Nonlinear Active Medium Research Articles

Q-switched triple-wavelength erbium-doped fiber laser with black phosphorus absorber

We achieved a notable advance in laser technology by generating a triple-wavelength output in a Q-switched Erbium-doped fiber laser (EDFL) using a new black phosphorous saturable absorber (BPSA). The BPSA was made by exfoliating multilayer BP material from a bulk crystal and transferring it onto a fiber ferrule tip. Upon integration into an EDFL ring cavity, this BPSA facilitated the production of Q-switched pulses at wavelengths of 1530.4, 1531.5, and 1532.6 nm. This distinctive triple-wavelength lasing phenomenon, characterized by uniform spacing, arises from standing wave interference within the ring cavity, leveraging the highly nonlinear active gain medium. With an increase in pumping strength from 147 mW to 223 mW, the repetition rate escalated from 41.15 to 60.83 kHz, accompanied by a reduction in pulse width from 8.45 µs to 6.06 µs. Notably, the highest recorded pulse energy peaked at 11.8 nJ. These findings highlight the efficacy of BP as a Q-switcher for the generation of multi-wavelength pulses, marking a significant advancement in laser technology.

Shortcuts to adiabatic soliton compression in active nonlinear Kerr media.

We implement variational shortcuts to adiabaticity for optical pulse compression in an active nonlinear Kerr medium with distributed amplification and spatially varying dispersion and nonlinearity. Starting with the hyperbolic secant ansatz, we employ a variational approximation to systematically derive dynamical equations, establishing analytical relationships linking the amplitude, width, and chirp of the pulse. Through the inverse engineering approach, we manipulate the distributed gain/loss, nonlinearity and dispersion profiles to efficiently compress the optical pulse over a reduced distance with high fidelity. In addition, we explore the dynamical stability of the system to illustrate the advantage of our protocol over conventional adiabatic approaches. Finally, we analyze the impact of tailored higher-order dispersion on soliton self-compression and derive physical constraints on the final soliton width for the complementary case of soliton expansion. The broader implications of our findings extend beyond optical systems, encompassing areas such as cold-atom and magnetic systems highlighting the versatility and relevance of our approach in various physical contexts.

Deformable Material as a Nonlinear Active Medium

Deformable Material as a Nonlinear Active Medium

High-order accurate schemes for Maxwell's equations with nonlinear active media and material interfaces

We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level modified equation approach for Maxwell's equations in second-order form for the electric field coupled to ODEs for the polarization vectors and population densities of the atomic levels. The resulting scheme has a large CFL-one time-step. Curved interfaces between different materials are accurately treated with curvilinear grids and compatibility conditions. A novel hierarchical modified equation approach leads to an explicit scheme that does not require any nonlinear iterations. The hierarchical approach at interfaces leads to local updates at the interface with no coupling in the tangential directions. Complex geometry is treated with overset grids. Numerical stability is maintained using high-order upwind dissipation designed for Maxwell's equations in second-order form. The scheme is carefully verified for a number of two and three-dimensional problems. The resulting numerical model with generalized dispersion and arbitrary nonlinear multi-level system can be used for many plasmonic applications such as for ab initio time domain modeling of nonlinear engineered materials for nanolasing applications, where nano-patterned plasmonic dispersive arrays are used to enhance otherwise weak nonlinearity in the active media.

A brief history of liquid computers.

