Beams In Nonlocal Nonlinear Media Research Articles

Adiabatic propagation of beams in nonlocal nonlinear media with gradual linear loss/gain

The linear loss is a crucial factor in optical communications, which is unavoidable in actual physical system. To overcome the effect of the linear losses, the linear amplification of the optical fields is often conducted. However, the optical beam will shed partial energy, then cannot restore to its original state after one period of propagation. We investigate the evolution of optical beam in the nonlocal nonlinear media with linear loss and gain using the variational approach and the numerical simulation. When the linear loss gradually changes to the linear gain, the optical beams can restore to their initial states, the phenomenon we called the “adiabatic propagation”. We have demonstrated that, as long as the changing rate of the linear loss and gain is small enough, the linear gain can exactly compensate the linear loss and the adiabatic propagation can occur for any beams with any profiles. The numerical simulations agree well with the variational results. In experiment, this kind of linear gain can be realized by distributed Raman amplification.

The dynamics, stability and modulation instability of Gaussian beams in nonlocal nonlinear media

The dynamics, stability and modulation instability of Gaussian beams in nonlocal nonlinear media

Propagation dynamics of modulated vortex beams in nonlocal nonlinear media

The propagation of modulated vortex beams in nonlocal media is numerically investigated. The beam presents the splitting property in free space, and multiple beam spots are observed. As modulated vortex beams propagate in nonlocal media, multiple solitons are generated, and the behavior of solitons depends on the nonlocality and initial amplitude. Different from beams with unmodulated vortex, the number of solitons can be controlled with the azimuthal vortex modulation. By adjusting the nonlocality and vortex modulation parameters, the linear relation between the number of solitons and modulation phase folds is analyzed. This kind of vortex beam can find potential applications in optical controlling.

Transmission dynamics of circular–linear edge dislocation solitons in nonlocal nonlinear media

In this paper, the nonlinear propagation dynamics of circular–linear edge dislocation beams (CLED beams) in nonlocal media are studied theoretically. The transport formulae of CLED beams in nonlocal nonlinear media is derived. The evolution of the beam width, curvature, and intensity distribution are discussed in detail. Two different incident cases of CLED beams, namely beam waist and non-beam waist incidences, are discussed and compared. It is found that the off-axial distance can effectively adjust the position of linear edge dislocation and play a key role on beam propagation. The initial beam power and non-beam waist distance also play a key role in propagation. In particular, when specific parameters are selected, the CLED beam can form a transmission state with beam width and transverse pattern both invariant, i.e., CLED soliton forms. For general parameters, the transverse multi-peak patterns of the CLED beam evolutes periodically, i.e., a generalized higher-order soliton or breather forms.

Background-enhanced collapse instability of optical speckle beams in nonlocal nonlinear media

We study the focusing dynamics of incoherent wave-packets (speckle beams) in the presence of a nonlocal nonlinear response in the framework of the nonlocal nonlinear Schrödinger (NLS) equation. In the highly nonlocal regime, we show that the speckle beam develops a collective incoherent collapse instability — at variance with a conventional collapse that is inherently a coherent object, here it is the incoherent beam as a whole that develops a collapse. More specifically, we study the impact of a homogeneous incoherent background on the development of the incoherent collapse instability. Despite the fact that the homogeneous background is modulationally stable, we show that it significantly strengthens the formation of the incoherent collapse instability. Our theoretical analysis is based on a wave turbulence formulation of the Vlasov equation, which allows us to introduce an effective hydrodynamic model that is subsequently solved by the method of characteristics. A quantitative agreement is obtained between the simulations of the NLS equation, the Vlasov equation and the hydrodynamic model, without using adjustable parameters. The interaction between the background and the collapsing structure is described by means of a coupled system for the singular and smooth components of the solution of the Vlasov equation. The theory reveals that the mechanism underlying the background-induced collapse enhancement is due to a transfer of momentum from the background to the collapsing structure, while there is no ‘mass’ exchange among them. Furthermore, we show that a strong background level significantly boosts the collapse dynamics. Our work should stimulate the development of nonlinear experiments aimed at observing the incoherent collapse phenomenon in nonlinear thermal media. From a broader perspective, these investigations pave the way for the study of novel forms of global incoherent collective behaviors in wave turbulence, such as the formation of incoherent rogue waves.

