Isotropic Nonlinear Medium Research Articles

Spatial self-phase modulation excited by fractional-order linearly polarized vector fields.

Compared to the integer-order vector field, the fractional-order vector field has an additional degree of control freedom, which will bring rich photophysical properties and what we believe to be novel nonlinear optical phenomena. In this work, we theoretically and experimentally investigate the focusing, propagation, and spatial self-phase modulation (SSPM) of fractional-order linearly polarized vector fields (FLPVFs). It is shown that the weak focusing field of FLPVF exhibits an asymmetric intensity distribution. Intriguingly, its state of polarization (SoP) has a hybrid polarization distribution. When this focused FLPVF propagates to the far field in free space, its SoP degenerates into a localized linearly polarization distribution. However, after the focused FLPVF passes through an isotropic nonlinear Kerr medium, its SoP exhibits a hybrid polarization distribution. Additionally, unlike the self-diffraction intensity pattern of integer-order linearly polarized vector field (ILPVF) with a concentric multi-ring structure, the SSPM pattern of FLPVF is a symmetry broken self-diffraction intensity pattern. The presented work provides a nonlinear optics approach for manipulating both the SoP and intensity distributions of the light field.

Propagation characteristics of astigmatic elliptic vortex beams in nonlocal media with anisotropic nonlinearity

The propagation characteristics of the astigmatic elliptic vortex beam (AEVB) in nonlocal media with isotropic and anisotropic nonlinearities are analytically and numerically investigated. Three different kinds of dynamics are discussed: AEVB in nonlinear isotropic media, elliptic vortex beam in nonlinear anisotropic media, and astigmatic circular vortex beam (ACVB) in nonlinear anisotropic media. The isotropic nonlinearity cannot support the formation of elliptic vortex solitons for any input power, and the initial phase-front curvature (IPC) will induce the pulsating behavior of the AEVB. For anisotropic nonlinearity, when the nonlinear anisotropic parameter (NAP) of the medium and the initial ratio of the beam width satisfy γx/γy = (w0y/w0x)2, a quasi-stable elliptic vortex soliton can be obtained, in which the vortex angular velocity and vortex rotation angle evolve periodically. Circular vortex soliton cannot exist in nonlinear anisotropic media, and the rotation of the ACVB can be controlled by adjusting the NAP and the IPC. In both isotropic and anisotropic nonlinear media, the rotation direction of the vortex core is opposite to that of the beam envelope.

Transformation of spin and orbital angular momentum in second-harmonic generation process by the near-surface layer of isotropic nonlinear medium.

We investigate the conversion between orbital and spin components of the angular momentum of light beams in the second-harmonic generation process from the near-surface layer of the nonlinear isotropic medium without spatial dispersion at oblique incidence of the elliptically polarized fundamental beam. The conservation of the projection of both spin and orbital angular momenta onto the normal to the surface of the medium during the transformation of the incident wave into a reflected double frequency wave has been demonstrated.

Asymmetrical, rotational and ultra-high amplitude fundamental polarized optical rogue waves associated with the coherent coupling

The dynamics of the fundamental rogue waves of the coupled nonlinear Schrödinger equations with the coherent coupling effect in the isotropic nonlinear medium is investigated. Firstly, via the Darboux-dressing transformation, we show the asymmetrical fundamental rogue waves and the rotational dynamics of fundamental rogue waves. Secondly, via the SO(2) rotation, we construct the fundamental rogue waves of ultra-high peak amplitude. With such transformation, we study the relation between ultra-high peak-background ratio and energy exchange. The fundamental rogue-wave excitation with ultra-high peak-background ratio in a chaotic background is confirmed via numerical simulations. The results discussed in this paper might contribute to the understanding of fundamental rogue wave phenomena in a variety of complex systems, from nonlinear optics to Bose-Einstein condensates.

A lattice method for seismic wave propagation in nonlinear viscoelastic media

SUMMARYNonlinear wave propagation is an important consideration in several geophysical problems as heterogeneities within the subsurface give rise to nonlinear stress–strain relationships in rocks. To address these problems, where the inclusion of subsurface complexity is accounted for, numerical solutions are required. Here, we outline a discrete particle or lattice numerical method that can simulate dynamic and static deformation in an isotropic viscoelastic nonlinear medium where the nonlinearity includes the fourth-order elastic tensor coefficients. The relationship between the local interaction constants in the lattice method and the macroscopic nonlinear coefficients is derived and the relationships presented. The theoretical dispersion properties of the system is determined from a nonlinear perturbation method and are validated against some numerical results. There is an excellent agreement between the theory and numerical results and the method reproduces the common features of nonlinear wave propagation, for example, harmonics, waveform distortion and spectra shifts. As expected the system is shown to be dependent on the wave amplitudes and an example is presented which shows the complexity that can arise in both dynamic and static deformation in a complex model where nonlinearity is included.

