Atom diffraction from magnetic gratings in the thin phase-grating approximation

The problem of atom diffraction from a reflecting magnetic diffraction grating is solved in the thin phase-grating approximation. The general problem for scalar diffraction is modelled using a semi-classical method in which the grating potential is separated into a reflecting term and a diffracting term. The trajectory of the atom in the reflecting potential is solved classically and the atom wave function in the diffracting potential found by integrating the phase change along the classical trajectory. The diffraction orders are obtained after Fourier transforming the result. This can be done independently of the grating potential resulting in a general formula for the diffraction efficiencies. The general result is applied to the problem of atom diffraction from a magnetic grating. Several approximations are required to reduce the problem to a form amenable to analytic solution. The results are compared with an accurate numerical method. Received 1st February 2001 and Received in final form 8 March 2001     

Photorefractive optical properties of volume phase gratings induced in sillenite crystals, when the grating vector lies on the (111) plane

We study the diffraction efficiency of volume phase gratings in Bi₁₂GeO₂₀, when the grating vector, lying on a (111) plane, is at an angle with respect to the crystallographic direction. An external bias field parallel to the direction is applied during recording, thus, the recording conditions depend on the grating vector orientation. The basic parameters determining the diffraction efficiency are the grating vector orientation, the rotatory power and the field-induced linear birefringence (primary and secondary). Analytic expressions for the diffraction efficiency have been obtained by taking into account all the above-mentioned parameters, provided that linearly polarized light is incident on the crystal. In this configuration, the influence of the secondary electro-optic effect (inverse piezoelectric and photoelastic effects) to the diffraction efficiency is actually stronger than the influence of the primary effect. Experimental results are given. Received: 3 January 2000 / Revised version: 6 June 2000 / Published online: 13 September 2000     

Effects of applied DC/AC fields in electrical fixing process with SBN:60

We present experimental investigations of electrical fixing techniques in Ce:SBN:60. The effect of crystal fatigue on the diffraction efficiency of electrically fixed photorefractive gratings is studied. We observed that applying an ac field to the crystal eliminated crystal fatigue and improved diffraction efficiency. A controllable diffraction efficiency of a photorefractive grating is presented. A reproducible diffraction efficiency of up to 75% is obtained using a write-reveal grating technique with high-voltage pulses of opposite polarity. We also show that the diffraction efficiency can be controlled by varying the intensity of the writing beams incident to the crystal during the recording process. A method of determining the hysteresis loop using the domain-fixing technique is proposed. The dependence of the diffraction efficiency on the direction of the applied electric field while writing the hologram is studied. Our experiments show that, during writing, when the electric field is applied opposite to the c axis the grating can be successfully revealed with both positive and negative dc voltages. However, when the grating is written with a field parallel to the c axis, the grating can be revealed only with a field applied in the opposite direction. Received: 28 October 2002 / Revised version: 28 February 2003 / Published online: 14 May 2003 RID="*" ID="*"Corresponding author. Fax: +1-812/872-6167, E-mail: azad.siahmakoun@rose-hulman.edu     

Atomic reflection from a magnetic mirror: Beyond the adiabatic approximation

We present theoretical calculations for the reflection of atoms from a magnetic surface with a sinusoidal magnetization. A fully quantum mechanical treatment is possible because the problem may be reduced to an effective one-dimensional one. Results of numerical wave-packet calculations are presented and compared with an analytical model in which the atoms separate into different internal state components which follow classical paths in different potentials. Received 21 October 1999 and Received in final form 18 January 2000     

Manipulation of cold atoms by an adaptable magnetic reflector

Adaptive optics for cold atoms has been experimentally realized by applying a bias magnetic field to a static magnetic mirror. The mirror consist of a 12-mm-diameter piece of commercial videotape, having a sine wave of wavelength 25.4 μm recorded in a single track across its width, curved to form a concave reflector with radius of curvature R=54 mm. We have studied the performance of the mirror by monitoring the evolution of a 24 μK cloud of ⁸⁵Rb atoms bouncing on it. A uniform static external magnetic field was added to the mirror field causing a corrugated potential from which the atoms bounce with increased angular spread. The characteristic angular distribution of the surface normal is mapped at the peak of the bounce for atoms dropped from a height of R/2 and at the peak of the second bounce for a drop height of R/4. In a second experiment a time-dependent magnetic field was applied and the angular distribution of the cloud was measured as a function of field frequency. In this scheme we demonstrate a corrugated potential whose time-dependent magnitude behaves like a diffraction grating of variable depth. Finally a rotating field was added to generate a corrugated potential that moves with a velocity given by the product of the external field rotation frequency and the videotape wavelength. This travelling grating provides a new method of manipulation as cold atoms are transported across the surface by surfing along the moving wave. Two theoretical methods have been developed to predict the behaviour of atoms reflecting from these stationary, variable magnitude and moving corrugated potentials. A simple analytic theory provides excellent agreement for reflection from a stationary corrugated potential and gives good agreement when extended to the case of a travelling grating. A Monte Carlo simulation was also performed by brute force numeric integration of the equations of motion for atoms reflecting from all three corrugated potential cases. Received: 1 December 1999 / Revised version: 3 February 2000 / Published online: 5 April 2000     

