Temperature dependence of linear electrooptic coefficients r 113 and r 333 in lithium niobate

A new method of determination of individual linear electrooptic coefficients is proposed. The technique is based on the dynamic polarimetric measurements and takes into consideration the temperature dependences of ordinary and extraordinary refractive indices. Results obtained for the electrooptic coefficients r₁₁₃ and r₃₃₃ in LiNbO₃ are presented. The coefficients are found to increase significantly within the considered temperature range 25-200°C. The temperature dependences of the intrinsic coefficients m₁₁₃ and m₃₃₃, defined in terms of the induced polarisation, are considered as well.     

Analysis of quadratic electrooptic response of BaTiO<Subscript>3</Subscript> crystal in ferroelectric phase

Using the example of BaTiO₃ in a ferroelectric phase it is shown that a large difference in magnitudes of individual linear electrooptic coefficients may be a reason of additional indirect quadratic contributions that are independent of real quadratic coefficients. For some directions of the applied field and light, the indirect contributions may be even larger than the real quadratic ones. Independently of nonlinear distortions that can affect applicability of technical devices, a large difference between linear electrooptic coefficients may lead to serious problems in measurements of the real quadratic electrooptic effect. The analysis is based on the extended Jones matrix calculus applied to a Gaussian beam.     

Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of hollow Gaussian beams (HGBs) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident HGBs propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of incident HGBs do not remain during propagating in crystals.     

双轴晶体电光调制器的最优设计

运用新的线性电光效应的耦合波理论，对双轴晶体KTP电光调制器的温度特性进行了理论研究.找到了一个入射光波矢的方向，在该方向上，出射光光强不随温度的变化而变化，而且此方向在一定的角度范围内变动，温度的稳定性是可以保持的.还进一步对晶体的通光长度和外加电场的方向进行了筛选，实现了双轴晶体KTP电光调制器的最优设计. 关键词： 电光效应 耦合波理论 电光调制器 最优设计     

Electro-optic modulation of light propagating near the optic axis with any polarization in uniaxial crystals

The electro-optic effect in uniaxial crystals for light propagating near the optic axis with any polarization has been analyzed. The passive and the electrically induced birefringences and the rotation of polarization direction in crystals have been calculated, and the conoscopic interference figures under orthogonal polariscopes for different polarizer directions have been plotted. The extinction areas caused by the rotation of polarization direction in crystals change with the polarizer direction, but the two heads of the induced optical axes do not vary, which are always on the induced principal axis with bigger refractive index. The directions of polariscopes are always extinction, and the ±45° directions with polarizer are always complete transmission. The conoscopic interference figures for LiNbO₃ crystals have been demonstrated experimentally by rotating polariscopes directions, which accord with the theoretically calculating plots.     

Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis

The analytical formulae for the Gaussian flat-topped beams propagating in uniaxial crystals orthogonal to the optical axis are derived. The numerical results show that the Gaussian flat-topped beams spread at different rates in the directions parallel and orthogonal to the optical axis due to anisotropic crystals. An analytical expression for the kurtosis parameter of the Gaussian flat-topped beams propagating in uniaxial crystals is derived and illustrated with numerical examples. It is shown that the evolution of the kurtosis parameters K_x and K_y depend on the ratio of extraordinary to ordinary refractive indices.     

Waves and rays in uniaxial birefringent crystals

In this paper, we present a more elaborate and complete way of the formalism that we have developed in successive steps for ray tracing through uniaxial birefringent media in view of the optical design. With the obtained formulas we analyze in detail what we see through a cleavage calcite crystal.     

Propagation of Airy Gaussian vortex beams in uniaxial crystals

The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated.     

Reflection and refraction by interfaces of uniaxial crystals

We present a simple and complete approach to determining the directions and amplitudes of rays propagating through arbitrary systems of homogeneous and/or uniaxial materials. In the process we extend the work of Gu and Yen to full generality.     

电光与磁光效应的互补特性及其传感应用

研究了兼有电光效应和磁光效应的晶体内电光与磁光效应的互补特性及其传感应用. 在光强度调制条件下, 晶体中偏振光波的电光调制与磁光调制具有互相补偿的效果, 从而能够使输出光强度保持为一个固定值. 基于这种互补特性, 提出了一种利用单块闪烁锗酸铋(Bi₄Ge₃O₁₂, BGO)晶体的电光补偿型光学电流(磁场)传感器, 其光学传感单元由两个偏振器和一块平行四边形BGO晶体组成. 该晶体自身能够产生π/2的光学相位偏置, 同时兼用作电流传感和电光补偿元件, 通过控制BGO晶体的外加电压, 能够实时补偿被测电流(磁场)变化引起的磁光旋转角和输出光强度的变化, 从而实现电流(磁场)的闭环光学测量. 实验测量了5.0 A范围内的工频交流电流, 所需要的电光补偿电压约为21.2 V/A, 补偿电压与被测电流之间具有良好的线性关系, 其非线性误差低于1.7%.     

Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of beams generated by Gaussian mirror resonator (GMR) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident beams generated by GMR propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of the incident beams generated by GMR do not remain during propagating in crystals.     