Polarization rotation and singularity evolution of fundamental Poincaré beams through anisotropic Kerr nonlinearities

We report a theoretical investigation on polarization rotation and singularity evolution of focused fundamental Poincaré beams in free-space propagation and through isotropic and anisotropic Kerr nonlinear media. It is found that the optical nonlinearity enhances the polarization rotation of the focused beams during propagation. Furthermore, the anisotropy of optical nonlinearity causes the symmetry breaking of the polarization distribution. Further studies show that the C-point and L-line singularities of the lemon Poincaré beams do not change while propagating in free space or through the isotropic nonlinear Kerr medium. Interestingly, the anisotropic Kerr nonlinearity evokes the C-point singularity splitting, and the distortion and birth of L-line singularities. However, the total singularity index always remains the conservation within the light field, regardless of the optical nonlinearity.

Quasiexact Theory of Three-Dimensional Optical Self-Focusing

We find a quasiexact three-dimensional analytic solution of the nonlinear Schrodinger equation describing the field of a stationary optical beam in an unbounded homogeneous nonlinear isotropic medium supporting a state of linear polarization.

"Terhune-like" transformation of the terahertz polarization ellipse "mutually induced" by three-wave joint propagation in liquid.

In this Letter, we show experimentally for the first time, to the best of our knowledge, the possibility to observe the effect of polarization mutual action of three elliptically polarized waves, with one of them at terahertz frequency, when they propagate in the isotropic nonlinear medium. When three light pulses are propagated at frequencies ω, 2ω, and ωTHz through liquid nitrogen, we observed the rotation of the ellipse main axis and the ellipticity change. We have shown that this effect is very well described theoretically in the framework of a physical approach analogous to the self-rotation of the polarization ellipse first described in 1964 by Maker et al., but expanded for the case of multi-frequency interaction.

Radial-variant nonlinear ellipse rotation.

The nonlinear ellipse rotation usually occurs when an elliptically polarized beam propagates through an isotropic nonlinear medium owing to the existence of χ1221(3). Here we report the radial-variant nonlinear ellipse rotation of a vector beam with structured elliptical polarization through isotropic Kerr nonlinearities. Due to the interaction of elliptically polarized vector beams (EPVBs) with isotropic nonlinear media, the distributions of both the orientation angle and the ellipticity angle of beams at the far-field observational plane exhibit multiple concentric ring structures with the circularly symmetry. Numerical simulations show that the self-diffraction intensity pattern, the distribution of the state of polarization, and the spin angular momentum (SAM) distribution of an EPVB could be manipulated by tuning both the isotropic optical nonlinearity and the chirality parameter of the vector beam, which may find direct applications in polarization-control optical switching, SAM manipulation, and optical polarization encoding or detection.

Transfer efficiency of angular momentum in sum-frequency generation and control of its spin and orbital parts by varying polarization and frequency of fundamental beams

Considering sum-frequency generation in an isotropic chiral nonlinear medium, we analyze the transfer of the spin angular momentum of fundamental elliptically polarized Gaussian light beams to the signal beam, which appears as the superposition of two Laguerre–Gaussian modes with both spin and orbital angular momentum. Only for the circular polarization of the fundamental radiation is its angular momentum fully transferred to the sum-frequency beam; otherwise, part of it can be transferred to the medium. Its value, as well as the ratio of spin and orbital contributions in the signal beam, depends on the fundamental frequency ratio and the polarization of the incident beams. Higher energy conversion efficiency in sum-frequency generation does not always correspond to higher angular momentum conversion efficiency.

The distinctive feature of long time adiabatic modulation in the context of cnoidal wave and Akhmediev breaser interaction

For a nonintegrable system of two coupled nonlinear Schrödinger equations the adiabatic approximation is extended for long time interaction. The method enables analytical description of the modulation of a cnoidal wave by Akhmediev breather in an isotropic nonlinear gyrotropic medium with Kerr nonlinearity and second-order group-velocity dispersion. The conditions which must be fulfilled for stable propagation of the obtained solution with amplitude and frequency modulation are determined.

Elliptically polarized breather in the nonintegrable problem of laser radiation propagation through an isotropic gyrotropic nonlinear medium

A particular analytical solution to the nonintegrable problem of plane electromagnetic wave propagation through an isotropic gyrotropic nonlinear medium is found in the form of elliptically polarized breather. The intensity ratio for the circularly polarized components of this wave, which remains constant during propagation, can be used to determine the ratio of local and nonlocal nonlinear susceptibilities describing the Kerr nonlinearity and its spatial dispersion.

Spectral representation of adiabatic interaction of cnoidal waves in an isotropic gyrotropic nonlinear medium

We analyse the evolution of the spectra of an approximate solution of the adiabatic interaction problem of two waves with orthogonal circular polarisations in an isotropic gyrotropic nonlinear medium with the second-order group velocity dispersion. It is shown that a gradual ‘chaotisation’ of the approximate solution for the amplitude of a rapidly changing wave is associated with its non-equidistant frequency spectrum.

