晶体的双参量调制及其应用

利用折射率椭球分析法,分析了某些具有多重光学效应的光学晶体在两个外场同时作用下的一些特有调制规律.结果表明,当晶体的折射率椭球方程的三个交叉项中只有一项x1x2不为零时,可以得到其外场诱导新主轴折射率及其主轴取向的简单计算式.据此可以揭示出某些晶体在两个外加电场同时作用下将具有双横向电光Pockels效应,例如ˉ6点群的电光晶体.但一般晶体在双横向应力作用下不具有与双横向电光效应类似的调制特性,其弹光双折射大小与其应力差成正比,其双折射主轴方向一般为固定值.在相互垂直的外加应力和电场同时作用下,某些晶体(例如ˉ43m点群晶体)的双折射大小与外加应力和外加电场的加权几何平均值成正比,且新折射率主轴旋转角由外加应力和外加电场的比值来确定.晶体的上述双参量调制特性对设计新型光学调制器或传感器具有重要指导意义.     

Acoustogyration diffraction of optical waves: case of SiO<Subscript>2</Subscript> and TeO<Subscript>2</Subscript> crystals

Interaction of acoustic and light waves with accounting for elastooptic and elastogyration effects is theoretically described. Collinear acoustogyration diffraction in quartz and paratellurite crystals is experimentally investigated and thoroughly analyzed. Piezogyration effect is experimentally studied for TeO₂ crystals. The acoustogyration efficiency and the acoustogyration figure of merit calculated for a number of crystals (GaAs, TeO₂ and SiO₂) are shown to be too small for experimental detection. On the other hand, we demonstrate that the light diffraction at periodical distribution of the imaginary part of dielectric permittivity related to the piezogyration effect should, in principle, be observed for the case of interaction of optical waves with enantiomorphous ferroelastic domain structure and in cholesteric liquid crystals.     

On the theory of second-harmonic generation in 2D nonlinear photonic crystals with arbitrary domain structures

Theoretical analysis is given to second-harmonic generation in 2D nonlinear photonic crystals of rectangular symmetry with rectangular domains. Formulas for the nonlinear response of the crystal with an arbitrary domain structure are derived within the approximation of a given field. A possibility of calculating time profiles of second-harmonic pulses down to the femtosecond range is demonstrated.     

Second-harmonic interferometers II

Experiments on interferometers based on second harmonic generation of light are described. These make use of the distortions of phase and amplitude produced by the phase mismatch of angle-matched crystals to provide information. The interferometers are directly sensitive to small wavefront tilts and do not require additional reference wavefronts.     

Optimum formation of the response of aperiodic nonlinear crystals in the process of second harmonic generation

The theory of second harmonic generation in nonlinear optical crystals that is caused by the quasiphase-matched interaction of the waves with a random domain structure is developed. The theoretical analysis is performed using the approximation of the intensity fixed within the domain length. It is shown that the developed method allows one to accurately describe the energy exchange between the interacting waves at any values of the efficiency of second harmonic generation. Within the framework of the developed theory, the so-called simulated-annealing algorithm for the formation of the response of the medium is created, which is responsible for the spectral dependence of the efficiency of the second harmonic generation with any specified profiles under conditions of energy depletion of the fundamental radiation.     

倾斜入射光入射于一维非线性光子晶体中带宽加宽的二次谐波的产生

研究了置于空气中的含缺陷的一维非线性光子晶体中二次谐波的产生.由于反射的二次谐波很强而不能忽略,缓变振幅近似在系统中是不适用的.本文提出了一种不采用缓变振幅近似来处理二次谐波产生问题的方法,并应用这种方法计算相关的二次谐波转换效率.结果表明:随着入射波角度的增加,缺陷模对应的波长将变短,并且通过调整基频波入射的角度,可以产生宽带宽并且高转换效率的二次谐波.这个方法适用于任何一维非均匀系统,可以简单方便地计算出二次谐波转换效率.     

