Strongly Nonlocal Nonlinear Media Research Articles

Propagation dynamics of multi-Gaussian Schell model beams in strongly nonlocal nonlinear media

The analytical propagation formulae of a single multi-Gaussian Schell model (MGSM) beam and two MGSM beams in strongly nonlocal nonlinear media (SNNM) are derived, and the optical breather characteristics of a single MGSM beam and two MGSM beams in SNNM are studied, respectively. It is found that a MGSM soliton is never formed because of the self-shaping feature of MGSM beams, but a MGSM breather can be formed. Furthermore, for a MGSM breather, the Gaussian-like profile and the flat-top profile alternate periodically during propagation. On the other hand, even if the separation distance is large enough, two MGSM breathers can be combined into a single breather due to nonlinearity when the threshold critical power arrives. Furthermore, the relationship between the threshold critical power and the MGSM beam parameters is also investigated.

Vectorial manipulation of twisted vector vortex optical fields in strongly nonlocal nonlinear media

Abstract We theoretically investigate the propagation properties and vectorial manipulation of twisted vector vortex beams (TVVB) with a cross-phase in a strongly nonlocal nonlinear medium (SNNM). The root mean square beam-width (RMS-BW) and the critical power required to retain the invariant RMS-BM of the TVVB in an SNNM are derived using the coupled nonlocal nonlinear Schrödinger equation. Numerical calculations reveal novel characteristics of the evolution of the state of polarization (SoP) and the optical intensity distributions during the TVVB propagating in an SNNM. It is found that mode conversions between a Laguerre Gaussian and a Hermite Gaussian mode take place during propagation in an SNNM, and the topological charge of the TVVB can be accurately measured by observing the interference intensity structure in the cross-section. Manipulation of the beam shape, SoP, and rotation of the TVVB is achieved by controlling factors such as the initial power, twisting coefficient, initial beam-width, and topological charge. These findings hold promise for applications in optical micro-manipulation, optical communication, and material processing.

Twisted partially coherent solitons in strongly nonlocal nonlinear media

The analytical propagation formulae of twisted partially coherent beams in strongly nonlocal nonlinear media (SNNM) are derived. It is shown that a twisted partially coherent soliton (TPCS) can be formed in SNNM when the critical power arrives. The analytical expressions of the characteristic parameters of TPCSs are also derived, e.g., the critical power, soliton width, soliton coherence width, and soliton twist parameter. It is found that the characteristics of TPCSs can be manipulated by the twist parameter. In particular, a TPCS may convert to a soliton without twist when the critical coherence width arrives.

Polarization state evolution of a twisted vector optical field in a strongly nonlocal nonlinear medium.

The evolution of the state of polarization (SoP) in a twisted vector optical field (TVOF) with an astigmatic phase in a strongly nonlocal nonlinear medium (SNNM) is investigated. The effect of an astigmatic phase on the propagation dynamics of the twisted scalar optical field (TSOF) and TVOF during propagation in the SNNM leads to reciprocally periodical evolutions of stretch and shrink, accompanied by the reciprocal transformation of the beam shape between an initial circle shape and threadiness distribution. The TSOF and TVOF rotate along the propagation axis if the beams are anisotropic. In particular, the reciprocal conversions between the linear and circular polarizations occur in the TVOF during propagation, which are strongly related to the initial powers, twisting strength coefficients, and initial beam reshapes. The numerical results confirm the analytical predictions by the moment method for the dynamics of the TSOF and TVOF during propagation in a SNNM. The underlying physics for the polarization evolution of a TVOF in a SNNM are discussed in detail.

Propagation characteristics of cosine-Gaussian cross-phase beams in strongly nonlocal nonlinear media

In this paper, the propagation expression of cosine-Gaussian cross-phase beams (CGCPBs) is derived based on the nonlocal nonlinear Schrödinger equation and the propagation characteristics of CGCPBs in strongly nonlocal nonlinear media (SNNM) are researched. It is worth noting that the mode of CGCPBs can be controlled by modifying the parameters of cosine term and cross phase term. CGCPBs can form generalized high-order breathers, which signifies that the multi-peak light intensity pattern and the beam width evolve periodically during the transmission process. Apart from that, the impact of the parameters on the light intensity mode, the phase and the beam width is discussed by changing the parameters in the initial incident transmission expression. The research content of this paper provides reference value for controlling beams.