Propagation characteristics of elliptic vortex beams in nonlocal nonlinear media

Optical patterns with the orbital angular momentum (OAM) can serve as “optical spanners”, and have attracted much attention for their applications in biophysics, micromechanics or microfluidics. In this work, we theoretically demonstrate the propagation characteristics of elliptic vortex beams carrying the OAM in nonlocal nonlinear media. The elliptic vortex beams cannot evolve as solitons due to their non-circular-symmetry, but can evolve as breathers in the nonlinear media without anisotropy. During breathing evolutions, the rotating phenomenon is observed. The rotations take place in both the vortex cores and the beam envelopes, which exhibit opposite rotating directions. The breathing and rotating evolutions both have close relations with the input power and the beam size. The analytical results are well confirmed by the numerical simulations. The results obtained in the paper might find potential applications in beam shaping, and in optical manipulations of rod-shaped micro-particles.

Quasi-stable fractional vortex solitons in nonlocal nonlinear media

This paper studied the propagations of fractional vortex beams in nonlocal nonlinear media, and found that quasi-stable solitons can form when the nonlocality is strong enough and the initial power is equal to the critical power. The propagation properties, including intensity patterns, phase structures, transverse energy flows, and rotation period, were all investigated. The critical power of solitons with different topological charges is the same, however, the orbital angular momentum (OAM) of that increases with the increase of fractional topological charge. In addition, we revealed that fractional vortex solitons have lateral shifts in the y-direction, and the shift values can be controlled by the fractional topological charge. Obviously, the quasi-stable fractional vortex solitons have important academic value and potential application to optical switches, optical wrenches and optical communications, etc.

Adiabatic evolution of optical beams in nonlocal nonlinear media of gradual nonlocality.

We theoretically investigate the evolution of optical beams in nonlocal nonlinear media of gradual nonlocality, which is governed by the nonlocal nonlinear Schrödinger equation with variable coefficient. With the variational approach, the evolution equation of beam width is derived. When the characteristic length of response function gradually changes with any functional forms, beams can exhibit a kind of adiabatic evolution. The variational results are well confirmed by numerical simulations.

Propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams in nonlocal nonlinear media

In this paper, the propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams (AHSGB) in strongly nonlocal nonlinear media are discussed. The propagation expression of the AHSGB is theoretically derived and the evolution characteristics of the light intensity distribution, the beam width, and the phase curvature are analyzed by using mathematical and numerical methods. We find that the parameters of the hyperbolic sinusoidal function, the initial power and the initial position are important factors that influence the propagation behavior of the beam.

Dynamics engineering of spatial beams in nonlocal nonlinear media

We addressed the mobilities of spatial beams in nonlocal nonlinear media with the aid of the analogy to the particles described by Newtonian mechanics. Various dynamics for spatial beam are predicated by equivalent kinematic laws, including the harmonic vibrations due to the off-centered shifts, the circular and elliptical motions to the combination of off-centered shifts and initial phase chirps, which can be equivalently regarded as the Hooke's force and the transverse velocities in mechanics, respectively. By a purposive engineering of several beams, we can achieve a variety of rotating clusters, such as clusters with opposite rotating directions along different circular orbits and those exhibiting both revolving and spinning rotations simultaneously. The predications about dynamics of spatial beams are confirmed by the numerical simulations.

