(1 + 2)-Dimensional sub-strongly nonlocal spatial optical solitons: Perturbation method

By extending the (1 + 1)-dimensional [(1 + 1)-D] perturbation method suggested by Ouyang et al. [S. Ouyang, Q. Guo, W. Hu, Phys. Rev. E. 74 (2006) 036622] to the (1 + 2)-D case, we obtain a fundamental soliton solution to the (1 + 2)-D nonlocal nonlinear Schrödinger equation (NNLSE) with a Gaussian-type response function for the sub-strongly nonlocal case. Numerical simulations show that the soliton solution obtained in this paper can describe the soliton states in both the sub-strongly nonlocal case and the strongly nonlocal case. It is found that the phase constant and the power of the (1 + 2)-D strongly nonlocal spatial optical soliton with a Gaussian-type response function are both in inverse proportion to the 4th power of its beam width.     

Optical beams in lossy non-local Kerr media

It is discussed that optical beams propagate in non-local Kerr medium waveguides with losses. A variational principle is carried out for the 1 + 1-D non-local non-linear Schrödinger equation in the presence of the losses. In the strongly non-local case, the approximate analytical solutions are obtained. The lossy soliton solution shows that, Unlike its local counterpart, such lossy strongly non-local soliton does not possess the adiabatic property anymore. In addition, the general approximate results for non-soliton cases are gained. The comparisons between our approximate analytic solutions and numerical simulations confirm our variational approximate solutions.     

Optical beams in sub-strongly non-local nonlinear media: A variational solution

Discussed is the propagation of optical beams in non-local nonlinear media modelled by 1 + 1D non-local nonlinear Schrödinger equation (NNLSE). In the sub-strongly non-local case, an approximate analytical solution is obtained for an arbitrary response function by a variational approach. Described by a combination of the Jacobian elliptic functions, the solution is periodic, and its period depends on not only the input power but also the initial beam width, which is confirmed by the numerical simulation of the NNLSE.     

Soliton switching in inhomogeneous nonlocal media

We address a simple way to achieve routing of optical spatial solitons via soliton interactions in the inhomogeneous nonlocal media. We reveal that the variation of the nonlocality disturbs the solitons pairs and splits them into two individual solitons which have the same escape angle but opposite deflection directions. In particular, the escape angle monotonically increases with the increase of the nonlocality variation rate. We demonstrate that the soliton pairs could form self-consistent waveguides that are able to controllably guide a weak signal by any output positions.     

Interaction of Nonlocal Incoherent White-Light Solitons

The propagation and interaction of nonlocal incoherent white-light solitons in strongly nonlocal kerr media is investigated. Numerical simulations show that the interaction properties of nonlocal incoherent white-light solitons are different from the case in local media. The interactions of nonlocal incoherent white-light solitons are always attractive independent of their relative phase, while the other parameters such as the extent of nonlocality and the input power have a great impact on the soliton interactions. Pertinent numerical examples are presented to show their propagation and interaction behaviour further.     

Interaction of nonlocal incoherent spatial solitons

We investigate numerically the interaction of nonlocal incoherent spatial solitons in strongly nonlocal kerr media based on the coherent density approach. Numerical simulations show that the incoherent soliton position is very similar to the case of coherent soliton, and show that the incoherence plays an important role in the soliton interaction, while the role of other parameters such as the phase difference, the separation, the extent of nonlocality and the input power play in the interaction is very similar to the case of nonlocal coherent soliton. Some interesting numerical examples are presented to illustrate their interaction behavior further. Pertinent physics features are addressed.     

Elliptic incoherent spatial solitons and their interactions in strongly nonlocal media with an anisotropic nonlocality

We investigate the propagation and interaction of elliptic incoherent spatial solitons (EISS) in strongly nonlocal kerr media with an anisotropic nonlocality based on the coherent density approach. An exact analytical solution of such EISS is obtained; the results show that such EISS can form with both isotropic and anisotropic coherence. Moreover, we find that the interaction properties of EISS are very similar to that of their coherent counterpart. Some numerical examples are presented and pertinent physics features are addressed.     

Discrete nonlinear Schrödinger equation with arbitrary nonlocality: Linear stability analysis and localized solution

The modulational instability of a plane wave for a discrete nonlinear Schrödinger equation with arbitrary nonlocality is analyzed. This model describes light propagation in a thin film planar waveguide arrays of nematic liquid crystals subjected to a periodic transverse modulation by a low frequency electric field. It is shown that nonlocality can both suppress and promote the growth rate and bandwidth of instability, depending on the type of a response function of a discrete medium. A solitary wave (breather-like) solution is built by the variational approximation and its stability is demonstrated.     

Laser induced self-phase modulation in nematic liquid crystals and effects of applied dc electric field

We investigated the ring-pattern characteristic of self-phase modulation in a homeotropic nematic liquid crystal cell induced by a focused Ar-ion laser beam. Laser induced self-phase retardation versus incident angle was experimentally studied, and good agreement with theory was found. Effects of applied dc electric field on the ring-pattern were studied, to our knowledge, for the first time. When the electric field was below a critical value, laser induced self-phase retardation could be varied by changing the electric field strength. Above this value, irregular shaped diffraction pattern accompanied by intense light scattering was observed, which is attributable to honeycomb-like domain formation.     

Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer

The nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer were investigated. The single beam Z-scan measurement showed the polymer film possessed a value of nonlinear refractive index n₂ = −1.07 × 10⁻⁹ cm²/W under a picosecond 532 nm excitation. Photoinduced anisotropy in the polymer was studied through dichroism and photoinduced birefringence. A photoinduced birefringence value Δn ∼ 10⁻² was achieved in the polymer film. The mechanism for the nonlinear optical response and the physical process of photoinduced anisotropy in the polymer were discussed.     

Incoherently coupled vector dipole soliton pairs in nonlocal media

We investigate the incoherently and strongly coupled Manakov vector dipole soliton pairs in nonlocal nonlinear media. We use variational approach, to describe analytical properties of these solutions in a strongly nonlocal regime. We show that the presence of fundamental component improve stability of the dipole nonlocal soliton. In the limit of highly nonlocal nonlinearity, the evolution behaviors of the vector solitons is determined by their total power.     

Incoherent solitons in strongly nonlocal media: The coherent density theory

We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum θ₀ as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic harmonic oscillation.     

Incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media

We theoretically investigate the propagation of incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media. It is found that multipole-mode soliton pairs with arbitrary different orders of Hermite-Gaussian shape can exist when the total power of two beams equals the critical power and the ratio of the beam widths for the Gaussian part is inversely proportional to the square root of the ratio of the wave numbers. When the total power does not equal the critical power, the Hermite-Gaussian breather pair exists and their beam widths evolve analogously. For general cases where the ratio of the beam widths is arbitrary, soliton-breather pairs or breather-breather pairs can be formed and their beam widths evolve synchronously in-phase or out-of-phase. Numerical simulations directly based on the nonlocal nonlinear Schrödinger equation are conducted for comparison with our theoretical predictions. The numerical stability analysis shows the higher-order Hermite-Gaussian solitons can not be stable for small nonlocality or for some media like liquid crystals.     

Generalized Theory of One-Dimensional Steady-State Optical Spatial Solitons

We present a generalized soliton theory based on the one-dimensional generalized nonlinear Schroedinger equation,from which one can easily obtain the bright, dark, and grey soliton waveforms, and their existence curves. We show that the forming conditions of spatial solitons are directly dependent on the relationship between the index perturbation and the intensity, no matter whether the index perturbation is positive or negative. Some relevant examples are presented when the solitons are supported by the photoisomerization nonlinearity.     

Propagation of a light pulse inside matter in a context of the Abraham–Minkowski dilemma

It is shown that a light pulse propagating in an optical medium exerts the optical pressure on the medium in the regions where leading and trailing edges are propagating. This effect is derived from analysis of unambiguous thought experiments which results contradict one other. It is shown that a magnitude of the pressure is equal to (n − 1/n)W₀, where n and W₀ is the refractive index of the medium and the momentum flux density of the same pulse in free space, respectively. The Abraham form of the momentum of light is redundant if the optical pressure is taken into account. In this case the dilemma disappears because one of the rival alternatives disappears.     

Transformation of Sign of Nonlinear Refraction between Mo（W）/S/Cu Planar Metal Clusters

Optical nonlinear refractive properties of a series of Mo（W）/S/Cu planar square clusters are investigated using the Z-scan technique with the ns laser pulses at the wavelength of 532 nm. The result shows that the planar metal clusters containing the halogen ligands demonstrate the self-focusing effect, and the other planar metal dusters demonstrate the self-defocusing effect. These facts indicate that the halogen ligands can act as crucial factors in determining the sign of the nonlinear refraction of the Mo（W）/S/Cu planar metal clusters. The analysis of the experimental data shows that the planar clusters with halogen ligands possess greater refraction volume of the excited state than that of the ground state, while the other planar clusters possess the smaller refraction volume of the excited state than that of the ground state.     

Interaction between Two-Dimensional White-Light Photovoltaic Dark Spatial Solitons

Using fully incoherent white light emitted from an incandescent bulb （a line source） and amplitude mask, we study experimentally the interaction between two 21） white-light photovoltaic dark spatial solitons with three different separations （40μm, 50μm and 60μm） and arrangement directions （parallel to, perpendicular to and tilted at 45° with respect to the crystalline c axis） propagating in parallel in close proximity in seff-defocusing LiNbO3：Fe crystal. Experimental results reveal that a 21） white-light dark soliton pair only experiences attractive forces when their mutual separation is sufflciently small （〈 60 μm）, and the degree of the attraction depends on their mutual separation and their arrangement direction. When the separation is larger than 60 μm, the interaction is not evident.     

Coherent and Incoherent Interactions between Discrete-Soliton Trains in Two-Dimensional Light-Induced Photonic Lattices

The coherent and incoherent interactions between discrete-soliton trains are numerically investigated in lightinduced two-dimensional photonic lattices. The solutions of discrete-soliton trains for diamond and square lattices are obtained by Petviashvili iteration method. It is found that for both the kinds of lattices, two in-phase （out- of-phase） discrete-soliton trains attract （repel） each other, and the intermediates are always accompanied with energy transfer. While the interaction forces between two incoherent discrete-soliton trains are always attractive.     

Gray spatial solitons in biased two-photon photovoltaic photorefractive crystals

This paper predicts that gray spatial solitons can exist in biased two-photon photovoltaic photorefractive crystals. Under appropriate conditions and in the steady state, the gray spatial solitons solution of the optical evolution equation is obtained. The properties associated with these solitons, such as their intensity profile, intensity full width at half-maximum, width, transverse velocity and phase distribution, are discussed as functions of their normalized intensity and degree of “grayness”. Relevant examples are provided.