Propagation properties of chirped cosh-Gaussian beams in strongly nonlocal nonlinear media

In this paper, we analytically investigated the evolution properties of chirped cosh-Gaussian beams in strongly nonlocal nonlinear media (SNNM). The expressions describing beam propagation, intensity distribution, and beam width are derived. The results show that in the absence of chirp, the evolution behavior of beam is similar to the solitons and breathers, which closely depends on the input power and initial parameter. In the presence of linear chirp, the optical beam periodically oscillates along a certain direction and exhibits the same structure as the unchirped beam. In the presence of quadratic chirp, the center symmetry of beam evolution is broken. Furthermore, we find that the evolution of beam width always changes periodically whatever the beam power is.

Twisted Gaussian Schell-model breathers and solitons in strongly nonlocal nonlinear media.

Based on the Snyder-Mitchell linear model and the cross-spectral density (CSD) function, the analytical propagation formula of twisted Gaussian Schell-model (TGSM) beams in strongly nonlocal nonlinear medium (SNNM) is derived. Then the propagation characteristics of TGSM beam are studied. It is found that the soliton radius is jointly determined by the initial power, coherence length, and twist factor; the degree of spatial coherence is adjusted by changing the twist factor without affecting the soliton intensity. In the case of non-soliton properties, there is a threshold of coherence length which makes partially coherent beams have the same evolution law as completely coherent beams. Furthermore, increasing the twist factor, decreasing the coherence length and initial power can improve the beam quality of the beam propagating in SNNM.

Propagation properties of the superimposed chirped Bessel–Gaussian vortex beams in strongly nonlocal nonlinear medium

In this paper, by applying the Collins integral formula, we obtain the analytical solution of the superimposed chirped Bessel–Gaussian vortex beam (SCBGVB) in strongly nonlocal nonlinear medium (SNNM). We investigate the SCBGVB’s propagation behaviors as well as the distribution of the intensity and the phase of the periodic self-focusing light field generated by the SNNM. And we can modulate its focusing times and the depth of the focus by choosing the appropriate factors. In this way, we can achieve a one-dimensional flat-topped light field with controllable length. In addition, we can manipulate the pattern of beam transmission, change its centroid position and regulate its focal intensity by choosing different components of SCBGVB’s vortex structure. What important is, we can also adjust its autofocusing position and control the ratio of two focal light intensity to form a series of high and low fluctuations without changing input power.

Propagation dynamics of vector vortex beams in a strongly nonlocal nonlinear medium with parity-time-symmetric potentials

We demonstrate the dynamical properties of a vector vortex optical field (VVOF) in a strongly nonlocal nonlinear medium (SNNM) with sine and cosine parity-time-symmetric potentials (SCPT) by using the coupled vector Snyder-Mitchell model. Our study shows that the shape of the optical field is chaotically distorted in different propagation distances due to the modulation of complex refractive index. Despite the distorted optical field, the VVOF reciprocally evolves in a periodic stretch and shrink behavior during propagation in the SNNM-SCPT. The reciprocal conversions between the linear and circular polarizations periodically occur during propagation. The evolution of VVOF and the linear and circular polarization conversions are strongly dependent on the modulation of the complex refractive index, the initial powers and the vortex topological charge numbers. These results can provide a new way to complexly manipulate the VVOF in a SNNM-SCPT.

Evolution properties of vortex beams through strongly nonlocal nonlinear media

The evolution properties of a vortex Hermite cosine-hyperbolic-Gaussian beam (vHChGB) propagating in a strongly nonlocal nonlinear media (SNNM) are examined theoretically based on the Snyder-Mitchell model. Mathematical and numerical calculations are performed to illustrate the propagation formula, the second-order intensity moment beam width and the curvature radius of an on-waist incident vHChGB in SNNM. The results reveal that under general conditions, the vHChGB evolves periodically upon propagation in SNNM, and the beam shape is strongly dependent on the power and the parameters of the incident beam. The beam evolution during propagation is generally breather-like, and when the incident beam power equals to the critical power value, the beam behaves like a soliton. The evolution behaviors of vHChGB in SNNM are well demonstrated, which could have promising applications in optical switch and micro-manipulations.

Propagation of Pearcey Gaussian beams in a strongly nonlocal nonlinear medium.

