Adiabatic self-focusing in media with spatially variable nonlinearity

An optical medium whose nonlinearity can be spatially adjusted is considered to study beam reshaping. The concept is applied to perform adiabatic self-focusing of broad beams. Experimental results are obtained in a photorefractive lithium niobate crystal where the self-focusing nonlinearity is controlled over propagation by a temperature gradient. As a demonstration, gradual self-focusing is shown to transform an incoming beam into an output circular spot 10 times smaller over a 2 cm long crystal submitted to a 30 °C temperature gradient. Once formed, the adiabatic self-focused beam has inscribed a funnel waveguide in the crystal.     

Gap soliton in a waveguide array with a saturating defocusing nonlinearity

We investigate radiation of the solitary waves in the first band gap of the waveguide array with a defocusing nonlinearities of different types (Kerr nonlinearity and saturating nonlinearity). We confirm recent findings that gap solitons (GSs) are unstable for their eigenfrequencies around the middle of the band gap for Kerr nonlinearity. The instability is mediated by four-wave mixing process and appears in the form of radiation of solitons into mode continua of the upper and lower bands. We find that this soliton radiation is reduced (and even suppressed completely) in case of a saturating nonlinearity, resulting in substantial stabilization of the GSs.     

Compensation for self-focusing by use of cascade quadratic nonlinearity

We demonstrate theoretically and experimentally compensation for positive Kerr phase shifts with negative phases generated by cascade quadratic processes. Experiments show correction of small-scale self-focusing and whole-beam self-focusing in the spatial domain and self-phase modulation in the temporal domain.     

A comparative numerical study of soliton switching in a nonlinear directional coupler with saturating nonlinearity

A detailed numerical study of soliton switching in a nonlinear directional coupler with saturating nonlinearity is carried out. All commonly used models have been studied. Relevant physical characteristics for switching have been determined, compared and discussed.     

Amplitude and polarization effects in self-focusing of laser radiation in media with spatial dispersion of nonlinearity

Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 9, pp. 1042–1052, September, 1988.     

The orientational mechanism of nonlinearity and the self-focusing of He-Ne laser radiation in nematic liquid crystal mesophase (theory and experiment)

A giant optical nonlinearity of self-focusing type in the oriented mesophase of nematic liquid crystals (NLC) due to the director reorientation under the action of a light wave field is predicted. Self-focusing of He-Ne laser radiation with power ～10^?2 W and power density ～50 W/cm² in a planar oriented 60 μm thick NLC layer has been carried out experimentally. The measured value of the nonlinearity effective constant ?₂ = 0.07 cm³/erg corresponds to theoretical predictions, and turns out to be larger than the CS₂ nonlinearity by ? 10⁹ times.     

光束自聚焦的矢量理论研究

 基于矢量非傍轴非线性Schr-dinger方程,利用调制理论研究了光束的自聚焦特性,比较了非零电场散度项和非傍轴项在消除自聚焦崩塌方面的贡献。结果表明,引入两项之一都可使光束聚焦到一有限宽度后开始散焦,然后又自聚焦,如此作聚焦-散焦的周期性循环。但是,在光束自聚焦点附近,非零电场散度项的作用要强于非傍轴项。     

New solutions in aesthetic field theory

We have obtained a large number of solutions to the aesthetic field equations. We discuss 19 solutions which appear to lead to bounded particle systems. One of the solutions is more complex (although only slightly) than the solution discussed in detail in Muraskin and Ring (1975). The solutions we have found have varied mathematical properties.     

光束自聚焦的矢量理论研究

基于矢量非傍轴非线性Schr-dinger方程,利用调制理论研究了光束的自聚焦特性,比较了非零电场散度项和非傍轴项在消除自聚焦崩塌方面的贡献。结果表明,引入两项之一都可使光束聚焦到一有限宽度后开始散焦,然后又自聚焦,如此作聚焦-散焦的周期性循环。但是,在光束自聚焦点附近,非零电场散度项的作用要强于非傍轴项。     

Phase transitions in a saturating chiral theory of nuclear matter

The formalism of a relativistically covariant saturating chiral field theory of nuclear matter is developed in the mean field approximation, and some of the properties are studied. The theory possesses the normal saturated state of nuclear matter. The finite temperature properties are examined. A normal gas-liquid phase equilibrium region exists below T ≈ 23MeV. The maximum mass for a neutron star is calculated, and it lies well above the lower bound set by observation. In the high-temperature regime, there is a second minimum in the free energy, on which branch the effective baryon mass is very small. However, this branch is everywhere mechanically unstable, and so is not a realizable state of the theory. Above a certain critical temperature there is in fact no stable state at low baryon density. There is no density or temperature regime where chiral symmetry is restored.     

Asymptotic theory of plane soliton self-focusing in two-dimensional wave media

An asymptotic method is developed to describe a long-term evolution of unstable quasi-plane solitary waves in the Kadomtsev-Petviashvili model for two-dimensional wave media with positive dispersion. An approximate equation is derived for the parameters of soliton transversal modulation and a general solution of this equation is found in an explicit form. It is shown that the development of periodic soliton modulation, in an unstable region, leads to saturation and formation of a two-dimensional stationary wave. This process is accompanied by the radiation of a small-amplitude plane soliton. In a stable region, an amplitude of the modulation is permanently decreasing due to radiation of quasi-harmonic wave packets. The multiperiodic regime of plane soliton self-focusing is also investigated.