Power steered modes conversions and rotations in nonlocal nonlinear media

Propagations of optical beams in nonlocal nonlinear media can be described by the nonlocal nonlinear Schrödinger equation (NNLSE). Hermite–Gaussian (HG) modes and Laguerre–Gaussian (LG) modes are two different sets of eigenmodes to the NNLSE. The inter-conversions can be achieved between the HG and the LG modes if they both carry a kind of cross phase. During the modes conversion processes, mode rotations appear. Furthermore, both the inter-conversions and the rotations between the two modes can be controlled exactly by the input optical power. These power induced mode conversions and rotations are discussed in the nematic liquid crystal as an exemplary nonlocal nonlinear media. The theoretical results provide potential applications in the beam shaping in optics.

Trajectories and rotations controlled off-axis winding beams in nonlocal nonlinear media.

Off-axis winding beams are discussed in nonlocal nonlinear media, whose trajectories and rotations can be controlled by the optical power and the orbital angular momentum (OAM). By changing optical power or the OAM, optical beams can propagate along different trajectories including ellipses, circles, rectangles, rhombus and so on. Due to the OAM stemming from a combination of the cross phase and the vortex phase, different parts of the optical beam exhibit distinct rotating characteristics. The elliptic envelope revolves around the beam center resulting from the cross phase, while optical peaks spin about their own axes because of the vortex phase. The two rotating velocities can be adjusted separately by the optical power and the OAM, respectively. Optical power plays a global role on the revolving velocity and the spinning velocity and can enhance the two rotations synchronously. In contrast, the OAM has a local effect and can change the relative magnitudes of these two velocities. Our results may provide a tailoring tool of evolution properties for optical beams. The property of controllable trajectories may find applications in all-optical controlling. While, the controllable rotating property can be used as in optical spanners to operate micro- or nanoparticles.

Soliton guidance and nonlinear coupling for polarized vector spiraling elliptic Hermite–Gaussian beams in nonlocal nonlinear media**Project supported by the National Natural Science Foundation of China (Grant No. 11604199) and the China Scholarship Council (Grant No. 201708410236).

We investigate the incoherent beams with two orthogonal polarizations in nonlocal nonlinear media, one of which is a fundamental Gaussian beam and the other is spiraling elliptic Hermite–Gaussian beam carrying the orbital angular momentum (OAM). Using the variational approach, we obtain the critical power and the critical OAM required for the vector spiraling elliptic Hermite–Gaussian solitons. In the strong nonlocality region, two components of the vector beam contribute to the nonlinear refractive index in a linear manner by the sum of their respective power. The nonlinear refractive index exhibits a circularly symmetrical profile in despite of the elliptic shapes for spiraling Hermite–Gaussian beams. We find that in the strong nonlocality region, the critical power and the rotational velocity are the same regardless of the relative ratio of the constituent powers. The nonlinear refractive index loses its circular symmetry in weak nonlocality region, and the nonlinear coupling effect is observed. Due to the radiation of the OAM, the damping of the rotation is predicted, and can be suppressed by decreasing the proportion of the spiraling elliptic component of the vector beam.

Revolving and spinning of optical patterns by two coaxial spiraling elliptic beams in nonlocal nonlinear media.

Rotating patterns can be produced by two coaxial spiraling elliptic beams in nonlocal nonlinear media. The two constituent beams carry the orbital angular momentum (OAM), which has the same or opposite signs. The resultant patterns exhibit revolving and spinning rotations similar to the Sun-Earth system. The revolving-typed rotation comes of the overall OAM, while the spinning-typed rotation results from the respective OAM of the constituent beam. A kind of soliton patterns can stably exist, for which a vortex is nested centrally in the rotating square-shaped optical envelope and four peaks appear at four corners. The centrally nested vortex splits into two single vortex for r≠1, with r being the power ratio between the two constituent beams. The two single vortexes align vertically for r<1 and horizontally for r>1, and their spacing increases with |r-1|. The theoretical results give a possibility of the transforming from cross-phase-typed OAM into the helical-phase-typed OAM, which may find potential applications in beam shaping and controlling. In addition, the square optical envelope may exhibit advantages in the integration of optical components.

