arXiv subjects

Marina Zajnulina

Publications and source records attributed to Marina Zajnulina.

7 recordsLinked to original sources

arXiv2026

Regimes and Transitions of the Nonlinear Temporal Talbot Effect: Underlying Mechanism for A-Type Breathers, Soliton Crystals, and Soliton Gas

A frequency comb generated from a phase-modulated continuous-wave laser is simultaneously subject to the temporal Talbot effect and modulational instability (MI) when propagating through a piece of optical fiber. The temporal Talbot effect refers to the dispersion-driven self-imaging of optical pulses and is, per se, linear in optical field amplitudes. MI is a nonlinear effect. Despite growing interest and a variety of possible applications, a concise theory of the nonlinear temporal Talbot effect that incorporates nonlinear effects is not yet available; the self-imaging of optical patterns under the influence of nonlinearity remains largely unexplored. Here, I derive a dispersion relation for frequency-comb spatial modes. It integrates the contributions of the linear temporal Talbot effect, self-phase modulation, and MI-driven cross-phase modulation and four-wave mixing (FWM) between frequency-comb lines, paving the way to the development of a concise theory of the nonlinear temporal Talbot effect. With the help of Soliton Radiation Beat Analysis, a technique for retrieving the soliton content of optical fields in fibers, I demonstrate that the temporal Talbot effect seeds the spatio-temporal distribution of the field by driving higher-order spatial-mode interference. Nonlinear effects modify this interference, linking Talbot effect to Fermi-Pasta-Ulam-Tsingou recurrence of optical pulses and producing input-power-dependent regime transitions between the linear Talbot effect, A-type breathers, soliton crystals, and soliton gas. I show that A-type breathers arise from regular FWM at lower input powers, whereas soliton crystals emerge from cascaded FWM at higher powers. This study advances the fields of Nonlinear Optics and Wave Theory.

physics.optics↗

arXiv2025

Shannon Entropy Helps Optimize the Performance of a Frequency-Multiplexed Extreme Learning Machine

Knowing the dynamics of neuromorphic photonic schemes would allow their optimization for controlled data-processing capability in possibly simplified designs and minimized energy consumption levels. In nonlinear substrates such as optical fibers or semiconductors, these dynamics can widely vary depending on the encoded inputs, even for a single set of physical parameters. Thus, other approaches are required to optimize the schemes. Here, I consider a frequency-multiplexed Extreme Learning Machine (ELM) that encodes information in the line amplitudes of a frequency comb and processes this information in a single-mode fiber subject to Kerr nonlinearity. Its performance is evaluated with Iris and Breast Cancer Wisconsin classification datasets. I introduce the notions of Shannon entropy of optical power, phase, and spectrum and numerically show that the optimization of system parameters (continuous-wave laser optical power and the modulation depth of the subsequent phase modulator as well as the fiber group-velocity dispersion and length) yields the ELM performance that places this neuromorphic scheme among the top-performing state-of-the-art computer-based machine-learning models. I show that the ELM's performance is robust against initial noise, paving the way for cost-effective designs. Using Soliton Radiation Beat Analysis, I show that information encoding symmetric in frequency-comb lines yields the formation of input-power-dependent Akhmediev-breather-like structures and Peregrine solitons, whereas asymmetric encoding of the comb exhibits an additional regime of soliton crystals. Also, I discuss that asymmetric encoding supports the theory of Four-Wave Mixing as a data processing mechanism, whereas symmetric encoding underlines the theory of soliton-mediated information processing. The findings advance the toolbox and knowledge of Neuromorphic Photonics and general Nonlinear Optics.

physics.optics↗

arXiv2024

Ising Hamiltonian for Coupled Fibre-Based Optical Parametric Oscillators

Here, I derive an Ising Hamiltonian for $N$ coupled fibre-based Optical Parametric Oscillators (OPOs). For this, I use the Lugiato-Lefever equation. The derivation of the Hamiltonian does not pretend to be mathematically correct, although it works under the assumption of plane waves propagating through the OPOs. Its objective is rather to be as close as possible to the Hamilton formalism than to be mathematically rigorous. The approach is based on the assumptions that are justified from the physical point of view and are implemented experimentally. The resulting Ising Hamiltonian contains all necessary terms that are connected to the appearance and evolution of phase solitons.

nlin.PS↗

arXiv2024

Temporal Talbot Effect: From a Quasi-Linear Talbot Carpet to Soliton Crystals and Talbot Solitons

