Discrete optical soliton scattering by local inhomogeneities

The nonlinear wave scattering by local inhomogeneities in discrete optical systems is studied both analytically and numerically. The presented theory describes the reflection and transmission of discrete optical solitons at a point defect. In particular, the derived expressions determine the reflected and transmitted pulses from the incident one. In the range of validity, the analytical results are in excellent agreement with the numerical simulations. It is demonstrated that the point defects in structured optical materials represent effective tool for controlling and manipulation of the nonlinear light pulses.     

X‐ray third‐order nonlinear plane‐wave Bragg‐case dynamical diffraction effects in a perfect crystal

Two‐wave symmetric Bragg‐case dynamical diffraction of a plane X‐ray wave in a crystal with third‐order nonlinear response to the electric field is considered theoretically. For certain diffraction conditions for a non‐absorbing perfect semi‐infinite crystal in the total reflection region an analytical solution is found. For the width and for the center of the total reflection region expressions on the intensity of the incidence wave are established. It is shown that in the nonlinear case the total reflection region exists below a maximal intensity of the incidence wave. With increasing intensity of the incidence wave the total reflection region's center moves to low angles and the width decreases. Using numerical calculations for an absorbing semi‐infinite crystal, the behavior of the reflected wave as a function of the intensity of the incidence wave and of the deviation parameter from the Bragg condition is analyzed. The results of numerical calculations are compared with the obtained analytical solution.     

Reflection of a focused light beam in a medium with Kerr nonlinearity. I. Estimates in the paraxial-beam approximation

The reflection intensity in a nonlinear dielectric layer is calculated in the approximation of paraxial incident and reflected light beams. It is shown that reflection is mainly determined by discontinuities of the refractive-index on the boundaries. Unlike reflection by a linear dielectric layer, reflection by a nonlinear layer occurs with a three-time decrease in the effective reflection area and the corresponding broadening of the angular spectrum. The intensity of the reflected wave is comparable to that of an incident wave with nearly critical beam power.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 7, pp. 867–875, July, 1996.This work was supported by the International Science Foundation and the Russian Federation Government (projects MR1000 and MR1300).     

Scattering of electromagnetic waves from nonlinear thin dielectric coatings

In this paper the reflection and diffraction properties of nonlinear thin dielectric coatings are investigated. A quite simple geometry consisting of two semi-infinite homogenous linear spaces separated by a non-linear coating is considered. An incident plane wave propagating along the z direction towards the nonlinear thin coating is taken. The nonlinear thin coating is divided into elementary sectors, within each one of which one propagating and one reflected wave exists. The boundary conditions are then applied in order to develop an efficient numerical alogirthm to study the properties of the nonlinear thin coating.     

Reflection of a pulse by multiple-dielectric layers

The reflection of a pulse by multiple-dielectric layers is treated theoretically. The reflected wave is obtained by expanding the reflection coefficient of an elementary plane wave in a series, including the special case for which total reflection occurs. The pulsed waves reflected by two-dielectric slabs are considered in detail both analytically and numerically. The effect of a carrier frequency of a pulse-modulated carrier wave on the reflected wave form is also discussed.     

准直透镜反射光引起的一个问题

准直透镜主要用于产生平行光束然而,由于其表面的反射作用,在准直后的平行光束中,还存在一束会聚光束这会聚光束与平行光束相比虽很微弱,但在其会聚点附近具有较高的强度,在安排光路时应注意避开它,否则会带来某种程度的干扰本文讨论了这种反射光对全息记录带来的影响和应注意的问题,并根据衍射理论导出了反射光的会聚位置,结果与实验符合甚好.     

