Functional quantum statistics of light propagation in a two-level system

The functional Fokker-Planck formalism developed in a preceding paper is applied to the problem of a radiation field propagating in a medium, which contains resonant two-level atoms. Besides the electromagnetic field also the medium is described by continuous space dependent fields. We give the masterequation and transform it into ac-number functional differential equation for a characteristic functional. This equation is reduced considerably by the projection onto one dimension and the introduction of the diffusion approximation. It forms a solid basis for the study of all types of light propagation in resonant media including classical and quantum noise. We give an approximate solution of this equation by considering the problem of an externally pumped optical transmission line, in the case that saturation effects are absent. The spectral function of the electric field strength is obtained which describes a statistical mixture of photons with the quasiparticles of the polarization field. It shows the onset of a condensation of the quasiparticles into a single state. Self excitation of the transmission line is obtained at a certain threshold of the atomic inversion. This threshold is characterized by a finite occupation number of one single quasiparticle state. The influence of a finite length of the transmission line is briefly considered.     

On the change in electromagnetic wave polarization in a smooth one-dimensionally inhomogeneous medium

Propagation of an electromagnetic wave in a smooth one-dimensionally inhomogeneous isotropic medium is considered in the second approximation of geometrical optics. The polarization evolution is studied extensively. It is known that in the first (Rytov) approximation of geometrical optics, there is only the rotation of the plane of polarization (with no change in the polarization shape and sign) for rays with torsion. In the case considered, both the shape of polarization ellipse and the sign of polarization change proportionally to the integral of the squared ray curvature even for plane rays. The effect is of nonlocal geometrical nature and can be described in terms of the generalized geometrical phase incursion between two linear polarizations.     

Nonholonomic relation between the electromagnetic field state and the torsion angle in a single-mode lightguide with linear birefringence

The relation between the electromagnetic field state and the torsion angle in a twisted single-mode fiber lightguide (SFL) with linear birefringence is considered for the case where the lightguide is stretched into a straight line. It is shown that this relation is nonholonomic, because of the noncommutativity of two infinitesimal but different changes in the length and torsion of the lightguide. This indicates that the relation between the radiation polarization and the torsion angle in a twisted lightguide is also nonholonomic, and so is the relation between the Pancharatnam geometric-optics phase increment due to the evolution of the light polarization state in an anisotropic optical medium and the SFL torsion angle. Institute of Applied Physics of the Russian Academy of Sciences, Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1125–1136, September, 1998.     

Dissipative optical solitons in dense media with optical pumping

The problem of nonlinear scattering of optical pulses in a dense three-level atomic medium with continuous pumping is considered with allowance for the local field effects. The physical requirements on the parameters of the medium and field are formulated, and the ranges of these parameters for which stationary solitons are effectively formed in the model of a quartz waveguide doped with ⁸⁷Rb atoms are determined using variational methods. It is found that disregarding the local field in this model results in violation of soliton stability in the predicted parameter range.     

Instability of Optical Solitons in the Boundary Value Problem for a Medium of Finite Extension

We consider an integrable nonlinear wave system (anisotropic chiral field model) which exhibits a soliton solution when the Cauchy problem for an infinitely long medium is posed. Whenever the boundary value problem is formulated for the same system but for a medium of finite extension, we reveal that the soliton becomes unstable and the true attractor is a different structure which is called polarization attractor. In contrast to the localized nature of solitons, the polarization attractor occupies the entire length of the medium. By demonstrating the qualitative difference between nonlinear wave propagation in an infinite medium and in a medium of finite extension (with simultaneous change of the initial value problem to the boundary value problem), we would like to point out that solitons may loose their property of being stable attractors. Additionally, our findings show the interest of developing methods of integration for boundary value problems.     

Electromagnetic radiation in a medium with a velocity gradient

A relativistic expression has been obtained for the curvature of trajectory of the wave vector of an electromagnetic wave in a moving optically transparent medium. It has been shown that the curvature of the trajectory and angular deviation of rays appear in a homogeneous isotropic medium if the gradient of the velocity field in the medium is nonzero. The bending of the trajectory in the medium with the velocity gradient is a firstorder effect in the ratio u/c.     

