Light diffraction on acoustophotorefractive holographic gratings

The intermediate regime of light diffraction on acoustophotorefractive holographic gratings written in cubic photorefractive crystals according to the synchronous-detection mechanism is studied. It is shown that the diffraction efficiency in sillenite-type gyrotropic crystals only slightly depends on the incident light polarization and the external electric field. The highest diffraction efficiency in nongyrotropic crystals was achieved for p-polarized writing and reading light and at a considerable external electric field strength.     

Polymeric photorefractive surface waves

We theoretically studied photorefractive surface waves supported by polymers with orientationally enhanced photorefractive effect. We find that the orientational enhancement and the dependency of the quantum efficiency of generating mobile holes on the electric field make the diffusion nonlinearity in photorefractive polymers dependent not on only the variation of light intensity but also on external electric field, which is very different from the external electric field independent diffusion nonlinearity in inorganic photorefractive crystals. Consequently the profile, frequency and especially the penetration depth of polymeric photorefractive surface waves strongly depend on external electric field, which makes it more controllable than that in photorefractive inorganic crystals. The stability of polymeric photorefractive surface waves, the effects of birefringence component and electro-optic component of orientationally enhanced photorefractive nonlinearity on the formation of x or y-polarized polymeric photorefractive surface waves are also discussed.     

The effect of nonlinearity of the recording media response on the properties of thick phase holograms

The effect of nonlinearity of a photosensitive medium response on the diffraction properties of thick phase holograms is analyzed on the basis of coupled-wave equations. It is shown that, for a typical dependence of the refractive index on the exposure, the response nonlinearity lowers the diffraction efficiency of a hologram illuminated by an s-polarized light. For the p polarization of the reading beam, the response nonlinearity reduces the hologram efficiency when the angle between the beams diffracted into the zero and second orders (into the minus first and first orders) is smaller than 90°, increases the efficiency for angles larger than 90°, and hardly affects the diffraction efficiency when this angle is close to 90°. The results for p polarization are obtained, to the best of our knowledge, for the first time. The analysis of angular selectivity of the gratings has shown that the effect of nonlinearity becomes particularly important for light waves incident on the hologram at angles close to the Bragg one. It is also found that, for any thickness of the photosensitive medium, there exists an optimum value of the maximum change in the refractive index, for which the diffraction efficiency may be close to 100% in a wide range of exposures. In this case, the nonlinearity for s polarization stabilizes, to some extent, the dependence of the diffraction efficiency on the exposure.     

Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor

Multi-layer dielectric (MLD) gratings for pulse compressors in high-energy laser systems should provide high diffraction efficiency as well as high laser induced damage thresholds (LIDT). Nonuniform optical near-field distribution is one of the important factors to limit their damage resistant capabilities. Electric field distributions in the gratings and multi-layer film region are analyzed by using Fourier modal method. Optimization of peak electric field in the gratings ridge is performed with a merit function, including both diffraction efficiency and electric field enhancement when the top layer material is HfO₂ and SiO₂, respectively. A set of optimized gratings parameters is obtained for each structure, which reduce the peak electric field within the gratings ridge to being respective 1.39 and 1.84 times the value of incident light respectively. Finally, we also discuss the effects of gratings refractive index, gratings sidewall angle and incident angle on peak electric field in the gratings ridge.     

The Bragg Diffraction of Light at Acoustophotorefractive Holographic Gratings in Gyrotropic Cubic Crystals

We investigate diffraction of light at phase holographic-type gratings recorded by a piezoactive ultrasonic wave in gyrotropic cubic photorefractive crystals. We show that the efficiency of diffraction at a holographic grating can be increased substantially by applying a d.c. field to a crystal under the conditions of a longitudinal electrooptical effect; elliptical polarization of diffracted light is determined by electrically induced anisotropy of a crystal in the piezofield of a photorefractive grating, by the external electric field, detuning of phase synchronism, gyrotropy of the crystal, ultrasound frequency, and the time of recombination of charge carriers.     

Analytical model of a corrugated optical waveguide

An analytical model of the diffraction energy exchange between the radiative and the waveguide modes in a planar optical waveguide corrugated by a waveguide grating with an arbitrary form of teeth is developed on the basis of the coupled-wave method. It is shown that the mechanism of the energy exchange between the modes is determined by the partial interaction of all components of the spatial frequency spectrum of the waveguide modes with the corresponding components of the spatial frequency spectrum of the grating. It is established that gratings with an asymmetric tooth profile providing a shift of the peak of the spatial frequency spectrum toward matching are characterized by a higher diffraction efficiency α; however, at small thicknesses δ of the waveguide grating, the efficiency is almost independent of the tooth profile. It is shown that gratings with a symmetric profile give on average a decreasing dependence α(δ), while gratings with an optimized asymmetric profile yield a monotonically increasing saturating dependence α(δ).     

