Upconversion assisted self-pulsing in a high-concentration erbium doped fiber laser

We report results on experimental and theoretical characterisation of self-pulsing in high concentration erbium doped fibre laser which is free from erbium clusters. Unlike previous models of self-pulsing accounting for pair-induced quenching (PIQ) on the clustered erbium ions, new model has been developed with accounting for statistical nature of the excitation migration and upconversion and resonance-like pumpto-signal intensity noise transfer. The obtained results are in a good agreement with the experimental data

Representation of grossone-based arithmetic in simulink for scientific computing

AbstractNumerical computing is a key part of the traditional computer architecture. Almost all traditional computers implement the IEEE 754-1985 binary floating point standard to represent and work with numbers. The architectural limitations of traditional computers make impossible to work with infinite and infinitesimal quantities numerically. This paper is dedicated to the Infinity Computer, a new kind of a supercomputer that allows one to perform numerical computations with finite, infinite, and infinitesimal numbers. The already available software simulator of the Infinity Computer is used in different research domains for solving important real-world problems, where precision represents a key aspect. However, the software simulator is not suitable for solving problems in control theory and dynamics, where visual programming tools like Simulink are used frequently. In this context, the paper presents an innovative solution that allows one to use the Infinity Computer arithmetic within the Simulink environment. It is shown that the proposed solution is user-friendly, general purpose, and domain independent

Rogue waves driven by polarization instabilities in a long ring fiber oscillator

We present an experimental and theoretical results of a study of a complex nonlinear polarization dynamics in a passively self-mode-locked erbium-doped fiber oscillator implemented in a ring configuration and operating near lasing threshold. The theoretical model consists of seven coupled non-linear equations and takes into account both orthogonal states of polarizations in the fiber. The experiment confirmed the existence of seven eigenfrequencies, predicted by the model due to polarization instability near lasing threshold. By adjusting the state of polarization of the pump and in-cavity birefringence we changed some eigenfrequencies from being different (non-degenerate state) to matching (degenerate state). The non-degenerate states of oscillator lead to the L-shaped probability distribution function and true rogue wave regime with a positive dominant Lyapunov exponent value between 1.4 and 2.6. Small detuning from partially degenerate case also leads to L-shaped probability distribution function with the tail trespassing eight standard deviations threshold, giving periodic patterns of pulses along with positive dominant Lyapunov exponent of a filtered signal between 0.6 and 3.2. The partial degeneration, in turn, guides to quasi-symmetric distribution and the value of dominant Lyapunov exponent of 42 which is a typical value for systems with a source of the strongly nonhomogeneous external noise

Multi-scale polarisation phenomena

Multi-scale methods that separate different time or spatial scales are among the most powerful techniques in physics, especially in applications that study nonlinear systems with noise. When the time scales (noise and perturbation) are of the same order, the scales separation becomes impossible. Thus, the multi-scale approach has to be modified to characterise a variety of noise-induced phenomena. Here, based on stochastic modelling and analytical study, we demonstrate in terms of the fluctuation-induced phenomena and Hurst R/S analysis metrics that the matching scales of random birefringence and pump–signal states of polarisation interaction in a fibre Raman amplifier results in a new random birefringence-mediated phenomenon, which is similar to stochastic anti-resonance. The observed phenomenon, apart from the fundamental interest, provides a base for advancing multi-scale methods with application to different coupled nonlinear systems ranging from lasers (multimode, mode-locked, random, etc.) to nanostructures (light-mediated conformation of molecules and chemical reactions, Brownian motors, etc.)

Excitation back transfer in a statistical model for upconversion in Er-doped fibres

We report a new analytical approach to evaluate the accuracy of a statistical model of the migration assisted upconversion in Er-doped fibres. Unlike the mean-field approach to the excitation back transfer which was used in previous statistical model, we use a new approximation accounting for the variance of population of the first excited level. Implementing these results, we find that the accuracy of upconversion rate calculations is within 13 % if the concentration of erbium ions is smaller than the critical one

Theory of highly loaded coal-water slurries

There has been analyzed the existing schemes of strapping of circulated system of drilling set during drilling with well washing by the foam and argued the necessity of its efficient raising; there has been chosen the scheme of strapping of circulated system during drilling with well washing by the foam for the possibility of the most rational usage of existing foamgenerating equipment.В статті проаналізовані існуючі схеми обв'язки циркуляційної системи бурової установки при бурінні з промиванням свердловини піною та обґрунтована необхідність підвищення їх ефективності; для можливості найбільш раціонального використання існуючого піногенеруючого устаткування передбачена схема обв'язки циркуляційної системи при бурінні з промиванням свердловини піною

Changes in normalized permutation entropy during non-coherent pulsepulse interaction in the laser cavity

Summary form only given. Statistically extreme events, that is to say, the events which have L-shaped probability distribution function (PDF, or in other words L-statistics) and, in particular, the rogue wave (RW) events, constitute a special family of natural phenomena. Curiously, this kind of events is more common than it is believed. It was observed that the behavior of the systems which obey L-shaped statistics is clustered. Periods of high predictability and low volatility are followed by periods of drastic changes and high volatility, for example, RWs [1], earthquakes, epileptic seizures etc. Permutation entropy (PE) is an indicator of dynamical predictability of the system [2, 3] which allows quantization of the predictability or volatility. We report an investigation of using it to characterize the uncertainty period which was observed during pulse-pulse interaction in a long ring laser resonator without a saturable absorber. These resonators, in particular, the resonator built using Er3+ doped fiber (Fig.1), have polarization dependent instability near the lasing threshold [4] which leads to the generation of pulses propagating with different speed, either randomly or regularly. Using this property, an investigator can observe the mechanism of the pulse-pulse interaction in detai

Slow deterministic vector rogue waves

For an erbium-doped fiber laser mode-locked by carbon nanotubes, we demonstrate experimentally and theoretically a new type of the vector rogue waves emerging as a result of the chaotic evolution of the trajectories between two orthogonal states of polarization on the Poincare sphere. In terms of fluctuation induced phenomena, by tuning polarization controller for the pump wave and in-cavity polarization controller, we are able to control the Kramers time, i.e. the residence time of the trajectory in vicinity of each orthogonal state of polarization, and so can cause the rare events satisfying rogue wave criteria and having the form of transitions from the state with the long residence time to the state with a short residence time