Soliton Transmission and Reflection Due to the Inhomogeneity

A new approach to nonlinear wave in one-dimensional discontinuous fluid-filled elastic tube is presented. As-a model, an elastic tube which has a discontinuity of radius, thickness and Young's modulus is considered. The incident, reffe cted and transmitted waves are described by KdV equations. The reflected and transmitted waves are constructed from incident wave analytically. Fission and reflection of a soliton due to the discontinuity are explicitly shown in the lowest order     

窄光束在掠反射条件下的特性

在掠入射条件下,由于部分平面波分量无法直接入射到反射面,从而不能按照常规方式被反射和透射. 而反射透射模式的逆过程被用来描述非直接入射的这部分平面波分量与反射区的相互作用. 基于这两个模式,采用平面波展开法导出了窄光束掠入射条件下出射光的场分布,理论计算结果与采用BPM方法的模拟值完全一致. 关键词： 掠反射 平面波展开法 导波模式 光波导开关     

Quasi-linear analysis of Smith-Purcell free-electron amplifier

Calculations are presented of the scattering of an electromagnetic wave from a periodic structure above which flows an electron beam. The reflected fields are computed and found to comprise two separate contributions: (1) the reflection in the homogeneous case (without the beam); and (2) the contribution of the beam. Both are shown to depend on the structure by means of its reflection properties, as expressed by a reflection matrix. The beam contribution is shown to be exponentially dependent on the longitudinal position. This contribution also includes the exponential decay, which depends on the distance between the beam and the structure, and is a characteristic of Smith-Purcell devices. Expressions for the local and global gains are obtained. The local gain is found to be proportional to the first velocity derivative of the electron distribution function. Considerations of nonlinear effects introduce spatial dependence to the expression for the local gain. This dependence is determined by a nonlinear diffusion equation. The gain in the nonlinear regime is found to depend on the first and second velocity derivative of the distribution function     

Nonlinear reflection of optical beams in the media with a thermal nonlinearity

The features of the reflection of optical beams in the media with a defocusing thermal nonlinearity are analyzed. The dependence of the angle of the nonlinear total reflection on the power of the pump wave and the initial distance between the beams is determined. The reflection effects are studied for the interaction of the green (24 mW) and red (0.7 mW) laser beams that intersect at a relatively small angle (about 0.01 rad) in a 5-cm-long cuvette with the stained alcohol. The theoretical results are in good agreement with the experimental data.     

单轴晶体内表面入射e光线的双反射

基于光线遵从的Fermat原理,从几何学的角度讨论和分析了在单轴晶体中入射的e光线在界面上的双反射,得到了确定光线反射方向的一般公式,并对几种特殊情况进行了讨论.指出了上述结果与由电磁波的边界条件计算所得结果是一致的.     

Goos-Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface

The Goos-Hänchen shift at the surface of a uniaxially anisotropic left-handed material film is investigated, for the situation of that there is an arbitrary angle between the optical axis and the interface of the material. The analytical expressions of the Goos-Hänchen shifts are derived, for both cases of that the total reflection occurs and does not occur at the first interface. The sign of the Goos-Hänchen shifts in the two situations is analysed. The results show that the Goos-Hänchen shift of the reflected wave is the same as that of the transmitted one for the case that the total reflection does not occur at the first interface; the Goos-Hänchen shift of the transmitted wave oscillates as the thickness of the film is increased, and its overall tendency is increased; the Goos-Hänchen shift of the transmitted wave realizes its absolute maximum when the transmitted wave resonances, the absolute maximum is almost several 10 times of the wavelength of the incident wave; the Goos-Hänchen shift of the transmitted wave is significantly influenced by the incident angle and the angle between the optical axis and the interface.     

Transformation of Nanosecond Laser Pulses under the Conditions of Total Internal Reflection from a Layer with Thermal Nonlinearity

The nonlinear, total internal reflection of a laser pulse from an absorbing layer of finite thickness in the presence of a retrodirective mirror has been considered in the framework of the plane-wave approximation. The dynamics of reflection of a pulse from a nonlinear layer has been investigated on the basis of the solution of Maxwell equations for a refracted wave and constitutive equations for a medium with thermal nonlinearity. The numerical solution of the unsteady equations obtained allows one to determine the evolution of the reflectance of a layer. The time evolution of the energy parameters and the shape of the reflected and transmitted pulses has been numerically simulated.     

The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.     