Fabrication of surface relief gratings on transparent dielectric materials by two-beam holographic method using infrared femtosecond laser pulses

Fabrication of surface relief-type gratings in transparent dielectrics, which are hard to machine, has been achieved by a holographic technique using two infrared femtosecond (fs) pulses from a mode-locked Ti:sapphire laser. The present method can be applied for a variety of transparent dielectrics, Al₂O₃ (sapphire), TiO₂, ZrO₂, LiNbO₃, SiC, ZnO, CdF₂, MgO, CaF₂ crystals, and SiO₂ glass. It is found that the grating formation is due primarily to laser ablation processes. Planar surface relief gratings can be fabricated by colliding two fs laser pulses on the surface of substrates which move at a constant speed, synchronized with the laser repetition rate. Received: 1 March 2000 / Published online: 7 June 2000     

横向衍射技术测量光纤光栅的特性

提出了一种用Ｈｅ－Ｎｅ激光侧面照射光纤光栅，从另一侧探测光栅的布拉格衍射效率来测量光纤光栅光谱特性的技术，并用该技术测量了光栅的折射率变化的分布。     

Development of thermally fixed photorefractive holograms without light

Holographic gratings are recorded and thermally fixed in iron-doped photorefractive lithium-niobate crystals. A spatially modulated concentration of filled and empty electron traps (Fe²⁺ and Fe³⁺) yields a modulated dark conductivity. As a consequence, dark diffusion currents and dark drift currents arise. Space–charge fields and electro-optic refractive-index changes build up. An additional refractive-index grating, which may originate from a modulated proton concentration, as well as a pronounced absorption grating arising from the modulated Fe²⁺ concentration are also observed. The dark development has practical advantages: thermally fixed holograms can be used in devices without the need to develop them freshly from time to time by illumination. Although with dark development diffraction efficiencies up to 50% are demonstrated, in general the efficiencies are smaller compared to those achieved by development with light. Received: 28 June 2000 / Published online: 8 November 2000     

Holographic determination of the irradiance dependence of linear-chain polymerization rates in photopolymer dry films

A method for the holographic determination of the chemical kinetic order of irradiance in linear-chain polymerization rates using phase gratings recorded over dry photopolymer films is derived. This method, based in the initial slope of the recorded diffraction efficiency, does not depend on any model of the grating growth, and it allows to collect information on the kinetic mechanisms involved in the polymerization. An acrylamide-based linear-chain photopolymer is analysed. Received: 2 August 1999 / Published online: 8 March 2000     

Extending the detection range of optical vortices by Dammann vortex gratings

We report a 2D static binary phase Dammann vortex grating that combines the features of a conventional vortex grating and a Dammann grating. This grating uniformly distributes energies among the diffraction orders, so the low-efficiency problem at higher diffraction orders of conventional vortex gratings is resolved and the detection range of the optical vortices (OVs) is greatly increased. Experimental results of OV detection using a fabricated 5×5 Dammann vortex grating are given, and the topological charge detection range from -12 to +12 is achieved. The potential applications of such gratings include transmitting, receiving, and multiplexing OV beams in optical communication systems.     

Atom optics using microfabricated structures

We present a novel method for fabricating precisely positioned small openings in thin silicon nitride membranes. Several optical elements for atoms have been constructed, including amplitude diffraction gratings and zone plates, and the results of experiments using these devices are presented. A method for creating a blazed diffraction grating is discussed.     

Crossed gratings: A theory and its applications

We introduce a rigorous formulation for the problem of the diffraction by a finitely-conducting, bi-periodic surface. The formationon is based on a coordinate transformation which maps the grating surface onto a plane. The transformed Maxwell equations are resolved using an iterative technique. The numerical implementation is tested against a number of criteria, including a comparison with two recently developed formalisms. As well, it is shown to give results in agreement with the Reciprocity Theorem, which is derived for efficiencies of crossed gratings in unpolarized light. The method has been shown to work throughout the whole range of values of surface conductivity. We investigate the effect of a surface-corrugation on the solar absorptance of a metallic mirror. We discuss a useful equivalence property linking the behaviour of crossed gratings with that of classical gratings. We exhibit for the first time a grating in a highly-reflecting metal capable of totally absorbing unpolarized incident light. On leave from the Department of Theoretical Physics, School of Physics, University of Sydney, Sydney, N.S.W., 2006, Australia     

用多级台阶量化相位光栅分离偏振光

构造了三角形轮廓多级台阶量化相位光栅模型,用傅里叶光学方法详细推导了光栅衍射场强的解析表达式。分析了这种光栅对偏振光的分离和聚焦特性,并优化设计了两个光栅。数值模拟和分析表明,模型光栅能够将o光和e光分离任意距离,并分别在指定的方向上聚焦。计算结果显示,取8～16个量化级就可以得到较大的衍射效率,两偏振光的能量比较均衡,偏振性能较好;量化级数的进一步增加只是衍射效率有所增加,并不能提高偏振性能。     