Calculation and optimization of parameters of deep groove gratings with multilayer dielectric coating for compression of high-power laser pulses

The method of calculating the electromagnetic wave field diffracted by a holographic grating with a multilayer dielectric coating is developed. The method consists of the representation of the field inside dielectric layers in the form of a plane-wave expansion for weakly damped harmonics and an expansion over functions of the concomitant coordinate system for strongly damped orders. This modification of the method allows calculation of the diffraction efficiency and the electric field strength for the deep groove gratings. It is shown that a diffraction element that possess high efficiency and radiation strength can be obtained even when the profile of the dielectric layers flattens with an increase in the distance from the grating’s metallic layer.     

On the Fresnel diffraction pattern of phase holographic gratings

The Fresnel diffraction pattern of phase diffraction gratings is studied on the example of idealized sinusoidal relief-phase plane holographic thermoplastic gratings. It is shown that, in the region of low spatial frequencies, which are more than two times lower than the inverse wavelength of the reading coherent radiation, the intensities of the main diffraction maxima, the diffraction efficiency, and the light-scattering power are independent of the spatial frequency of the phase gratings under investigation, which are characterized by a sinusoidal law of modulation of the reading-radiation phase. It is established that the range of spatial frequencies at which a plateau is observed in these dependences increases with decreasing amplitude of the phase modulation of the reading light. These dependences are also observed to have similar character for the thermoplastic holographic gratings under study. Calculations were performed to analyze the influence of real profiles of thermoplastic strain on the diffraction efficiency and light-scattering power of such gratings. On the basis of analysis of the results obtained, recommendations on using holographic and raster techniques of recording data on phase carriers are given that make it possible to improve the quality of the restored optical image.     

Diffraction efficiency and energy transfer during hologram formation in reduced KNbO3

Volume phase-hologram formation by the photorefractive effect in KNbO₃ is accompanied by a stationary energy transfer between writing beams. The change in energy transfer by applying an electric field on the reduced crystals is shown to be due to an efficient increase in migration length which can reach values comparable or larger than the fringe spacing. It is demonstrated that photovoltaic contribution to the diffraction efficiency and energy transfer is rather small in reduced KNbO₃ and that diffusion of photogenerated free holes is the dominant charge transport for the photorefractive effect in unbiased crystals. The experimental results for diffraction efficiency and energy transfer as a function of grating spacing, electric field, light intensity and temperature is well described by a recent theory of Kukhtarev and Vinetskii.     

Enhancement of the diffraction efficiency of the hologram recorded in photorefractive media under the action of external electric field

Diffraction efficiency as a function of the applied electric field for the non-linear regime has been calculated by solving numerically the beam coupling equations. The refractive index variation used in the beam coupling equations was calculated directly from the material rate equations via the total space charge field. The diffraction efficiency of the holograms recorded in photorefractive media is not only a function of the applied external electric field but also a function of crystal thickness, diffusion field, reduced fringe contrast modulation ratio and absorption coefficient of the materials. The effects of these parameters on the efficiency of the holograms have been studied in details. In the absence of the external applied field, it is found that the diffraction efficiency of the holograms could be maximized for a thinner photorefractive crystal having lower absorption coefficient and higher value of diffusion field, which could exist at a much lower value of reduced fringe contrast modulation ratio of the index grating. More efficient holograms can be recorded in the presence of the externally applied electric field as compared to the case of no external field.     

Analysis of Interdigital Electro-optic Bragg Diffraction Grating

Some integrated optics devices can be made based on the interdigital electro-optic Bragg diffraction grating. The point-matching method is extended to the analysis of interdigital electro-optic Bragg diffraction gratings. This method provides a simple and fast analytic expression of the electric field in the structure. The field distributions are used to calculate the optical and electrical characteristic parameters of the gratings. The effects of finite conductor thickness have been taken into account in the analysis. It is shown that the simulation results agree well with the measured data.     

Steady holographic gratings in semiconductor multiple quantum wells

A theoretical model based on the Dember mechanism is proposed to describe the steady state photorefractive gratings generated in semiconductor multiple quantum wells (MQW). It has been applied to an GaAs/AlGaAs MQW in parallel configuration (external electric field applied parallel to the MQW layers) for which recent experimental data are available. The model predicts a dependence of the first-order diffraction efficiency on the applied field in qualitative accordance with experiments, including the occurrence of saturation at high field values. Absolute values of the efficiencies are in good agreement with the experimental ones. Finally, high second-order diffraction efficiencies, associated with the development of a perpendicular space charge field, are also predicted by the model.     