A substrate does not have to be solid to compute. It is possible to make a computer purely from a liquid. I demonstrate this using a variety of experimental prototypes where a liquid carries signals, actuates mechanical computing devices and hosts chemical reactions. We show hydraulic mathematical machines that compute functions based on mass transfer analogies. I discuss several prototypes of computing devices that employ fluid flows and jets. They are fluid mappers, where the fluid flow explores a geometrically constrained space to find an optimal way around, e.g. the shortest path in a maze, and fluid logic devices where fluid jet streams interact at the junctions of inlets and results of the computation are represented by fluid jets at selected outlets. Fluid mappers and fluidic logic devices compute continuously valued functions albeit discretized. There is also an opportunity to do discrete operation directly by representing information by droplets and liquid marbles (droplets coated by hydrophobic powder). There, computation is implemented at the sites, in time and space, where droplets collide one with another. The liquid computers mentioned above use liquid as signal carrier or actuator: the exact nature of the liquid is not that important. What is inside the liquid becomes crucial when reaction-diffusion liquid-phase computing devices come into play: there, the liquid hosts families of chemical species that interact with each other in a massive-parallel fashion. I shall illustrate a range of computational tasks, including computational geometry, implementable by excitation wave fronts in nonlinear active chemical medium. The overview will enable scientists and engineers to understand how vast is the variety of liquid computers and will inspire them to design their own experimental laboratory prototypes. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Nonperturbative Kinetic Description of Electron-Hole Excitations in Graphene in a Time Dependent Electric Field of Arbitrary Polarization

On the basis of the well-known kinetic description of e − e + vacuum pair creation in strong electromagnetic fields in D = 3 + 1 QED we construct a nonperturbative kinetic approach to electron-hole excitations in graphene under the action of strong, time-dependent electric fields. We start from the simplest model of low-energy excitations around the Dirac points in the Brillouin zone. The corresponding kinetic equations are analyzed by nonperturbative analytical and numerical methods that allow to avoid difficulties characteristic for the perturbation theory. We consider different models for external fields acting in both, one and two dimensions. In the latter case we discuss the nonlinear interaction of the orthogonal currents in graphene which plays the role of an active nonlinear medium. In particular, this allows to govern the current in one direction by means of the electric field acting in the orthogonal direction. Investigating the polarization current we detected the existence of high frequency damped oscillations in a constant external electric field. When the electric field is abruptly turned off residual inertial oscillations of the polarization current are obtained. Further nonlinear effects are discussed.

Nonlinear Effects with Semiconductor Optical Amplifiers

Abstract This study has presented the nonlinear medium such as passive nonlinear medium like highly nonlinear fiber (HNLF) and active nonlinear medium like SOA. The FWM effects have ended up plainly huge at high optical power levels and have become even more meaningful when the capacity of the optical transmission line is increased, which has been reached through decreasing the channel separations. Also, anatomy has been done to analyze the performance of FWM when unequal channel spacing is considered. The outcomes indicate that when unequal channel spacing is used, the power levels of the beat frequency generated due to FWM effect in WDM system was increased to large values, so the performance of the wavelength division multiplexing (WDM) system is not enhanced, on the other hand when equal channel separations are used, and at the same bandwidth required to transmit 4 input channels the quality of receiving signal is greater than the system used unequal channel separation. This means that in the WDM system equal channels separation is more efficient than unequal channels separation-based SOA. The simulation is done using 4 channel wave division multiplexing signals at a rate of 10 Gb/s.

Complete Characterization of Structure of Rule 54

The dynamics of rule 54 one-dimensional two-state cellular automaton (CA) are a discrete analog of a space-time dynamics of excitations in nonlinear active medium with mutual inhibition. A cell switches its state 0 to state 1 if one of its two neighbors is in state 1 (propagation of a perturbation) and a cell remains in state 1 only if its two neighbors are in state 0. A lateral inhibition is because a 1-state neighbor causes a 1-state cell to switch to state 0. The rule produces a rich spectrum of space-time dynamics, including gliders and glider guns just from four primitive gliders. We construct a catalogue of gliders and describe them by tiles. We calculate a subset of regular expressions $\Psi_{R54}$ to encode gliders. The regular expressions are derived from de Bruijn diagrams, tile-based representation of gliders, and cycle diagrams sometimes. We construct an abstract machine that recognizes regular expressions of gliders in rule 54 and validate $\Psi_{R54}$. We also propose a way to code initial configurations of gliders to depict any type of collision between the gliders and explore self-organization of gliders, formation of larger tiles, and soliton-like interactions of gliders and computable devices.