Using a grating structure for phase compensation in achieving an efficient round-trip optical parametric process in periodically poled lithium niobate with an incomplete quasi-phase-matching period

An incomplete period of the last quasi-phase-matching (QPM) segment in a periodically poled nonlinear crystal represents a key problem in implementing a nonlinear wavelength-conversion device with round-trip or oscillating waves of interaction. Such a segment at the crystal end implies broken QPM periodicity for the reflected waves of interaction. We demonstrate numerically that with a grating structure at the crystal end for the reflecting signal the wavelength-dependent phase shift at Bragg reflection can compensate for the phase mismatch of the reflected signal, idler, and pump of an optical parametric process. Therefore, by slightly shifting the signal wavelength we can maintain the phase-matching condition with any length of the last QPM segment. It is shown that with a grating structure the conversion efficiency of the round-trip optical parametric process can always be optimized.     

Harmonic generation of an obliquely incident ultrasonic wave in solid-solid contact interfaces

The conventional acoustic nonlinear technique to evaluate the contact acoustic nonlinearity (CAN) at solid-solid contact interfaces (e.g., closed cracks), which uses the through-transmission of normally incident bulk waves, is limited in that access to both the inner and outer surfaces of structures for attaching pulsing and receiving transducers is difficult. The angle beam incidence and reflection technique, where both the pulsing and receiving transducers are located on the same side of the target, may allow the above problem to be overcome. However, in the angle incidence technique, mode-conversion at the contact interfaces as well as the normal and tangential interface stiffness should be taken into account. Based on the linear and nonlinear contact stiffness, we propose a theoretical model for the reflection of an ultrasonic wave angularly incident on contact interfaces. In addition, the magnitude of the CAN-induced second harmonic wave in the reflected ultrasonic wave is predicted. Experimental results obtained for the contact interfaces of A16061-T6 alloy specimens at various loading pressures showed good agreement with theoretical predictions. Such agreement proves the validity of the suggested oblique incidence model.     

扫描近场光学显微镜光纤锥中导波反射特性

利用局部模耦合模型理论上分析了扫描近场光学显微镜光纤的光场性质,给出光纤维中存在的正,反向传播的基模场微分方程,以及基模反向耦合系数的数值计算结果,其最高反射系数达１％左右。这种反射光可起着光纤维激光器谐振腔输出端镜的作用。     

Bloch-wave packet control in truncated modulated optical lattices

We study the reflection of Bloch wave packets at the interface of an optical lattice possessing a shallow longitudinal out-of-phase refractive index modulation in the adjacent waveguides. We show that the relation between the transmitted and reflected energy flows can be efficiently controlled by tuning the frequency and depth of the modulation. Thus, complete beam reflection may be achieved for a set of resonant modulation frequencies at which light tunneling between adjacent guides of modulated lattice is inhibited.     

NONLINEAR WAVES PROPAGATING IN AN INHOMOGENEOUS BLOOD VESSEL

A model for describing blood pressure propagation wave in artery is proposed. Considering blood viscosity, slowly varying arterial parameters and arterial bifurcations, we obtain the dynamical equation of blood flow. We show that the blood viscosity attenuate the nonlinear blood wave amplitude mainly in small artery. On the other hand, the variation of arterial parameters (such as radius and Young's modulus) amplify the amplitude of the nonlinear blood wave in large arteries. We also investigate how the nonlinear blood wave (or a soliton) is reflected and transmitted at the arterial bifurcations. It can be concluded that the parameters at the bifurcation determine whether there is substantial reflection or not, but the transmission in each bifurcation is approximately the same as the incident wave.     

平面电磁波在任意方向运动的介质-介质界面上的反射和透射

研究平面电磁波从一种介质入射到另一种以任意方向运动的介质时,在介质界面上发生的反射和透射现象,从Maxwell方程组、运动界面的边值关系和运动介质的本构关系出发,得到了反射波和透射波电磁场矢量与入射波电磁场矢量的关系的表达式、反射和透射系数,讨论了反射波、透射波与入射波之间的能量关系,电磁波对运动介质作用力的性质,并得出一些新的结论． 关键词：