The temporal Talbot effect refers to the periodic self-imaging of pulse trains in optical fibers. The connection between the linear and nonlinear temporal Talbot effect is still not fully understood. To address this challenge, we use Soliton Radiation Beat Analysis and numerically investigate the evolution of a phase-modulated continuous-wave laser input in a passive single-mode fiber. We identify three input-power-dependent regimes and their Talbot carpets: the quasi-linear regime for low input powers, the intermediate one, and separated Talbot solitons for higher powers. We show that the intermediate regime hosts soliton crystals rather than rogue waves, as reported in the literature. The Talbot-solitons beating can be used for pulse repetition-rate multiplication in the nonlinear regime. We also show two types of solitons involved: some encoded in the whole frequency comb and the individual solitons carried only by particular comb lines.

physics.optics↗

arXiv2023

Deep Photonic Reservoir Computer Based on Frequency Multiplexing with Fully Analog Connection Between Layers

Reservoir computers (RC) are randomized recurrent neural networks well adapted to process time series, performing tasks such as nonlinear distortion compensation or prediction of chaotic dynamics. Deep reservoir computers (deep-RC), in which the output of one reservoir is used as the input for another one, can lead to improved performance because, as in other deep artificial neural networks, the successive layers represent the data in more and more abstract ways. We present a fiber-based photonic implementation of a two-layer deep-RC based on frequency multiplexing. The two RC layers are encoded in two frequency combs propagating in the same experimental setup. The connection between the layers is fully analog and does not require any digital processing. We find that the deep-RC outperforms a traditional RC by up to two orders of magnitude on two benchmark tasks. This work paves the way towards using fully analog photonic neuromorphic computing for complex processing of time series, while avoiding costly analog-to-digital and digital-to-analog conversions.

cs.ET↗

arXiv2023

Weak Kerr Nonlinearity Boosts the Performance of Frequency-Multiplexed Photonic Extreme Learning Machines: A Multifaceted Approach

We provide a theoretical, numerical, and experimental investigation of the Kerr nonlinearity impact on the performance of a frequency-multiplexed Extreme Learning Machine (ELM). In such ELM, the neuron signals are encoded in the lines of a frequency comb. The Kerr nonlinearity facilitates the randomized neuron connections allowing for efficient information mixing. A programmable spectral filter applies the output weights. The system operates in a continuous-wave regime. Even at low input peak powers, the resulting weak Kerr nonlinearity is sufficient to significantly boost the performance on several tasks. This boost already arises when one uses only the very small Kerr nonlinearity present in a 20-meter long erbium-doped fiber amplifier. In contrast, a subsequent propagation in 540 meters of a single-mode fiber improves the performance only slightly, whereas additional information mixing with a phase modulator does not result in a further improvement at all. We introduce a model to show that, in frequency-multiplexed ELMs, the Kerr nonlinearity mixes information via four-wave mixing, rather than via self- or cross-phase modulation. At low powers, this effect is quartic in the comb-line amplitudes. Numerical simulations validate our experimental results and interpretation.

physics.optics↗

arXiv2022

Advances of Artificial Intelligence in Classical and Novel Spectroscopy-Based Approaches for Cancer Diagnostics. A Review

Cancer is one of the leading causes of death worldwide. Fast and safe early-stage, pre- and intra-operative diagnostics can significantly contribute to successful cancer identification and treatment. Artificial intelligence has played an increasing role in the enhancement of cancer diagnostics techniques in the last 15 years. This review covers the advances of artificial intelligence applications in well-established techniques such as MRI and CT. Also, it shows its high potential in combination with optical spectroscopy-based approaches that are under development for mobile, ultra-fast, and low-invasive diagnostics. I will show how spectroscopy-based approaches can reduce the time of tissue preparation for pathological analysis by making thin-slicing or haematoxylin-and-eosin staining obsolete. I will present examples of spectroscopic tools for fast and low-invasive ex- and in-vivo tissue classification for the determination of a tumour and its boundaries. Also, I will discuss that, contrary to MRI and CT, spectroscopic measurements do not require the administration of chemical agents to enhance the quality of cancer imaging which contributes to the development of more secure diagnostic methods. Overall, we will see that the combination of spectroscopy and artificial intelligence constitutes a highly promising and fast-developing field of medical technology that will soon augment available cancer diagnostic methods.

q-bio.TO↗