High-temperature-recorded index gratings in periodically poled lithium niobate

Holographic index gratings based on a zero-electric-field photorefractive effect are recorded at high temperatures in copper-doped periodically poled lithium niobate crystals. The interplay between the domain structure and the index grating is studied: the fundamental grating with spatial frequency K is strongly suppressed. Pronounced sideband gratings with K(s)=K+sG appear, where G is the domain grating vector and s is an integer number. After development, an additional grating based on the electro-optic effect shows up. In contrast with the previously mentioned gratings, this grating allows anisotropic diffraction.     

Polarization holographic and surface-relief gratings at 257 nm in an amorphous azobenzene polyester

Polarization holographic and surface-relief gratings have been recorded in an amorphous azobenzene polyester by use of a frequency-doubled argon-ion laser beam at 257 nm. Higher excited states of azobenzene in the trans and cis configurations contribute to the formation of a diffraction grating in this experiment. A combination of right and left circularly polarized writing beams has been found to give the highest diffraction efficiency. The contributions to the total phase difference that arise from anisotropy and surface relief have been separated experimentally, and it is shown that the surface-relief grating contributes a larger phase difference than that which is due to anisotropy.     

Measurement of phase differences between the diffracted orders of deep relief gratings

Measurement of the phase difference between the 0th and the 1st transmitted diffraction orders of a symmetrical surface-relief grating recorded on a photoresist film is carried out by replacement of the grating in the same setup with which it was recorded. The measurement does not depend on lateral shifts of thereplaced grating relative to the interference pattern, on environmental phase perturbations or on the wave-front quality of the interfering beams. The experimental data agree rather well with theoretical results calculated for sinusoidal profiled gratings.     

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).     

Relaxation of the optical density of glass modulated with bichromatic radiation

Exposure of oxide glass to two coherent light beams with different frequencies ω and 2 ω leads to the buildup of spatial index gratings in the glass. The kinetics of the writing and relaxation of the gratings is investigated. Illumination with one beam or a background illumination of the sample accelerates the relaxation process; this acceleration is due to the appreciable photoconductivity of the glass. The diffraction is found to reach a residual self-maintaining level when a grating is illuminated continuously with a beam at the fundamental frequency. The results are analyzed on the basis of a model that includes the coherent photogalvanic current, the accumulation of a grating of nonuniform charges under the action of this current, and the back-effect of the static field, via electrooptic effects, on the propagation of the beams. It is shown that an optical instability of the photoinduced index gratings exists in the glass. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 166–170 (10 February 1996)     

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.     

A detailed study of metallic surface-relief grating

This paper presents a more detailed interaction of an electromagnetics light with a metallic surface-relief subwavelength grating utilizing the rigorous coupled-wave analysis. The focus of this work is the accurate modeling of undetermined aspects of diffraction patterns produced by binary metallic grating structures, specially gold grating. First-order diffraction efficiency for rectangular-groove gold grating with equal groove and ridge widths are presented for various wavelengths as a function of period, groove depth, polarization and angle of incidence. We also studied diffraction efficiency of both of TE and TM polarization modes against increasing of incident angle as well as TE polarization against increment of grating period. As a result, very low reflectivity at zero-order was found out for TE and TM polarizations at the pitch of Λ = 2λ. Having been studied diffraction efficiency of metallic surface-relief gratings, we also examined polarization-dependent efficiency of diffraction orders, for different groove depths. Simulation results have been completely presented.     

金纳米颗粒掺杂光致聚合物的体全息混合光栅模型

金纳米颗粒掺杂光致聚合物在全息曝光过程中,光产物周期分布会形成折射率调制相位型主光栅,同时金纳米颗粒周期分布形成由局域表面等离子体共振引起强吸收的振幅型辅助光栅。研究基于耦合波理论的一种混合光栅模型,分析了光栅的体全息光学特性。结果表明,混合光栅中的折射率光栅和吸收光栅都能够提升体光栅的衍射效率; 体光栅的角度选择性也可以得到明显的改善。     

Nonlinear Model of Record and Readout of Holographic Transmission Diffraction Gratings in Absorbent Photopolymers. II. Numerical Modeling and Experiment

The temporal dynamics of harmonic amplitudes and refractive index grating profiles is modeled numerically for the theoretical model of the (N+1)th spatial harmonic of the refractive index grating constructed on the basis of the solution of coupled kinetic photopolymerization equations derived in [1] with allowance for the absorption for N = 2. Solutions of the self-consistent diffraction problem [1] are used to analyze numerically the diffraction efficiency and angular selectivity of recorded gratings. Model parameters of the experimentally investigated photopolymer material are estimated by means of a comparison of the experimental data on the diffraction kinetics and angular selectivity with the results of model calculations presented in [1]. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 85–92, July, 2005.     

Thermomechanical modification of diffraction gratings

The most accurate approaches to fabrication of diffraction gratings are known to be the lithographic and holographic methods. The lithographic methods allow fabrication of arbitrarily chirped gratings whose performance, however, is degraded by stitching errors. The holographic methods are free from stitching errors; however, they are limited in the achievable spatial variations of their grating periods. We suggest a method of diffraction grating modification by nonuniform heating and stretching that is much more flexible than the holographic approach and does not suffer from the problem of stitching error. We demonstrate our approach for quartz phase masks that have a characteristic grating period of 1 microm and a length of several centimeters. Our approach allows the grating periods of the phase masks to vary in a range from a few picometers to a few nanometers and a spatial resolution of a few millimeters. It is shown that the grating period can be modified with a negligible effect on the profile of the gratings.     