Hybrid silicon on insulator/polymer electro-optical intensity modulator operating at 780 nm

Currently inorganic materials prevail as the nonlinear active medium for light modulation in electro-optical (EO) device technology. A recent promising trend is to consider organic nonlinear optical materials for application in EO modulators due to their multiple advantages including low costs and high EO coefficients. In this paper, we proposed a new type of polymer EO modulator whose fabrication is compatible with the currently used silicon on insulator technology. Our numerical optimization of the proposed structure demonstrates that it is theoretically possible to achieve a half-wave voltage as low as 1.56 V for a 1 cm long modulator structure operating at 780 nm. Based on the results of the numerical calculations, we also outline the advantages and drawbacks of the design.

Repetitive sub-gigawatt rf source based on gyromagnetic nonlinear transmission line

We demonstrate a high power repetitive rf source using gyromagnetic nonlinear transmission line to produce rf oscillations. Saturated NiZn ferrites act as active nonlinear medium first sharpening the pumping high voltage nanosecond pulse and then radiating at central frequency of about 1 GHz: shock rise time excites gyromagnetic precession in ferrites forming damping rf oscillations. The optimal length of nonlinear transmission line was found to be of about 1 m. SINUS-200 high voltage driver with Tesla transformer incorporated into pulse forming line has been designed and fabricated to produce bursts of 1000 pulses with 200 Hz repetition rate. A band-pass filter and mode-converter have been designed to extract rf pulse from low-frequency component and to form TE(11) mode of circular waveguide with linear polarization. A wide-band horn antenna has been fabricated to form Gaussian distribution of radiation pattern. The peak value of electric field strength of a radiated pulse at the distance of 3.5 m away from antenna is measured to be 160 kV/m. The corresponding rf peak power of 260 MW was achieved.

Second- and third-harmonic generation in metal-based structures

We present a new theoretical approach to the study of second and third harmonic generation from metallic nanostructures and nanocavities filled with a nonlinear material, in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons, and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and to harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple re-examination of the basic equations reveals additional exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.

On the spectrum of spatial Lyapunov exponents for a nonlinear active medium described by a complex Ginzburg-Landau equation

A new method is proposed for calculating the spectrum of Lyapunov exponents for spatially distributed systems. The proposed method is applied to a distributed nonlinear active medium described by a complex Ginzburg-Landau equation with periodic boundary conditions.

Extremely short dissipative solitons in an active nonlinear medium with quantum dots

A medium consisting of quartz with embedded active (amplifying) or passive (absorbing) impurities, i.e., quantum dots, is proposed for producing extremely short dissipative solitons on the basis of the effect of enhanced self-induced transparency. The calculations show that, in such a medium, the initial standard femtosecond pulses can be transformed into extremely short dissipative solitons with a peak intensity of ∼1011 W/sm2, with a duration corresponding to the inverse frequency of transitions in impurities, and with the coherent spectral supercontinuum covering almost the entire transmission region of quartz.

Spatiotemporal order out of noise

Natural systems are undeniably subject to random fluctuations, arising from either environmental variability or thermal effects. The consideration of those fluctuations supposes to deal with noisy quantities whose variance might at times be a sizable fraction of their mean levels. It is known that, under these conditions, noisy fluctuations can interact with the system's nonlinearities to render counterintuitive behavior, in which an increase in the noise level produces a more regular behavior. In systems with spatial degrees of freedom, this regularity takes the form of spatiotemporal order. An overview is presented of the mechanisms through which noise induces, enhances, and sustains ordered behavior in passive and active nonlinear media, and different spatiotemporal phenomena are described resulting from these effects. The general theoretical framework used in the analysis of these effects is reviewed, encompassing the theory of stochastic partial differential equations and coupled sets of ordinary stochastic differential equations. Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

A glassy model for random lasers

We report on a recent model introduced to describe the behaviour of light in a nonlinear active random medium, i.e. a random laser. The emitted radiation is described by a disordered mean-field Hamiltonian for the phases of the complex amplitudes of the electromagnetic field modes. Using the replica trick the thermodynamics can be exactly solved. A replica-symmetry breaking phase transition is predicted, corresponding to mode-locking processes in random lasers. The expected random laser phase diagram varying the pumping rate is reported, together with some perspectives opened by the present study.