Polarization singularities in a sum-frequency light beam generated by a bichromatic singular beam in the bulk of an isotropic nonlinear chiral medium

Expressions for the electric field at a sum frequency generated by a collinear elliptically polarized Gaussian beam and circularly polarized Laguerre-Gaussian beam in an isotropic chiral nonlinear medium are obtained in quadratures. The amount and locations of $C$ points in the cross section of a signal beam at a sum frequency are shown to be dependent on frequency and diffraction lengths ratios of fundamental beams and on the ellipticity degree of the Gaussian beam's polarization ellipse. Possible values of total topological charges of the emergent $C$ points are determined by the topological charge of the Laguerre-Gaussian beam and remain constant while the radiation propagates in nonlinear media. In case of nonzero total topological charge $C$ lines form helical structures, the parameters of which depend on the wave-vector mismatch. Otherwise, $C$ lines form a loop. As the wave-vector mismatch grows the loop undergoes deformation and breaks up, creating new $C$ lines.

Adiabatic interaction between a dark soliton and a cnoidal wave with orthogonal circular polarizations in an isotropic gyrotropic nonlinear medium

An analytical solution to the one-dimensional (plane waves) nonintegrable problem of interaction (collision) of a dark soliton with a cnoidal wave (control and information signals with orthogonal circular polarizations) in an isotropic gyrotropic medium with Kerr nonlinearity and second-order groupvelocity dispersion is obtained in the adiabatic approximation. The asymptotic behavior of the obtained solution is considered. It is shown that the role of the control signal is reduced to strong amplitude and frequency modulation, which is localized only in the region of variation in the control signal intensity.

A Ray Type Solution for the Wave of Finite Deformation in Physically Linear, Nonlinear Inhomogeneous Elastic Media

The paper is devoted to ray type solutions for waves of finite deformation in nonlinear, physically linear elastic media. These waves are generalizations of Bland plane waves for isotropic nonlinear media. For the waves considered, the fast oscillation and slow oscillation parts interact in the process of propagation. The forms of waves change adiabatically. An example of plane waves in inhomogeneous elastic media is considered.

Adiabatic modulation of a cnoidal wave by a breather with orthogonal circular polarization in an isotropic gyrotropic nonlinear medium.

An approximate analytical solution of the non-integrable problem of steady-state adiabatic interaction of a cnoidal wave with a breather is obtained. The solving algorithm is described by the example of one-dimensional problem of steady-state interaction of a plane cnoidal wave with circular polarization (the "information" signal) with orthogonally polarized rational soliton (the "control" signal) in an isotropic nonlinear gyrotropic medium with Kerr nonlinearity and second-order group-velocity dispersion. It is shown that such the interaction results in a strong amplitude and frequency modulation of the information signal and this modulation is localized in the region where intensity of the control signal changes.

Adiabatic interaction of a cnoidal wave and a soliton with orthogonal circular polarizations in an isotropic gyrotropic nonlinear medium

In the adiabatic approximation, an approximate analytical solution for a nonintegrable problem of interaction (collision) of a soliton with a cnoidal wave is obtained. An algorithm for solving is described by the example of a one-dimensional problem of interaction of a plane cnoidal wave with circular polarization (an ‘information’ signal) with an orthogonally polarized bright soliton (a ‘control’ signal) in an isotropic gyrotropic nonlinear medium with Kerr nonlinearity and second-order group-velocity dispersion. It is shown that, in addition to the amplitude modulation, localized within the soliton width (change of the ‘instantaneous’ amplitude of the cnoidal wave), a no less important consequence of the interaction is the drastic frequency modulation, localized in the same region (change of the ‘instantaneous’ frequency of the cnoidal wave).

Z-scan characterization of optical nonlinearities of an imperfect sample profits from radially polarized beams

We present the Z-scan technique using azimuthal-variant vector beams for characterizing the nonlinear refractive index of an isotropic nonlinear medium. Compared with the conventional Z-scan measurements, the reliability of the vector beam Z-scan is improved because the focused azimuthal-variant vector beam exhibits a uniform-intensity focal ring instead of a focal spot. Experimentally, our investigation demonstrates that the Z-scan using radially polarized beams is a preferable technique for characterizing the optical nonlinearity of an imperfect sample.

Adiabatic approximation and aperiodic dynamics of an elliptically polarized light wave in an isotropic gyrotropic nonlinear medium

Adiabatic approximation is used to find an analytical solution to the nonintegrable propagation problem for a plane elliptically polarized light wave in an isotropic gyrotropic medium with local and nonlocal components of Kerr-type nonlinearity and second-order dispersion of group velocity. Aperiodic consistent dynamics of bound (attributable to the nonlinearity) states of two light field components with orthogonal circular polarizations is described. It is shown that this dynamics corresponds to generalization of consistent propagation of ‘soliton–multisoliton complex’ pairs to the cases with nonlinear interaction of periodic solutions—cnoidal waves.