A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Interaction dynamics in small networks of nonlinear elements

We study a small circuit of coupled nonlinear elements to investigate general features of signal transmission through networks. The small circuit itself is perceived as building block for larger networks. Individual dynamics and coupling are motivated by neuronal systems: We consider two types of dynamical modes for an individual element, regular spiking and chattering and each individual element can receive excitatory and/or inhibitory inputs and is subjected to different feedback types (excitatory and inhibitory; forward and recurrent). Both, deterministic and stochastic simulations are carried out to study the input-output relationships of these networks. Major results for regular spiking elements include frequency locking, spike rate amplification for strong synaptic coupling, and inhibition-induced spike rate control which can be interpreted as a output frequency rectification. For chattering elements, spike rate amplification for low frequencies and silencing for large frequencies is characteristic

Pattern formation in volumetrically heated fluids

Finite element simulations have been performed along side normal mode analysis on the linear stability that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.

Optical wave turbulence

We review recent progress in optical wave turbulence with a specific focus on the fast growing field of fibre lasers. Weak irregular nonlinear interactions between a large number of resonator modes are responsible for practically important characteristics of fibre lasers such as spectral broadening of radiation. Wave turbulence is a fundamental nonlinear phenomenon which occurs in a variety of nonlinear wave-bearing physical systems. The experimental impediments and the computationally intensive nature of simulating of hydrodynamic or plasma wave turbulence often make it rather challenging to collect a significant number of statistical data The study of turbulent wave behaviour in optical devices offers quite a unique opportunity to collect an enormous amount of data on statistical properties of wave turbulence using high-speed, high precision optical measurements during a relatively short period of time. We present recent theoretical, numerical and experimental results on optical wave turbulence in fibre lasers ranging from weak to strong developed turbulence for different signs of fibre dispersion. Furthermore, we report on our studies of spectral wave condensate in fibre lasers that make interdisciplinary links with a number of other research fields.

Optical wave turbulence

We review recent progress in optical wave turbulence with a specific focus on the fast growing field of fibre lasers. Weak irregular nonlinear interactions between a large number of resonator modes are responsible for practically important characteristics of fibre lasers such as spectral broadening of radiation. Wave turbulence is a fundamental nonlinear phenomenon which occurs in a variety of nonlinear wave-bearing physical systems. The experimental impediments and the computationally intensive nature of simulating of hydrodynamic or plasma wave turbulence often make it rather challenging to collect a significant number of statistical data The study of turbulent wave behaviour in optical devices offers quite a unique opportunity to collect an enormous amount of data on statistical properties of wave turbulence using high-speed, high precision optical measurements during a relatively short period of time. We present recent theoretical, numerical and experimental results on optical wave turbulence in fibre lasers ranging from weak to strong developed turbulence for different signs of fibre dispersion. Furthermore, we report on our studies of spectral wave condensate in fibre lasers that make interdisciplinary links with a number of other research fields.