Measurements of absolute values of electrooptic coefficients in a ferroelectric liquid crystal

Weak external electric field E causes two effects in chiral smectic liquid crystals: linear change of the optic axis direction and modification of the shape of the indicatrix. The relative changes in the light intensity consist of two components. The first component represents the modulation with the fundamental frequency f and the second one, with the doubled frequency 2f (second harmonic). We carried out measurements of the electrooptic modulation at both the first and second harmonics frequency. The applied calibration procedure allowed for expressing the experimental results as angular quantities independent of experimental conditions. Therefore we were able to determine the absolute values of the coefficients describing both effects of the electric field on the optical properties of the sample. We studied the temperature dependence of the first and second order coefficients in the ferroelectric smectic C? and paraelectric smectic A phases. The experiments delivered an information on the structure of tilted smectic liquid crystals and its dependence on the electric field.     

Non-linear electrooptic effect in antiferroelectric liquid crystal

Electrooptic phenomena caused by weak electric fields, much lower than those needed for the helix unwinding, in helical smectic liquid crystals were studied in thin planar samples. The investigations were performed in chiral liquid crystal 4-(1-methyl-heptyloxycarbonyl) phenyl 4′-(3-butanoyloxy propyl-1-oxy) biphenyl-4-carboxylate which exhibits antiferro-electric properties. We have found that electric field applied to a helical smectic liquid crystal caused two effects. First, the helix was deformed and the position of effective optic axis changed by an angle proportional to the field strength. The second effect, quadratic in field, causes the change in the shape of the indicatrix. As a consequence, the relative changes in the light intensity caused by external electric field consist of two components. The first component represents the modulation with the fundamental frequency and the second one with the doubled frequency (second harmonic of the electrooptic effect). The ab- solute values of the first- and second-order electrooptic coefficients have been determined and their temperature dependence discussed.     

Study on the anisotropic photonic band gaps in three-dimensional tunable photonic crystals containing the epsilon-negative materials and uniaxial materials

In this paper, the properties of anisotropic photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of the anisotropic positive-index materials (the uniaxial materials) and the epsilon-negative (ENG) materials with body-centered-cubic (bcc) lattices are theoretically studied by a modified plane wave expansion (PWE) method, which are the uniaxial materials spheres inserted in the epsilon-negative materials background. The anisotropic photonic band gaps (PBGs) and one flatbands region can be achieved in first irreducible Brillouin zone. The influences of the ordinary-refractive index, extraordinary-refractive index, filling factor, the electronic plasma frequency, the dielectric constant of ENG materials and the damping factor on the properties of anisotropic PBGs for such 3D PCs are studied in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in such 3D PCs with bcc lattices composed of the ENG materials and uniaxial materials, and the complete PBGs can be obtained compared to the conventional 3D PCs containing the isotropic materials. The calculated results also show that the anisotropic PBGs can be manipulated by the parameters as mentioned above except for the damping factor. Introducing the uniaxial materials into 3D PCs containing the ENG materials can obtain the larger complete PBGs as such 3D PCs with high symmetry, and also provides a way to design the tunable devices.     

Orientation dependence in high harmonics of ZnO with polarization corrections to counteract the birefringent effect

We investigate the influence of the birefringence on the high-order harmonics in an a-cut Zn O crystal with midinfrared laser pulses. The high harmonics exhibit strong dependence on the alignment of the crystal with respect to the laser polarization. We introduce the Jones calculus to counteract the birefringent effect and obtain the harmonics with polarization corrections in Zn O. We show that the birefringent effect plays an important role in the orientation dependence of HHG.     

Power splitting between refracted ordinary and extraordinary waves in uniaxial crystals with absorption

The refraction of a plane wave into a uniaxial crystal with possible absorption is analysed. The Poynting vector of the transmitted wave is formulated and succinct conditions for the decomposability of its normal component into the normal components of the Poynting vectors of the ordinary and extraordinary refracted waves are derived. The implications for raytracing in anisotropic media with absorption are discussed.     

A simplified model for second-harmonic generation in uniaxial crystals: phase matching condition

The phase matching condition for second-harmonic generation can be satisfied by a simplified model making use of the conservation of energy and momentum. By using the crystal indicatrix together with our model, we are able to classify uniaxial crystals as Type I and II non-linear optical materials.     

Dielectric measurements of new antiferroelectric liquid crystals

Three new pure antiferroelectric materials, synthesized at the Military University of Technology (MUT), were investigated by dielectric means. Clear relaxation modes were detected, i.e., Soft, Goldstone, low frequency in-phase (P_L) as well high frequency anti-phase (P_H) modes for paraelectric Sm A*phase, ferroelectric Sm C* phase and antiferroelectric Sm C_A* phase, respectively. Additionally, a high relaxation mode in Sm C_A* was found. The relaxation frequencies f_R of the observed modes were calculated from Cole-Cole diagrams.     

Holographic solitons in centrosymmetric photorefractive crystals

The conditions necessary for obtaining holographic solitons in centrosymmetric photorefractive crystals are discussed. When both the intensity modulation of the two interacting waves and the angle between the vector of each beam and the longitudinal axis are small, centrosymmetric photorefractive crystals with a positive (or negative ) effective quadratic electro-optic coefficient are able to support bright (or dark) holographic solitons. The intensity width at half maximum of bright and dark solitons is inversely proportional to the external bias field. The holographic solitons can also exit in dissipative centrosymmetric photorefractive crystals when the applied external bias field is large enough.