Diffraction testing of ultrasonically-produced phase gratings using a double beam illumination method

An optical far-field method is described for studying ultrasonically-produced phase gratings with very small phase variations. An ultrasonic grating is illuminated by two plane waves mutually inclined at an angle properly matched to the diffraction angle of the inspected grating. The expressions for the time-dependent irradiance in the far-field diffraction orders are derived. They enable the extraction of the Raman-Nath parameter of a progressive ultrasonic beam. The application of the technique to pulsed ultrasound beams is proposed.     

Diffraction efficiency anomalies of multicoated dielectric gratings

The diffraction efficiency curves of multicoated dielectric gratings are measured as a function of wavelength and angle of incidence for S and P polarization in the visible region. Strong anomalies are observed, due to the excitation of guided waves in the grating.     

Neutron diffraction by laser-generated volume phase gratings

Cold neutrons are diffracted by thick phase gratings which have been produced by light-optical holography in poly-(methyl methacrylate) (PMMA). The neutron diffraction efficiency is investigated in the Laue case as a function of the angle of incidence by rocking the sample. The dynamical theory of neutron diffraction allows to relate the measured diffraction efficiency to the modulation amplitude of the neutron-optical refractive index. The absence of higher order diffraction peaks proves that this modulation is sinusoidal. Further experimental parameters are shown to influence the diffraction in accordance with the dynamical theory: the wavelength of neutrons, the sample thickness, and the grating period. Laser diffraction experiments allow us to give upper limits for the uniformity of the grating constant throughout the sample volume. The gratings show properties which are promising for the fabrication of high-precision control samples for cold and very cold neutron spectrometers, for the construction of neutron-optical instruments, and the possibility to measure photoinduced changes of neutron-optical potentials.     

Diffraction gratings of isotropic negative-phase velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric-magnetic half-spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive- or the negative-phase velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings — the Rayleigh-hypothesis method, a perturbative approach, and the C formalism — are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half-space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.     

Modelling the diffraction of laser-cooled atoms from magnetic gratings

The diffraction of laser-cooled atoms from a spatially-periodic potential is modelled using rigorous coupled-wave analysis. This numerical technique, normally applied to light-diffraction, is adapted for use with atomic de Broglie waves incident on a reflecting diffraction grating. The technique approximates the potential by a large number of constant layers and successively solves the complex eigenvalue problem in each layer, propagating the solution up to the surface of the grating. The method enables the diffraction efficiencies to be calculated for any periodic potential. The results from the numerical model are compared with the thin phase-grating approximation formulae for evanescent light-wave diffraction gratings and idealised magnetic diffraction gratings. The model is applied to the problem of diffracting Rb atoms from a grating made from an array of permanent magnets. Received 13 June 2000 and Received in final form 15 December 2000     

Simultaneous diffraction of two finite waves at non-uniform dynamic volume reflection gratings

Based on the two-dimensional coupled-wave theory, the simultaneous diffraction of two finite waves with non-constant amplitude distribution at a finite non-uniform dynamic volume reflection grating is described. A coupled differential equation is derived and solved numerically with the aid of a two-dimensional Runge-Kutta method. The results for the chosen example of a planar volume reflection grating both for pure phase and absorption gratings show the dependence of the fidelity and diffraction efficiency on the normalized parameter grating strength, on the phase shift with respect to the interference pattern of the read-out waves and on the absorption modulation. In contrast to the transmission grating, a high fidelity of the enhanced beam can be achieved for reflection gratings. The numerical results are compared with the solution of the one-dimensional theory.     

Holographic formation of dynamic transmission diffraction gratings in a photopolymer material in the process of two-beam interaction at low contrasts

In the present study, the process of formation of holographic transmission diffraction gratings in photopolymer media is investigated at low contrasts with allowance for self-diffraction of recording waves. A theoretical model for the first spatial harmonics of the refractive index grating is constructed based on a solution of the coupled kinetic photopolymerization and diffraction equations. The temporal dynamics of amplitude and phase spatial profiles of harmonics, diffraction efficiency, and angular selectivity of recorded gratings is theoretically investigated. The calculated and experimental data are compared. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 35–42, November, 2006.     