Random distributed feedback fibre lasers

The concept of random lasers exploiting multiple scattering of photons in an amplifying disordered medium in order to generate coherent light without a traditional laser resonator has attracted a great deal of attention in recent years. This research area lies at the interface of the fundamental theory of disordered systems and laser science. The idea was originally proposed in the context of astrophysics in the 1960s by V.S. Letokhov, who studied scattering with "negative absorption" of the interstellar molecular clouds. Research on random lasers has since developed into a mature experimental and theoretical field. A simple design of such lasers would be promising for potential applications. However, in traditional random lasers the properties of the output radiation are typically characterized by complex features in the spatial, spectral and time domains, making them less attractive than standard laser systems in terms of practical applications. Recently, an interesting and novel type of one-dimensional random laser that operates in a conventional telecommunication fibre without any pre-designed resonator mirrors-random distributed feedback fibre laser-was demonstrated. The positive feedback required for laser generation in random fibre lasers is provided by the Rayleigh scattering from the inhomogeneities of the refractive index that are naturally present in silica glass. In the proposed laser concept, the randomly backscattered light is amplified through the Raman effect, providing distributed gain over distances up to 100km. Although an effective reflection due to the Rayleigh scattering is extremely small (~0.1%), the lasing threshold may be exceeded when a sufficiently large distributed Raman gain is provided. Such a random distributed feedback fibre laser has a number of interesting and attractive features. The fibre waveguide geometry provides transverse confinement, and effectively one-dimensional random distributed feedback leads to the generation of a stationary near-Gaussian beam with a narrow spectrum. A random distributed feedback fibre laser has efficiency and performance that are comparable to and even exceed those of similar conventional fibre lasers. The key features of the generated radiation of random distributed feedback fibre lasers include: a stationary narrow-band continuous modeless spectrum that is free of mode competition, nonlinear power broadening, and an output beam with a Gaussian profile in the fundamental transverse mode (generated both in single mode and multi-mode fibres).This review presents the current status of research in the field of random fibre lasers and shows their potential and perspectives. We start with an introductory overview of conventional distributed feedback lasers and traditional random lasers to set the stage for discussion of random fibre lasers. We then present a theoretical analysis and experimental studies of various random fibre laser configurations, including widely tunable, multi-wavelength, narrow-band generation, and random fibre lasers operating in different spectral bands in the 1-1.6μm range. Then we discuss existing and future applications of random fibre lasers, including telecommunication and distributed long reach sensor systems. A theoretical description of random lasers is very challenging and is strongly linked with the theory of disordered systems and kinetic theory. We outline two key models governing the generation of random fibre lasers: the average power balance model and the nonlinear Schrödinger equation based model. Recently invented random distributed feedback fibre lasers represent a new and exciting field of research that brings together such diverse areas of science as laser physics, the theory of disordered systems, fibre optics and nonlinear science. Stable random generation in optical fibre opens up new possibilities for research on wave transport and localization in disordered media. We hope that this review will provide background information for research in various fields and will stimulate cross-disciplinary collaborations on random fibre lasers. © 2014 Elsevier B.V.

Adiabatic soliton laser

The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity - the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.

Convection induced by instabilities in the presence of a transverse seepage

The transition of laterally heated flows in a vertical layer and in the presence of a streamwise pressure gradient is examined numerically for the case of different values Prandtl number. The stability analysis of the basic flow for the pure hydrodynamic case ( Pr = 0 ) was reported in [1]. We find that in the absence of transverse pumping the previously known critical parameters are recovered [2], while as the strength of the Poiseuille flow component is increased the convective motion is delayed considerably. Following the linear stability analysis for the vertical channel flow our attention is focused on a study of the finite am- plitude secondary travelling-wave (TW) solutions that develop from the perturbations of the transverse roll type imposed on the basic flow and temperature profiles. The linear stability of the secondary TWs against three-dimensional perturbations is also examined and it is shown that the bifurcating tertiary flows are phase-locked to the secondary TWs.

Nonlinear pulse shaping in fibres for pulse generation and optical processing

The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science. Nonlinear phenomena occurring in optical fibres have many attractive features and great, but not yet fully explored, potential in signal processing. Here, we review recent progress on the use of fibre nonlinearities for the generation and shaping of optical pulses and on the applications of advanced pulse shapes in all-optical signal processing. Amongst other topics, we will discuss ultrahigh repetition rate pulse sources, the generation of parabolic shaped pulses in active and passive fibres, the generation of pulses with triangular temporal profiles, and coherent supercontinuum sources. The signal processing applications will span optical regeneration, linear distortion compensation, optical decision at the receiver in optical communication systems, spectral and temporal signal doubling, and frequency conversion. © Copyright 2012 Sonia Boscolo and Christophe Finot.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Nonlinear pulse shaping in fibres for pulse generation and optical processing

The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science. Nonlinear phenomena occurring in optical fibres have many attractive features and great, but not yet fully explored, potential in signal processing. Here, we review recent progress on the use of fibre nonlinearities for the generation and shaping of optical pulses and on the applications of advanced pulse shapes in all-optical signal processing. Amongst other topics, we will discuss ultrahigh repetition rate pulse sources, the generation of parabolic shaped pulses in active and passive fibres, the generation of pulses with triangular temporal profiles, and coherent supercontinuum sources. The signal processing applications will span optical regeneration, linear distortion compensation, optical decision at the receiver in optical communication systems, spectral and temporal signal doubling, and frequency conversion. © Copyright 2012 Sonia Boscolo and Christophe Finot.

Kerr nonlinear switching in a core-shell microspherical resonator fabricated from the silicon fiber platform

We investigate the Kerr nonlinearity in a core-shell microspherical resonator fabricated from a silicon fiber. By exploiting the ultrafast wavelength shifting, sub-picosecond modulation is demonstrated. © OSA 2015.