Focus wave modes in optical parametric generators

It is shown that in the paraxial approximation the conditions for noncollinear phase matching for three-wave parametric interaction in a nonlinear crystal coincide with the conditions for generation of focus wave modes. As a result, the creation of broadband localized optical fields (pulsed beams without diffraction and dispersion spreading) inside the crystals of parametric generators is feasible.     

倾斜入射光入射于一维非线性光子晶体中带宽加宽的二次谐波的产生(英文)

研究了置于空气中的含缺陷的一维非线性光子晶体中二次谐波的产生.由于反射的二次谐波很强而不能忽略,缓变振幅近似在系统中是不适用的.本文提出了一种不采用缓变振幅近似来处理二次谐波产生问题的方法,并应用这种方法计算相关的二次谐波转换效率.结果表明:随着入射波角度的增加,缺陷模对应的波长将变短,并且通过调整基频波入射的角度,可以产生宽带宽并且高转换效率的二次谐波.这个方法适用于任何一维非均匀系统,可以简单方便地计算出二次谐波转换效率.     

AWG中波导间耦合造成的相位畸变的分析

用(1,1)阶Pad啨近似的广角BPM计算了阵列波导光栅(AWG)中由于阵列波导间耦合造成的相位畸变以及由于相位畸变引起的相位误差分别考虑了光从中心/非中心输入波导入射两种情况结果表明,波导间的耦合会造成显著的相位畸变,但由此引起的相位误差却很小,光从中心输入波导入射时对应的相位误差10-3rad,从非中心输入波导入射时的相位误差约为10-2rad针对波导阵列边缘效应引起的相位畸变,设计AWG结构时,在阵列部分两侧增加了边缘辅助波导结构,从而消除了边缘效应,使得边缘阵列波导对应的相位误差从10-1rad量级减小为10-3(10-2)rad量级.     

On the theory of the second optical harmonic in nonlinear crystals with a regular domain structure

The theory of the second-harmonic generation in crystals with a regular domain structure (RDS) is developed in the approximation of the fixed intensity of the fundamental radiation. An analytical expression for the second-harmonic intensity is derived. The results are compared with the data obtained in the fixed-field approximation and the numerical solution. The maximum number of layers n _max at which the theory remains valid is determined. Numerical estimates of n _max are presented for the frequency doubling of an ultrashort light pulse in the LiNbO₃ RDS crystal.     

Nonlinear optics and the defect solid state

Abstract

The condition for the generation of second harmonics in the dipole approximation is that the nonlinear crystal medium lack a center of inversion. Conversely, a center of inversion precludes optical second harmonic generation. It is well known, however, that lattice defects introduced into a crystal may alter the local point symmetry in the medium, and in fact may convert local inversion symmetry to that which corresponds to a noncentrosymmetric point group. It is thus clear that selected defects in nonlinear media may be of interest for studying nonlinear optical processes which depend on the square of the electric field strength. The specific case of second harmonic generation employing spatially ordered FA-centers in alkali halide crystals is considered.     

单轴晶体Ⅰ类匹配相位畸变光束二次谐波理论分析

理论上研究了单轴晶体Ⅰ类匹配时相位畸变光束二次谐波的转换，其中考虑了衍射、离散效应，给出了相位畸变小信号解。在此基础上，以KDP晶体为例分析并给出了有像差高斯光束的转换效率随晶体长度的变化规律，对于任意光强分布和有任意相位畸变光束的谐波转换也是同样适用的。     

The effect of off-center Cu2+ ions on the phase transition in lead germanate crystals

The properties of Pb₅Ge₃O₁₁: Cu²⁺ crystals near the temperature of the ferroelectric phase transition are discussed in terms of a phenomenological approach. Assuming a quadratic interaction with the order parameter, the effect of Cu²⁺ is considered a result of static distortions, which result from the off-center position of the copper impurity ions in the lead germanate structure. In this approximation, Cu²⁺ jumps between off-center positions do not affect the dynamic properties of the crystal matrix near T _C.     