Generation of pulses upon nonresonant acousto-electromagnetic interaction

New mechanisms of generation of acoustic and electromagnetic soliton-like pulses in an optoelastic medium upon nonlinear nonresonant interaction of the polarization components of an electromagnetic field with acoustic oscillations in the medium are considered. It is shown that the acousto-electromagnetic interaction in such a system may lead to the formation of coherent soliton excitations in a thin crystal plate. It is found that a modulation instability occurs in an extended medium, which is caused by the spatial effects and leads to the generation of transverse sound waves. The evolution of a light field in a one-dimensional extended periodic optoelastic medium is also considered. It is shown that acoustic and electromagnetic solitons can be generated due to the mixing of direct and backward optical waves and their nonresonant interaction with a sound wave.     

Anharmonic pulses due to transition radiation

The possibility of using the transition radiation of an electron bunch to generate nonstationary anharmonic pulses in free space and in a dispersive medium is demonstrated. It is shown that the transition radiation of the bunch gives rise to an infinite train of nonstationary anharmonic pulses described by solutions to the Klein-Gordon equation. The polarization of the resulting field at its leading edge appears to be different from the field polarization at the interface. The leading edge becomes steeper with time. It is shown that the bunch density longitudinal distribution and the parameters of the dispersive medium can be determined from the values of the fields and their derivatives near the leading edge of the resulting signal.     

Polarization effects in nanoaggregates of silver caused by local and nonlocal nonlinear-optical responses

A theoretical and experimental study is made into the combined manifestation of local and nonlocal optical responses in a cubic nonlinear isotropic medium such as an aggregated colloidal silver solution. The phenomenological treatment of polarization effects is performed for the general case with due regard for the frequency dispersion of both local and nonlocal nonlinearities and for the noncollinear propagation of pump and probe light waves. The inverse Faraday effect, the optical Kerr effect, and the self-rotation of the polarization ellipse in a fractal-disordered nonlinear medium are observed for the first time. The tensor components of the local and nonlocal cubic nonlinearities of colloidal silver solutions are measured for different degrees of aggregation. It is demonstrated that, as the size of silver aggregate increases, the nonlocal nonlinear response increases much more strongly than the local one. An inference is made that the mechanical motion of metal nanoparticles because of their dynamic interaction with the light wave field can contribute to the nonlinear polarization effects.     

高斯轨迹参量的线性变换对于电子光学象差的影响

本文从比较普遍的观点出发,采用矢量形式描写高斯轨迹,运用矩阵形式表示象差,从而讨论了普遍的高斯轨迹参量线性变换下的电子光学系统的三级象差和象差系数及其偏微商。由此得到了电子光学广义的Fraunhofer条件(即消除各向同性和各向异性彗差的条件),证明了在此条件下,象散和场曲取极值或稳定值。利用上述的普遍公式和结果,讨论了固定束和扫描束电子光学系统中光阑位置变化的影响,还讨论了阴极发射系统中磁浸没的影响。 关键词：     

Weakly nonparaxial spatial solitons in a medium with Kerr nonlinearity

A version of perturbation theory is developed that intends to determine the field distribution of spatial solitons with a 2D transverse profile in a Kerr medium in the case of small deviations from paraxial conditions. An approximate master equation for transverse components of the electric field in the case of wide solitons is derived. By solving this equation starting from the unperturbed soliton, i.e., Townes mode with linear polarization of radiation, a solution with an axially symmetric field distribution is found. Dependences of the main soliton characteristics on the degree of paraxiality are determined.     

光折变介质中空间光孤子自弯曲现象研究

光折变非线性介质在外加直流电压时会引起介质内部电荷移动,而移动后的电荷又会导致空间电荷的扩散效应,从而产生非局域非线性现象。从理论上研究了具有流动和扩散非局域非线性的光折变晶体中所支持的空间光学孤子的传播行为。应用等效粒子近似方法分析了这类介质中(1 1)维空间光学孤子动力学行为,得出孤子运动"加速度"显式解。孤子的有效"加速度"决定于孤子参量和光折变非局域参量。所得的解析结果可在一定参量范围内直接用来计算孤子的传播轨迹。对孤子在光折变非局域非线性作用下的传播动力学行为做了仿真模拟,数值模拟结果与理论分析结论符合得很好。     

High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam

Diffraction of uniformly polarized laser beams with vortex phase singularity is theoretically analyzed using the plane wave expansion. It is shown that for a high numerical aperture, an intense longitudinal electric field component is formed on the optical axis in this case. It is numerically demonstrated that an analogous effect is ensured for diffraction of a conventional Gaussian beam from asymmetric binary axicons. The field intensity on the optical axis can be varied either by rotating the optical element or by changing the direction of polarization of radiation.     