Reaction-Diffusion Navigation Robot Control: From Chemical to VLSI Analogic Processors

We introduce a new methodology and experimental implementations for real-time wave-based robot navigation in a complex, dynamically changing environment. The main idea behind the approach is to consider the robot arena as an excitable medium, in which moving objects-obstacles and the target-are represented by sites of autowave generation: the target generates attractive waves, while the obstacles repulsive ones. The moving robot detects traveling and colliding wave fronts and uses the information about dynamics of the autowaves to adapt its direction of collision-free motion toward the target. This approach allows us to achieve a highly adaptive robot behavior and thus an optimal path along which the robot reaches the target while avoiding obstacles. At the computational and experimental levels, we adopt principles of computation in reaction-diffusion (RD) nonlinear active media. Nonlinear media where autowaves are used for information processing purposes can therefore be considered as RD computing devices. In this paper, we design and experiment with three types of RD processors: experimental and computational Belousov-Zhabotinsky chemical processor, computational CNN processor, and experimental RD-CNN very large-scale integration chip-the complex analog and logic computing engine (CACE1k). We demonstrate how to experimentally implement robot navigation using space-time snapshots of active chemical medium and how to overcome low-speed limitation of this wetware implementation in CNN-based silicon processors.

Nonreciprocity of losses and shift of the zero point in a laser gyroscope

Results of calculations of intensities, losses, and frequencies of counterpropagating waves in a ring resonator containing a weakly nonlinear active medium and an aperture are given. It is shown that inequalities of frequencies and intensities of generation of counterpropagating waves occur in such a resonator. The behavior of these inequalities is determined by the nonreciprocity of frequency-dependent losses of the counterpropagating waves.

Intracavity sequential quasi-synchronous interactions in an active nonlinear medium with a regular domain structure

A theory is developed to describe sequential quasi-synchronous wave interactions in an active non-linear medium with a regular domain structure inside a cavity. In particular, sequential processes of quasi-synchronous third-harmonic generation and quasi-synchronous parametric amplification that occur in a Nd:Mg:LiNbO3 crystal with a regular domain structure under low-frequency pumping are analyzed. The efficiency of these nonlinear optical processes is studied as a function of both the reflection coefficient of the exit mirror and the linear loss in the medium.

Splitting of oscillation frequencies of a ring gas laser caused by the diffraction lens effect: II. Nonlinear theory

An analysis is made of the problem of generating the fundamental mode in a laser cavity containing a weakly nonlinear active medium and an aperture. Frequency-dependent nonlinear loss of counterpropagating waves is calculated. The loss was found to have a jumpwise decrease at the boundary of the lasing region. An explanation is given regarding the mechanism responsible for the asymmetry of loss about the central frequency of the transition. It is shown that counterpropagating waves differ in loss, as well as in the phase velocity, which is one of the reasons of that the counterpropagating waves of a ring laser, without special nonreciprocal devices, have different frequencies and intensities.

A Three-Dimensional Autowave Turbulence

Autowave vortices are topological defects in autowave fields in nonlinear active media of various natures and serve as centers of self-organization in the medium. In three-dimensional media, the topological defects are lines, called vortex filaments. Evolution of three-dimensional vortices, in certain conditions, can be described in terms of evolution of their filaments, analogously to that of hydrodynamical vortices in LIA approximation. In the motion equation for the filament, a coefficient called filament tension, plays a principal role, and determines qualitative long-time behavior. While vortices with positive tension tend to shrink and so either collapse or stabilize to a straight shape, depending on boundary conditions, vortices with negative tension show internal instability of shape. This is an essentially three-dimensional effect, as two-dimensional media with the same parameters do not possess any peculiar properties. In large volumes, the instability of filaments can lead to propagating, nondecremental activity composed of curved vortex filaments that multiply and annihilate in an apparently chaotic manner. This may be related to a mechanism of cardiac fibrillation.