Design of high-efficiency diffraction gratings based on total internal reflection for pulse compressor

We present designs of high-efficiency compression grating based on total internal reflection (TIR) for picosecond pulse laser at 1053 nm. The setup is devised by directly etching gratings into the bottom side of a prism so that light can successfully enter (or exit) the compression grating. Dependence of the −1 order diffraction efficiencies on the constructive parameters is analyzed for TE- and TM-polarized incident light at Littrow angle by using Fourier modal method in order to obtain optimal grating structure. The electric field enhancement within the high-efficiency TIR gratings is regarded as another criterion to optimize the structure of the TIR gratings. With the criterion of high diffraction efficiency, low electric field enhancement and sufficient manufacturing latitude, TIR compression gratings with optimized constructive parameters are obtained for TE- and TM-polarized incident light, respectively. The grating for TE-polarized light exhibits diffraction efficiencies higher than 0.95 within 23 nm bandwidth and relatively low square of electric field enhancement ratio of 5.7. Regardless of the internal electric field enhancement, the grating for TM-polarized light provides diffraction efficiencies higher than 0.95 within 42 nm bandwidth. With compact structure, such TIR compression gratings made solely of fused silica should be of great interest for application to chirped pulse amplification (CPA) systems.     

多层介质膜脉宽压缩光栅的严格矢量分析

用于展宽和压缩激光脉冲的多层膜脉宽压缩光栅是由多层介质高反膜和位于其顶层的浮雕光栅构成。以设计的高反射多层膜为基础,利用傅里叶模式理论分析了其衍射场分布,给出了TE波自准直角入射的使用条件下,多层介质膜脉宽压缩光栅衍射效率的表达式。以-1级衍射效率为评价函数,分别讨论了HfO2和SiO2为顶层材料时,多层膜脉宽压缩光栅-1级衍射效率高于0.95的光栅结构参量范围。结果表明,在该条件下,选择HfO2为顶层材料时,光栅结构参量有较大的取值范围。给出了优化的光栅结构参量,并分析了光栅制作误差及其使用条件的宽容度,对光栅制作工艺和使用具有一定的指导意义。     

叉指电光布拉格衍射光栅分析

叉指电光布拉格衍射光栅能够用于制作集成光学器件。将点匹配法扩展应用于又指电光布拉格衍射光栅分析,将光栅各区域的势函数表示为该区域中满足拉普拉斯方程的一系列基函数的级数,匹配边界上有限个点的边界条件以确定出级数项的系数,从而得到叉指电傲电场分布的解析表达式,在此基础上得到了叉指电光布拉格衍射光栅的一些重要的光学与电学特性参量。将分析结果与测量值进行了对比,发现二者十分吻合。所提出的分析方法简便快捷、精度高,所导出的电场分布的解析表达式和分析结果对叉指电光衍射光栅的优化设计具有重要的意义。     

Space-charge gratings in photorefractive crystals controlled by an external variable electric field

Specific features of space-charge gratings excited in photorefractive crystals in the presence of an external variable electric field that exhibits power-law time dependence are studied. It is demonstrated that the process under study substantially depends on a parameter of an increase in the external electric field over a time interval that corresponds to the generation of space-charge gratings in the absence of the field. At a relatively small parameter, the charge can be increased in accordance with variations in the field, charge oscillations with increasing amplitude can be induced, and identical excitation of the gratings can be maintained. At a relatively large parameter, the charge of the gratings is proportional to the time of external action, so that the charge can be controlled using external variable electric field.     

Frequency shift and anomalous resistivity of turbulent plasmas in external electric and magnetic fields

Accounting for the modified orbits of plasma particles due to constant external electric and magnetic fields, a general expression for the velocity space diffusion tensor of a turbulent plasma is derived. The nonlinear frequency shift and the anomalous resistivity in the presence of external fields are calculated. It is shown that the effect of a strong external electric field on the frequency shift is to reduce its magnitude. Furthermore, the dependence of the anomalous resistivity on the external magnetic field is obtained.     

Formation of holographic transmission and reflecting gratings in photopolymers under light-induced absorption

The formation of holographic transmission and reflection gratings is examined taking into consideration photoinduced absorption in photopolymer materials. The holographic gratings are assumed to be formed by light beams with arbitrary amplitude profiles. The problem is solved analytically in the zero-and first-harmonic approximation of the monomer concentration and refractive index with allowance for the interference-pattern contrast, an arbitrary degree of photopolymerization nonlinearity, and the dependence of the diffusion coefficient on the degree of polymerization. The effect of beam-amplitude profiles and light-induced absorption on the spatial profiles of holographic gratings is studied using numerical simulation. The effect of light-induced absorption on the diffraction characteristics of holographic gratings is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 81–89, October, 2006.     

Multiwave Interaction of Light in a Bismuth Silicon Oxide Crystal in an Applied Meander Electric Field

An analysis is made of photorefractive nonlinearity resulting from the interaction between the charge gratings formed in a bismuth silicate crystal in an applied meander electric field under illumination by a strong reference and two signal light beams. It is shown that the nonlinear cross interaction between the primary holographic gratings recorded in the crystal should be taken into account where the intensities of the reference and signal light beams differ from one another in magnitude (less than 300 times).__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 24–29, February, 2005.