Vortex nucleation in nonlocal nonlinear media

Spontaneous vortex nucleation is a universal feature of open and nonlinear physical systems. We investigate theoretically vortex rings and vortex lines emerging during propagation of self-trapped wave beams in nonlocal nonlinear media. We demonstrate how radially perturbed fundamental solitons exhibit extremely robust and long-lived oscillations with the spontaneous generation of a regular set of vortex rings at the wave beam periphery. We find numerically a class of cylindrically symmetric higher-order spatial solitons and investigate their stability and nonlinear dynamics. The formation of external vortex rings, similar to fundamental soliton, is accompanied by emergence of additional internal vortex-antivortex pairs nucleating from the edge-ring phase dislocation of perturbed higher-order soliton.

Incoherent interactions of Airy beams in nonlocal nonlinear media

We investigate, for the first time to our best knowledge, the incoherent interactions of incoherently coupled vector Airy beams in both local and nonlocal nonlinear media. In local media, an anomalous phenomena happens with repulsion appears in the incoherent interactions of Airy beams for some beam intervals. Otherwise, bound states of soliton pairs can form. In the regime of strong light (large amplitude or power), repulsion appears for all the beam intervals. In particular, repulsion and attraction of breathing solitons can coexist. Nonlocality provides a long range attractive force between Airy beams, leading to the formation of bound states of breathing Airy solitons. We also demonstrate the incoherent interactions of Airy beams with different amplitudes in detail.

Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation

Based on the nonlocal nonlinear Schrödinger equation that governs phenomenologically the propagation of laser beams in nonlocal nonlinear media, we theoretically investigate the propagation of sinh-Gaussian beams (ShGBs). Mathematical expressions are derived to describe the beam propagation, the intensity distribution, the beam width, and the beam curvature radius of ShGBs. It is found that the propagation behavior of ShGBs is variable and closely related to the parameter of sinh function (PShF). If the PShF is small, the transverse pattern of ShGBs keeps invariant during propagation for a proper input power, which can be regarded as solitons. If the PShF is large, it varies periodically, which is similar to the evolution of temporal higher-order solitons in nonlinear optical fiber. Numerical simulations are carried out to illustrate the typical propagation characteristics.

Anomalous interactions of nonparaxial accelerating beams in nonlocal nonlinear media

We numerically investigate the anomalous interaction dynamics of nonparaxial accelerating beams in nonlocal nonlinear media. We find that stationary breathing bound states of spatial solitons can be formed with the help of nonlocality in the in-phase case. But it would be difficult to generate the bound states when the input amplitudes between the separated beams are different. Interestingly, the spatial solitons formed in the interactions with different amplitudes can propagate along the sinusoidal path, and the path can be modulated flexibly by altering the degree of nonlocality. Furthermore, it is found that the nonoverlapping bound states can be generated from anomalous interactions in the out-of-phase case. In addition, the parameter of longitudinal vortex of order can have different impacts on the interaction dynamics of the in-phase case and out-of-phase case, respectively. Especially, it is noted that the paraxial limit is taken on all the simulation results for simplicity.

Spiraling elliptic solitons in lossy nonlocal nonlinear media

We address the propagation dynamics of the spiraling elliptic beams in nonlocal nonlinear media with losses based on the variational approach. It is found that the spiraling elliptic beams exhibit complicated behaviors, which result from the combined effects of the losses and orbital angular momentum (OAM). The OAM brings in an effective anisotropic diffraction and rotation for the spiraling elliptic beams. However, due to the losses, the rotation of the spiraling beams slows down. Besides, the ellipticity of the spiraling elliptic beams is greatly affected by the lossesand the OAM. When the OAM is not equal to its critical value, a periodic oscillation of the ellipticity is found in the presence of losses. However, when the OAM is equal to the critical one, the ellipticity of the spiraling elliptic beam remains unchanged during propagation regardless of the loss factor. The comparisons between our approximate analytic solutions and numerical simulations confirm our results.

Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media

We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.