Vladimir L. Kalashnikov, now at the Norwegian University of Science and Technology, does research in the fields of applied mathematics and theoretical physics including chaos theory, space-time nonlinear and stochastic dynamics, soliton theory, general relativity, and quantum cosmology. His main activity was connected closely with ultrafast nonlinear optics, laser physics, and the theory of dissipative solitons.
Interdisciplinary concept of dissipative soliton is unfolded in connection with ultrafast fibre lasers. The different mode-locking techniques as well as experimental realizations of dissipative soliton fibre lasers are surveyed briefly with an emphasis on their energy scalability. Basic topics of the dissipative soliton theory are elucidated in connection with concepts of energy scalability and stability. It is shown that the parametric space of dissipative soliton has reduced dimension and comparatively simple structure that simplifies the analysis and optimization of ultrafast fibre lasers. The main destabilization scenarios are described and the limits of energy scalability are connected with impact of optical turbulence and stimulated Raman scattering. The fast and slow dynamics of vector dissipative solitons are exposed.
Part of the book: Fiber Laser
Existence of different, frequently incommensurate scales is a common phenomenon in nature. Interactions between processes characterized by different scales can result in a multitude of emergent phenomena when a system cannot be described as a scale-separated hierarchy of underlying processes but presents a substantially new entity with qualitatively new properties and behavior. Striking examples are life, fractals, and chaos. Here, we shall demonstrate the quite nontrivial phenomena: chaotic and stochastic resonances and anti-resonance on examples of laser systems. The phenomena of resonant stochastization (stochastic anti-resonance), self-ordering (stochastic resonance), and resonant chaotization of coherent structures (dissipative solitons) are considered on the examples of mode-locked lasers and Raman fiber amplifiers. Despite a well-known effect of noise suppression and global regularization of dynamics due to the resonant interaction of noise and regular external periodic perturbation, here we report about the reverse situation when the regular and noise-like perturbations result in the emergent phenomena ranging from the coherent structure formation to the fine-grained chaotic/noisy dynamics. We guess that the nonlinear optical systems can be considered in this context as an ideal test-bed for “metaphorical modeling” in the area of deterministic and stochastic dynamics of resonance systems.
Part of the book: Resonance
In the last decades, rapid progress in modern nonlinear science was marked by the development of the concept of dissipative soliton (DS). This concept is highly useful in many different fields of science ranging from field theory, optics, and condensed matter physics to biology, medicine, and even sociology. This chapter aims to present a DS appearance from random fluctuations, development, and growth, the formation of the nontrivial internal structure of mature DS and its breakup, in other words, a full life cycle of DS as a self-organized object. Our extensive numerical simulations of the generalized cubic-quintic nonlinear Ginzburg-Landau equation, which models, in particular, dynamics of mode-locked fiber lasers, demonstrate a close analogy between the properties of DS and the general properties of turbulent and chaotic systems. In particular, we show a disintegration of DS into a noncoherent (or partially coherent) multisoliton complex. Thus, a DS can be interpreted as a complex of nonlinearly coupled coherent “internal modes” that allows developing the kinetic and thermodynamic theory of the nonequilibrious dissipative phenomena. Also, we demonstrate an improvement of DS integrity and, as a result, its disintegration suppression due to noninstantaneous nonlinearity caused by the stimulated Raman scattering. This effect leads to an appearance of a new coherent structure, namely, a dissipative Raman soliton.
Part of the book: Complexity in Biological and Physical Systems
Energy scaling of femtosecond laser pulses has a lot of applications in nanoscale micromachining, precision time-resolution spectroscopy, high-harmonic generation, surgery, etc. Besides applied sciences and technology, there are fundamental applications of energy harvesting at femtosecond scale. In particular, it is possible to study and control intra-atom and molecular dynamics at attosecond level as well as to map the quantum processes directly with unprecedented spatial and temporal resolution. This “mesoscopic” union of classical and quantum phenomena provides with new insights into fundamental issues of quantum mechanics of open systems including possible application in the field of quantum computing. In this work, we consider a theory of femtosecond pulse energy harvesting using the dissipative soliton generation in both solid-state and fiber mode-locked lasers and the femtosecond pulse enhancement in an external resonator. The femtosecond pulse energy, width, and spectrum scaling laws are presented in the explicit and physically meaningful form.
Part of the book: High Power Laser Systems