Second-order grazing-angle scattering in uniform wide holographic gratings

Grazing-angle scattering (GAS) is a type of Bragg scattering in slanted wide periodic gratings. It occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates at a grazing angle to the grating boundaries. Previous research has been concerned only with first-order GAS, which has been shown to be a highly unusual type of scattering characterised by a strong resonant increase of amplitudes of the scattered and incident waves in the grating. In this paper, a rigorous numerical study of second-order GAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong resonances in the grating, which is strongly different from that for first-order GAS, is predicted, described, and discussed. Physical interpretations of the predicted results are presented. In particular, a special new type of eigenmodes in a slanted wide periodic grating with large amplitude is predicted. These eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed. Received: 16 September 2002 / Revised version: 4 November 2002 / Published online: 22 January 2003 RID="*" ID="*"Corresponding author. Fax: +61-7/3864-9079, E-mail: d.pile@osa.org     

Light modulation from crossed phase gratings

A new device, consisting of two phase gratings oriented with a small angle between their grating grooves, acts as a variable-profile diffraction grating that produces variations in the diffraction orders as the illumination region is moved across the device. Combinations of phase gratings that optimize the effect and act as passive light modulators are given. An experiment that demonstrates the principle is described.     

高密度相位光栅的偏振选择性

高密度光栅具有与传统光栅不同的性质,其衍射特性往往是偏振相关的。本文针对1550nm波长TE/TM偏振入射光和0.5的光栅占空比,利用严格耦合波分析数值计算了不同光栅周期下0级及-1级的衍射效率。研究表明,相比周期为1550nm的光栅,当周期为1200nm时,偏振相关衍射效应明显增强,当光栅周期为890nm时,TE偏振光的衍射效率随着光栅深度呈正余弦变化,而TM偏振光的衍射效率始终集中在0级,具有偏振选择性。通过模式方法,利用模式中的有效折射率概念,研究了不同周期下被入射光所激发的两种光波模式通过光栅区域传播所累积的相位差;基于双光束干涉,模拟了0级和-1级的衍射效率。结果表明,利用严格耦合波分析的数值计算结果符合模式方法的理论预期,对于高密度相位光栅的偏振选择性给予了合理的物理机制解释。     

The multiwave regime of light diffraction and focusing effect in volume phase gratings

Some pecularities of multiwave light diffraction in optically thin and thick phase unslanted gratings have been considered. An approximate solution of the wave equation is derived by the eiconal method. The solution is valid for gratings which are both optically thin and thick. This is verified by comparison of approximate solutions with numerical calculations. A range of parameters is found where the solution gives a reliable result. It has been found that the phase grating has the property of focusing light in planes with a maximum value of refractive index if the grating thickness is close to the focal distance introduced.     

Genetic algorithm-based design method for multilevel anisotropic diffraction gratings

We developed a method for the design of multilevel anisotropic diffraction gratings based on a genetic algorithm. The method is used to design the multilevel anisotropic diffraction gratings based on input data that represent the output from the required grating. The validity of the proposed method was evaluated by designing a multilevel anisotropic diffraction grating using the outputs from an orthogonal circular polarization grating. The design results corresponded to the orthogonal circular polarization grating structures that were used to provide outputs to act as the input data for the process. Comparison with existing design methods shows that the proposed method can reduce the number of human processes that are required to design multilevel anisotropic diffraction gratings. Additionally, the method will be able to design complex structures without any requirement for subsequent examination by a human designer. The method can contribute to the development of optical elements by designing multilevel anisotropic diffraction gratings.     

Study on measuring refractive index modulation of volume phase holographic gratings

In this paper, we present an approach to measure the refractive index modulation of volume phase holographic gratings (VPHG) by use of its angular selectivity, with the advantage of avoiding the diffraction efficiency errors induced by noise. Based on Kogelnik's coupled wave theory for volume holographic gratings, the wave vectors matching relationship for reflective VPHG at different readout wavelengths is deduced and the diffraction efficiency as a function of readout angle is also obtained. Then an all-fiber experimental system is designed to measure corresponding diffraction efficiency with different readout angles for VPHG recorded in dichromate gelatin. By seeking the Bragg angle where diffraction efficiency is maximum and the blank angle where diffraction efficiency drops to the minimum value, the refractive index modulation can be calculated. The experiment results proves the feasibility of the method.     