X-ray spectroscopy of thermally distorted electronic states in crystals

A new type of x-ray spectroscopy is proposed which can detect the thermal-motion-induced distortions of atomic electronic states in crystals. It is shown that those distortions can cause extra Bragg reflections (so-called forbidden reflections) and that their intensity should grow with increasing temperature. The reason is that the thermal displacements, which change the symmetry of atomic environment, can modify the tensor amplitude of x-ray resonant scattering. In the first approximation, the structure factor of extra reflections is proportional to the reflection vector H and to the mean-square thermal displacement for optical phonons. It is demonstrated that the forbidden resonant reflections, observed recently in Ge, could be caused by the thermal motion. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 12, 885–889 (25 June 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Method for calculating coefficients of concentrational variations in lattice constants and the distribution of impurity atoms between sublattices in intermetallic compounds

A method is proposed for calculating coefficients of concentrational variations in lattice constants in solid solutions, based on first-principles determination of the total energy of solid solutions and the continual approximation in the solutions theory, allowing for the deformation interaction of impurity atoms due to distortions of the solvent crystal lattice.     

Elastooptic effect and sources of the spontaneous birefringence in Gd2(MoO4)3

It is shown that a shear stress applied to support the spontaneous shear in improper ferroelectric Gd₂(MoO₄)₃(GMO) reduces the birefringence Δn'₁₂ measured when viewing along the c-axis. The elastooptic coefficient p₆₆^E in the paraelectric phase has been determined including sign. Using these and known electrooptical data, the soft mode, electrooptic and elastooptic contributions to Δn′₁₂ of GMO are evaluated. The two latter contributions have opposite sign to that of the soft mode which plays a prevailing role.     

Elimination of geometric distortions in stereoscopic systems with converging optical axes

The problem on the possibility of eliminating the vertical disparity and depth plane curvature by representing the left and right perspective views in two intersecting planes of observation is successfully solved in the framework of the geometrical optics approximation. The expressions are found for the angle of intersection of the planes of observation providing the elimination of each of the studied distortions. It is shown that both studied distortions are eliminated for the same angle of intersection of the planes of observation.     

Computing for second harmonic generation in one-dimensional nonlinear photonic crystals

A numerical study of second harmonic generation (SHG) in one-dimensional nonlinear photonic crystals based on full nonlinear system of equations, implemented by a combination of the method of finite elements and fixed-point iterations, is reported. This model is derived from a nonlinear system of Maxwell’s equations, which partly overcomes the known shortcoming of some existing models relied on the undepleted-pump approximation. We derive a general solution of SHG in one-dimensional nonlinear photonic crystals structures. The convergence of our method is fast. Numerical simulations also show the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental wave are located at the photonic band edges or are assigned to the designed defect states.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

The development of new borate-based UV nonlinear optical crystals

The developments of nonlinear optical (NLO) crystals in the last decade are reviewed from two aspects. In the theoretical part, on the ab initio plane-wave pseudopotential energy method, calculation of the optical responses, including the second harmonic generation coefficients, a computer-program package, and a real-space atom-cutting method are described and employed to evaluate the degree of approximation of the anionic group theory for nonlinear optical crystals. The ab initio method combined with the anionic group theory gives much more insight into the understanding of the relationship between the optical responses and microscopic structures of NLO crystals, borate-based NLO crystals in particular. In the experimental part, we describe how to use the anionic group theory method and an experimental evaluation system to develop a series of borate-based UV-NLO crystals such as KBe₂BO₃F₂ (KBBF) and K₂Al₂B₂O₇ (KABO). The capability of these new UV-NLO crystals in producing deep-UV harmonic output is evaluated and determined. Finally, recent advances in the generation of deep- and vacuum-UV harmonic output with these new NLO crystals are reported. PACS 42.65.Ky; 42.70.Mp