Optical Magnus effect in metamaterials fabricated from ferromagnetic microwires

In homogeneous negative phase velocity media, the Doppler and Cherenkov-Vavilov effects and the refraction and pressure of light are anomalous: they are inverse with respect to the corresponding effects in conventional media. Using the geometrical optics approximation, it is shown that the optical Magnus effect in inhomogeneous negative phase velocity media is also anomalous. The effect is demonstrated by considering a metamaterial consisting of parallel amorphous ferromagnetic microwires in a magnetic field. The metamaterial proves to be a left-handed one in the realistic region of the electromagnetic spectrum. The optical properties of such a left-handed medium can be controlled by the external magnetic field.     

电磁诱导透明系统中的暗孤子

利用电磁诱导透明效应提供的高色散和非线性系数, 研究暗孤子的形成环境以及孤子演化与环境参数的关系. 为了提高电磁诱导透明的稳定性和可操作性, 用双势阱半导体作为基质材料. 将量子理论和经典场理论结合, 获得了非线性薛定谔方程. 以非线性薛定谔方程为基础, 研究暗孤子的形成条件, 以及孤子演化与环境参数的关系. 研究结果表明: 当介质为反常色散同时交叉相位调制为负时, 在该介质中可以形成和传播暗孤子; 暗孤子演化中, 脉宽、灰度与相位相互关联, 脉宽越小、灰度越大, 相位增长越迅速. 此外, 研究了系统的调制不稳定性, 探讨了在调制不稳定下的增益谱.     

Incoherently coupled bright-dark photovoltaic soliton pairs based on two-photon photorefractive effect

The coupling of two mutually incoherent optical beams with the same polarization and wavelength in two-photon photovoltaic photorefractive crystal is studied, it is predicted theoretically that incoherently coupled bright-dark photovoltaic spatial soliton pairs are possible due to two-photon photorefractive effect. The existing conditions of these soliton pairs in the crystal are discussed in detail. The intensity profile of these soliton pairs is shown by numerical calculation under the parameters of relevant crystal.     

Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.     

Specific features of the self-action of elliptically polarized light pulses and the formation of vector solitons in an isotropic medium with the anomalous frequency dispersion and the spatial dispersion of cubic nonlinearity

Numerical methods are used to study the effect of local and nonlocal nonlinear optical susceptibilities on the parameters of a soliton whose degree of ellipticity depends on time and that is formed at a distance of several dispersion lengths in a medium with the anomalous frequency dispersion. The rotation angle of the major axis of the polarization ellipse does not depend on time and linearly increases with an increasing propagation coordinate. If the tensor components of the local nonlinear susceptibility have opposite signs, the incident elliptically polarized pulse can propagate in the regime that involves the pulse splitting into components for which the absolute values of the electric-field degrees of ellipticity are close to unity. In this case, the electric-field vector at the center of the pulse rotates in the opposite direction with respect to the rotation at the edges.     

Amplification of extremely short pulses in optical media

The dynamics of pulses with durations comparable to the inverse transition frequency that propagate in an optical medium is studied in terms of two integrable systems of Maxwell-Bloch equations. The first model describes the field interaction with a nondegenerate medium with a permanent dipole moment and permanent external pumping. A general formula is derived for the N-soliton solution. Particular solutions are used as examples to investigate the effect of permanent dipole moment and pumping on the soliton dynamics. The second model describes the interaction between two-component electric-field pulses and a two-level degenerate medium with permanent upper-level pumping. For different initial magnetic-sublevel populations, soliton solutions are used as examples to show that pumping causes a change in polarization dynamics. A two-soliton solution is used to analyze the interaction of solitons in a two-level medium with external pumping.