Design of High-Efficiency Diffraction Gratings Based on Rigorous Coupled-Wave Analysis for 800nm Wavelength

We report on the design of a high diffraction efficiency multi-layer dielectric grating with wide incident angle and broad bandwidth for 80Ohm. The optimized grating can achieve 〉 95% diffraction efficiency in the first order at an incident angle of 5° from Littrow and a wavelength from 77Ohm to 83Ohm, with peak diffraction efieieney of 〉 99.5% at 80Ohm. The electric field distribution of the optimized multi-layer dielectric grating within the gratings ridge is 1.3 times enhancement of the incidence light, which presents potential high laser resistance ability. Because of its high-effieieney, wide incident, broad bandwidth and potential high resistance ability, the multi-layer dielectric grating should have practical application in Ti：sapphire laser systems.     

Thin and thick diffraction gratings: Thin matrix decomposition method

A brief review of the properties of transmission diffraction gratings is presented. Two types of gratings will be analyzed: thin and volume gratings explaining how the efficiency of the different orders that propagate inside the gratings can be calculated in both cases. For thin diffraction gratings the so-called amplitude transmittance method is applied in order to get the amplitude of the different orders, whereas in the case of volume gratings more complex methods are needed, such as Coupled Wave or modal theories. We will comment on the thin matrix decomposition method (TMDM), firstly proposed by Alferness, which gives a very intuitive approach and connects the properties of thin gratings to the properties of volume ones. The thin matrix decomposition method consists in dividing the volume grating in a number of thin gratings and applying the amplitude transmittance method to each thin grating. In this way the output of a grating will be considered as the input of the next and any individual grating can be treated by the amplitude transmittance method. The novelty of this work is that a comparison is made between the analytical expressions obtained by Alferness using the TMDM with the numerical results obtained using the coupled wave (CW) and rigorous coupled wave (RCW) theories for the efficiencies of the zero, first and second order when a plane wave incides onto a sinusoidal diffracion grating at the second on-Bragg replay angular condition.     

Total internal reflection diffraction grating in conical mounting

The main conditions and parameters for obtaining surface relief total internal reflection diffraction gratings in conical mounting are presented. Calculated and experimental investigations reveal that there are ranges of grating periods, incidence angles, diffraction angles and gratings depths for which such gratings could be obtained, both for TE and TM polarizations. With optimized grating parameters the diffraction efficiency of the total internal reflection diffraction gratings can be greater than 90%.     

透射光栅衍射率的实验标定和数值计算

简要介绍了实验室中使用的三种透射光栅的结构，在北京同步辐射源上实验标定了这些光栅的相对衍射效率。借助于光栅模型，得到了光栅的重要结构参数，并对光栅的绝对衍射效率进行模拟计算和讨论。     

Phase interpretation for polarization-dependent near-field images of high-density gratings

It has been described that the near-field images of a high-density grating at the half self-imaging distance could be different for TE and TM polarization states. We propose that the phases of the diffraction orders play an important role in such polarization dependence. The view is verified through the coincidence of the numerical result of finite-difference time-domain method and the reconstructed results from the rigorous coupled-wave analysis. Field distributions of TE and TM polarizations are given numerically for a grating with period d = 2.3λ, which are verified through experiments with the scanning near-field optical microscopy technique. The concept of phase interpretation not only explains the polarization dependence at the half self-imaging distance of gratings with a physical view, but also, it could be widely used to describe the near-field diffraction of a variety of periodic diffractive optical elements whose feature size comparable to the wavelength.     

Diffraction grating eigenvector for translational and rotational motion

Future energy scaling of high-energy chirped-pulse amplification systems will benefit from the capability to coherently tile diffraction gratings into larger apertures. Design and operation of a novel, accurate alignment diagnostic for coherently tiled diffraction gratings is required for successful implementation of this technique. An invariant diffraction direction and phase for special moves of a diffraction grating is discussed, allowing simplification in the design of the coherently tiled grating diagnostic. An analytical proof of the existence of a unique diffraction grating eigenvector for translational and rotational motion that conserves the diffraction direction and diffracted wave phase is presented.     

Dynamic properties of multiple grating formation in doped and thermally treated lead germanate

During holographic recording in lead germanate (Pb₅Ge₃O₁₁) crystals two types of refractive-index gratings are observed. One has a very fast response whereas the second builds up comparably slowly. Measurements of diffraction efficiency and two-beam coupling are carried out to study the formation of both gratings and to obtain the relative phase between them. Differently doped and thermally treated samples are divided into four classes due to their different time evolution of diffraction efficiency and of the energy transfer direction during two-beam coupling. The classification depends on doping and treatment. For Ni-doped and thermally treated samples dark and photo conductivities corresponding to the slow grating are determined, indicating that Ni-doping combined with oxidation enhances the properties of the slow grating. Received: 18 November 1998 / Published online: 7 April 1999