We introduce the propagation of Pearcey Gaussian (PG) beams in a strongly nonlocal nonlinear medium (SNNM) analytically. Our results show that PG beams propagating in the SNNM have two different focusing positions. The intensity peak appears at different focusing positions depending on the selection of the nonlinear parameters. In addition, the effects of the nonlinear parameters and the scaling factor on the trajectory, the position of the intensity focusing, the intensity evolution between focus locations, and the radiation force are studied.

Periodic propagation of complex-valued hyperbolic-cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media

In this study, the propagation characteristics of complex-valued hyperbolic-cosine-Gaussian (CVHCG) beams were studied based on the nonlocal nonlinear Schrödinger equation in strongly nonlocal nonlinear media (SNNM). The CVHCG beams exhibited some unique propagation characteristics. By adjusting the complex-valued parameters, CVHCG beams can propagate with different forms in SNNM, including Gaussian-like, nearly flat-topped, multi-peak, and four-peak forms. CVHCG beams can form shape-invariant solitons and breathers under certain incident parameters. In addition, CVHCG beams can also form generalized shape-variant high-order spatial solitons and breathers. In general, the beam width and light intensity pattern of the CVHCG beams always change periodically. A complete theoretical model was constructed, and the expressions for the propagation, light intensity, and second-order moment beam width were obtained analytically. Some typical propagation characteristics were demonstrated via numerical simulations. The results of this study can be extended to investigate other complex-valued beams.

Research on Statistical Properties and Application of Off‐Axis Gaussian Schell‐Model Beams

AbstractThe analytical expression of the average intensity of an off‐axis Gaussian Schell‐model beam during propagation is derived and such focused beam's ability to capture particles is analyzed. It is found that the spectral density along propagation direction in strongly nonlocal nonlinear media (SNNM), and in SNNM under off‐waist incident condition, both presents a periodical distribution. Further, the propagation trajectory of the beam center is quantitatively analyzed. Results show that the trajectory of the beam center upon propagation is a sinusoidal curve. This focused beam is helpful to capture high‐index particles. In addition, the linear factor and coherent length also have an effect on the distribution of radiation force.

Propagation of hollow sinh-Gaussian beams in strongly nonlocal nonlinear media

Based on the Snyder-Michell model and using the ABCD matrix description of a strongly nonlocal nonlinear media (SNNM), the propagation properties of hollow sinh-Gaussian beams (HsGBs) through SNNM are investigated. The propagation formula, the second-order intensity moment beam width and the critical power for an on-waist incident HsG beam in SNNM are derived. The evolution of the intensity distribution pattern and the beam width of the HsGB are illustrated, graphically and analyzed with numerical examples. It is found that the HsGB pattern evolves periodically during propagation in SNNM, and its evolution behavior is strongly affected by the initial beam power and beam parameters. For a critical input power, the beam width keeps invariant during propagation, which can be regarded as a HsGB-soliton.

Vectorial effect on the evolution of fractional-order vector vortex beams in a strongly nonlocal nonlinear medium.

Propagation of a vector vortex optical field (VVOF) with both fractional order of polarization topological charge $m$m and fractional order of vortex topological charge $n$n with spatially variant states of polarization (SoP) in a strongly nonlocal nonlinear medium (SNNM) is studied. The optical field always evolves reciprocally with a cycle of stretch and shrink in a SNNM with dark stripes forming at $z=t\pi {z_p}$z=tπzp ($t$t denotes an integer number, and ${{z}_p}$zp is a parameter that depends on the initial power of the VVOF and the material constant associated with the response function), as a result from the coherent superposition of the vortices with different order of topological charges and weighting coefficients. In particular, the conversions between linear and circular polarization components occur during propagation, and the converted SoP distributions in different propagation distances depend closely on the topological charges and the initial powers. The evolutions of the Stokes parameters of the fractional-order VVOF (FO-VVOF) during propagation in a SNNM show that the spatial distributions of different polarization components are closely related to the topological charges, the initial powers and the propagation distances, implying that the FO-VVOF can be regarded as a superposition of two different fractional-order vortices with orthogonal circular polarization components. These results provide new strategies on tailoring polarization states in a structured optical field with fractional topological charges.

Three-dimensional chirped Airy Complex-variable-function Gaussian vortex wave packets in a strongly nonlocal nonlinear medium.

