelocked Er fibre laser incorporating a chrped in fibre Bragg reflection grating as one end mirror to the cavity, acting as a lumped highly dispersive element. In one oreientation the grating shifted the cavity into normal dispersion regime and pulses of -25ps duration were produced. In the opposite oreintation, the cavity dispersion was anomalous and ~8ps pulses were produced with characterisitics typical of solitons propagating in a periodically perturbed system.

Evaluating the Capacity of Phase Modulator-Controlled Long-Haul Soliton Transmission

We review recent developments in the use of optical solitons for communication systems spanning transoceanic distances. The implementation of "soliton control" to alleviate the detrimental impact of effects such as amplifier noise is shown to be critical for obtaining advantages over competing technologies. The potential performance of two control strategies, namely straight line filtering and synchronous phase modulation, is examined in detail. Design diagrams are used to determine the maximum permissible amplifier spacing, which is a key determinant of system economics. To focus the enquiry, two example system spans are taken, representing transatlantic and transpacific distances. It is concluded that straight line filtering provides very little improvement over a basic design without control. However synchronous phase modulation, which may be implemented using a handful of actively driven components, provides very substantial benefits. These may be used either to extend the overall bit-rate-distance product of the system or to increase the amplifier spacing at more moderate capacities. © 1995 Academic Press. All rights reserved.

Picosecond soliton transmission using concatenated nonlinear optical loop-mirror intensity filters

The issues involved in employing nonlinear optical loop mirrors (NOLMs) as intensity filters in picosecond soliton transmission were examined in detail. It was shown that inserting NOLMs into a periodically amplified transmission line allowed picosecond solitons to be transmitted under conditions considered infeasible until now. The loop mirrors gave dual function, removing low-power background dispersive waves through saturable absorption and applying a negative feedback mechanism to control the amplitude of the solitons. The stochastic characteristics of the pulses that were due to amplifier spontaneous-emission noise were investigated, and a number of new properties were determined. In addition, the mutual interaction between pulses was also significantly different from that observed for longer-duration solitons. The impact of Raman scattering in the computations was included and it was shown that soliton self-frequency shifts may be eliminated by appropriate bandwidth restrictions.

Optimising transmission capacity: long distance and terrestrial applications

This paper identifies the important limiting processes in transmission capacity for amplified soliton systems. Some novel control techniques are described for optimizing this capacity. In particular, dispersion compensation and phase conjugation are identified as offering good control of jitter without the need for many new components in the system. An advanced average soliton model is described and demonstrated to permit large amplifier spacing. The potential for solitons in high-dispersion land-based systems is discussed and results are presented showing 10 Gbit s$^{-1}$ transmission over 1000 km with significant amplifier spacing.

Picosecond soliton control using nonlinear optical loop mirrors

We show that by inserting nonlinear optical loop mirrors into an optical fibre transmission line, that 1.5 ps solitons may be transmitted over at least 750 km, with amplifiers spaced at 15 km intervals.

16,000 km, 10 Gbits-1 soliton transmission over standard fibre by reduction of interactions through optimum amplifier positioning

We show that by optimizing the amplifier position in a two-stage dispersion map, the (dispersion-managed) soliton-soliton interaction can be reduced, enabling transmission of 10-Gbits-1 solitons over standard fiber over 16,000 km

Intermediate asymptotics in nonlinear optical systems

Using a fiber laser system as a specific illustrative example, we introduce the concept of intermediate asymptotic states in finite nonlinear optical systems. We show that intermediate asymptotics of nonlinear equations (e.g., coherent structures with a finite lifetime or distance) can be used in applications similar to those of truly stable asymptotic solutions, such as, e.g., solitons and dissipative nonlinear waves. Applying this general idea to a particular, albeit practically important, physical system, we demonstrate a novel type of nonlinear pulse-shaping regime in a mode-locked fiber laser leading to the generation of linearly chirped pulses with a triangular distribution of the intensity.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.