Chaotic, Stochastic Resonance, and Anti-Resonance Phenomena in Optics

Abstract

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 scaleseparated 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.

Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities

“…The reverse phenomenon, Stochastic Resonance (SR), has been studied in the context of periodic occurrences of ice ages [1]. A few examples of SR were described and analyzed in [1,2], such as particle in a double well, animal behavior, sensory neurons and ionic channels in biological cells, optical systems, electronic devices, and so on. In one of these studies [2], SAR in laser systems was also analyzed.…”

“…A few examples of SR were described and analyzed in [1,2], such as particle in a double well, animal behavior, sensory neurons and ionic channels in biological cells, optical systems, electronic devices, and so on. In one of these studies [2], SAR in laser systems was also analyzed. All these examples exhibit a bell-shaped Signal-to-Noise Ratio (SNR) as a function of the applied noise level.…”

50 nJ 250 fs all-fibre Raman-free dissipative soliton oscillator

“…Theoretical studies of the HCDS regime in fibre oscillators predict an almost unlimited growth of pulse energy at a proper combination of the parameters, so-called dissipative soliton resonance (DSR) [4,5]). However, the maximum available energy in experiments is limited by an optical damage of the laser cavity elements, as well as by the physical effects of a fundamental nature such as quantum noise [6], mode instability (at large mode area) [7] or stimulated Raman scattering (SRS) [8]. A threshold with a particular limiting effect is defined by the specifics of the laser cavity configuration.…”