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.     

Millimeter wave beams diffracted from reflecting gratings

According to the angular-spectrum method, a radiation beam of an antenna horn in the Fresnal region is decomposed into the plane waves with the fast Fourier transform algorithm and the waves diffracted from a reflection grating are superposed as a diffracted beam. Compared with the reflected beam from the same size mirror, the radiation half width of the diffracted beam from a grating is narrower and its lateral shape is shift. These performances have been experimentally verified at Ka-band by: (1). The relative diffraction efficiencies in the first order with two triangular gratings which is put along propagating direction of a beam produced by a conical lens-horn. (2). H-plane lateral width with power—3dB lapsed of the focus beam from a grating and a mirror in a grating spectrometer for millimeter waves (25–100 GHz).     

Diffraction efficiency of sequentially stored gratings in reflection volume holograms

On the basis of the theory of coupled waves the amplitudes of the first-order diffracted waves and the diffraction efficiency is calculated for sequentially superposed phase gratings stored in dielectric reflection holograms. The investigations are restricted to the case of a fixed reference wave during recording and Bragg-angle incidence.By analogy to the transmission volume grating the coupling effects which appear between incident beams and diffracted waves give the possibility of building up beam-couplers and -splitters with certain coupling parameters determined by the recording process. Moreover, reflection gratings allow a favourable combination between coupling and reflecting properties and avoid the diffraction efficiency oscillations that are characteristic of transmission gratings. The performance of the reconstruction process with several waves simultaneously allows the tuning of the intensities of diffracted waves with dependence on amplitude or phase differences between incident beams.     

Coupling coefficients of gratings with graded refractive index waveguides

In this paper, the effective coupling coefficient κeff and the self-coupling coefficient ζ1 are introduced to describe the characteristic of gratings in a resonant situation when the effects of radiation and other partial waves coupling are considered. The dependence of these two coupling coefficients on grating tooth shapes and depths and the dimensions of graded refractive index (GRIN) waveguides is numerically analysed. The results show that the gratings with linear GRIN waveguides have the largest |κeff|. The possibility of realizing a complex-coupled DFB laser, even a pure gain or loss coupled DFB laser, employing only a real refractive index coupled grating is also discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

多层介质膜脉冲压缩光栅近场光学特性分析

利用傅里叶模式理论分析了TE波自准直角入射的使用条件下，多层介质膜光栅的光栅区和多层膜区电场分布的特点.分别讨论了HfO₂和SiO₂为顶层光栅材料时，光栅结构参数对光栅脊峰值电场的影响，结果表明，对于不同膜厚的顶层材料，存在一个最佳膜厚度，使光栅脊峰值电场最小，并且当膜厚增大时，设计大高宽比的光栅可以降低该电场峰值.最后，在大角度条件下使用多层膜光栅也可以降低光栅脊处的峰值电场. 关键词： 衍射光学 多层介质膜光栅 模式理论 损伤阈值     

Characterization and dynamics of gratings induced in glasses by femtosecond pulses

We characterize the gratings induced in commercial SF57 glass by femtosecond pulses. A simple technique enables us to measure both the real and the imaginary parts of the refractive index and shows that the induced grating is mainly a phase grating. An index variation of as much as 6x10(-3) is reported. Then we study the diffraction efficiency of the grating with respect to the intensity of the femtosecond pulse. Permanent structures are induced above the damage threshold. Below this threshold, the grating relaxes. The long-time dynamics of the decay is studied and described by two models. The formation of transient and permanent gratings in various other glasses is observed.     

Beam splitting, combining, and cross coupling through multiple superimposed volume-index gratings

We investigate the diffraction properties of multiple-superimposed index gratings from a vector synthetic viewpoint using coupled wave analysis with Bragg and non-Bragg readout. The vector synthetic gratings consist of two volume-index gratings with different grating wave vectors, which can be obtained in photorefractive materials, in optical fibers or in Bragg cells with two driving acoustic waves. This structure can realize beam splitting, beam combining, and beam cross coupling, etc. Analytic expressions for the diffraction efficiency as well as the amplitude of the waves involved are obtained. The results are presented and discussed.