Three-dimensional chirped Airy Complex-variable-function Gaussian vortex (CACGV) wave packets in a strongly nonlocal nonlinear medium (SNNM) are studied. By varying the distribution parameter, CACGV wave packets can rotate stably in a SNNM in different forms, including dipoles, elliptic vortices, and doughnuts. Numerical simulation results for the CACGV wave packets agree well with theoretical analysis results under zero perturbation. The Poynting vector related to the physics of the rotation phenomenon and the angular momentum as a torque corresponding to the force are also presented. Finally, the radiation forces of CACGV wave packets acting on a nanoparticle in a SNNM are discussed.

Hollow sine breathers induced by initial wavefront curvature in nonlinear Schrödinger equation

Based on the nonlinear Schrödinger equation, we analytically investigate a hollow sine beam (HSB) with an initial wavefront curvature propagating in strongly nonlocal nonlinear media (SNNM). Analytical evolution expressions of the beam propagation, the size of beam spot and the wavefront curvature of HSBs are derived. It is found that an HSB with an initial wavefront curvature is always presented as a breather on propagation in SNNM. The breathing behavior is discussed in detail. Numerical simulations are also performed to illustrate the typical behaviors.

Propagation properties of Airy hollow Gaussian vortex beams through the strongly nonlocal nonlinear media

We introduce a class of Airy hollow Gaussian vortex (AiHGV) beams and derive the analytical propagating expression of the AiHGV beams in strongly nonlocal nonlinear media (SNNM) using the transfer matrix method for the first time. The nonlinear factor $$\varOmega$$ can significantly increase the intensity of the side lobe and the hollow range becomes obvious, which causes the propagation pattern to dramatically change. Moreover, the distribution factor $$\alpha$$ can prominently affect the focusing range and the decay factor a can also flexibly change the focusing position. In addition, 3D propagation and the center of mass are fully described to enrich the propagation properties of the AiHGV beams. Interestingly, the variations of the nonlinear factor $$\varOmega$$ and the decay factor a are proportional to the Poynting vector, the angular momentum and the gradient force at the focusing position, in which the effect of the distribution factor $$\alpha$$ is totally different.

Controllable linear-circular polarization conversion of radial variant vector beams in a strongly nonlocal nonlinear medium

The dynamical properties of radial-variant vector beams in strongly nonlocal nonlinear (SNN) media are theoretically demonstrated. The analytical expressions for the variation of root-mean-square (RMS) beam width and the critical powers Pcr that keep the RMS beam widths invariant during propagation are derived using the moments method. When the initial power Pin does not equal the critical power Pcr, the RMS beam widths evolve periodically. The coherent superposition of different polarization components with different evolution trajectories during propagation in an SNN medium leads to the linear-circular polarization conversion. The linear-circular polarization conversion occurs, especially in the beam center, and the propagation distances between the peak intensities of the converted polarizations can be manipulated by the initial distribution of polarization states and the initial powers. The conversion efficiency and the converted polarization purity during propagation are also analyzed.

Polarization Evolution of a Vector Vortex Optical Field in a Strongly Nonlocal Nonlinear Medium

The evolution of a vector vortex optical field (VVOF) with a spiral phase and azimuthally-variant polarization distributions in the field cross-section in a strongly nonlocal nonlinear (SNN) medium is demonstrated. The dynamics of interplay between the singular points of polarization and vortex during propagation in the SNN medium leads to novel phenomena. When the topological charge number of the polarization is equal to that of the vortex, the singular point in the beam center is annihilated and the energy can accumulate in the beam center due to the self-focus effect. Furthermore, the linear-circular polarization conversion occurs and can be controllable in the beam center or the periphery of VVOF depending on the different topological charge numbers of the vortex and polarization, due to the coherent superposition of the different polarization components during propagation in an SNN medium. The VVOF rotates along the propagation axis in an SNN medium because of the existence of the vortex, and the optical field as well as the distribution of polarization in the field cross-section always evolves reciprocally with cycles of stretch and shrink in an SNN medium. The numerical results confirm the analytical predictions by the moment method for the vector dynamics of the VVOF during propagation in an SNN medium. The underlying physics for the linear-circular polarization conversion in a VVOF during propagation in an SNN medium are discussed in detail.