基于多路复用体全息光栅的角度放大器设计

为设计基于多路复用体全息光栅的角度放大器, 建立了多路复用角度放大器(MAM)模型, 从效率均衡性和角度分布均匀性两个方面归纳了其设计规则; 研究了光刻过程中的误差对MAM性能的影响; 分析了实际发散光束对MAM性能的影响. 研究表明:控制光栅空间频率和光栅倾斜角可以实现需要的MAM角度分布, 控制光栅厚度和折射率调制深度可以实现MAM最佳衍射效率; MAM最大复用路数不超过10路; 增大光栅倾角或者记录光与工作光波长之比有利于抑制参考光角度误差带来的MAM出射角分布误差, 减小光栅厚度有利于抑制厚度误差与折射率调制深度误差对衍射效率的影响; 当远场发散角大于光栅角半宽时, 最佳衍射效率下降到50%以下且角度选择曲线失去局部最小值; 增大空间频率或者光栅厚度可以减小所需的折射率调制深度, 增多MAM可复用路数, 但是不利于效率均衡性设计和抑制发散光束的影响.     

基于多路复用体全息光栅的角度放大器设计

为设计基于多路复用体全息光栅的角度放大器, 建立了多路复用角度放大器(MAM)模型, 从效率均衡性和角度分布均匀性两个方面归纳了其设计规则; 研究了光刻过程中的误差对MAM性能的影响; 分析了实际发散光束对MAM性能的影响. 研究表明:控制光栅空间频率和光栅倾斜角可以实现需要的MAM角度分布, 控制光栅厚度和折射率调制深度可以实现MAM最佳衍射效率; MAM最大复用路数不超过10路; 增大光栅倾角或者记录光与工作光波长之比有利于抑制参考光角度误差带来的MAM出射角分布误差, 减小光栅厚度有利于抑制厚度误差     

Electric field assisted holographic recording of surface relief gratings in an azo-glass

The formation of holographic gratings in an azo-glass is investigated for the simple case of an intensity grating in the s-polarization of the recording beams. A dual grating is formed as a function of time with a refractive index grating and a relief grating. The diffraction efficiency as a function of recording time is discussed in a model of two consecutive processes with a phase shift. A material transport process is involved in the formation of relief patterns. An additional electrical corona field perpendicular to the sample leads to a magnification of the relief pattern. This process also works in case of a homogeneous exposure. PACS 78.66.Qn; 42.40.Eq; 42.70     

Studies of shrinkage as a result of holographic recording in acrylamide-based photopolymer film

We studied the shrinkage in acrylamide-based photopolymer by measuring the Bragg detuning of transmission diffraction gratings recorded at different slant angles and at different intensities. Transmission diffraction gratings of spatial frequency 1000 lines/mm were recorded in an acrylamide-based photopolymer film having 60±5 μm thickness. We have obtained the grating thickness and the final slant angles from the Bragg curve and hence calculated the shrinkage caused by holographic recording. The shrinkage of the material was evaluated for three different recording intensities 1, 5 and 10 mW/cm², while the total exposure energy was kept constant at 80 mJ/cm². From the experimental results it can be seen that the shrinkage of the material is higher for recording with lower intensities and the corresponding values are 1.9%, 1.3% and 1%.     

Detection of higher nonlinear harmonics of volume photorefractive gratings in reflection geometry

A comprehensive technique has been used to detect diffraction from the second and the third nonlinear spatial harmonic components, along with the fundamental harmonic of volume photorefractive gratings recorded in a channel waveguide in a LiNbO₃ substrate. For the first time to our knowledge, efficient diffraction from the higher spatial harmonic components of a photorefractive grating has been detected in reflection geometry. The dependence of a Bragg wavelength shift on the order of nonlinearity is also reported.     

High-efficiency holographic volume index gratings in DR1-dye-doped poly(methyl methacrylate)

Holographic volume index gratings with high diffraction efficiency (greater than 80%) are recorded in a thick sample of Disperse Red 1-doped poly(methyl methacrylate) with red light (647 nm), which is far away from the absorption peak (488 nm) of the material. Measurements of photoinduced birefringence and polarization holography recording confirm that the azo-dye reorientation mechanism is responsible for the grating formation. Energy coupling between the two writing beams is observed even when the incident beams have equal intensity.     

Photoinduction of surface-relief gratings during all-optical poling of polymer films

Using the all-optical poling method, we observed the formation of a surface-relief grating (SRG) in an amorphous polymer film containing azo dye molecules in side chain positions. The experiment consists of a seeding-type process. We used a recently described experimental setup that permits a periodic nonlinear pattern to be produced by the index dispersion of glass. The particular configuration permits photoinduced translation diffusion of the azo chromophores to be observed as the origin of the SRG formation. Analyses of the gratings recorded by use of s (TE) and p (TM) polarization of the writing beams are conducted by atomic-force microscopy. The effect is attributed to mass transport from regions of high isomerization activity to regions of lower activity.     

Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on the birefringence and surface relief grating properties

The polarization properties of the optical set-up used for holographic recording of diffraction gratings on azopolymer thin films are analyzed. The state of polarization of circularly polarized light is fully analyzed after reflection on a mirror at various incidences (Lloyd-mirror set-up). The Stokes analysis is performed using a photopolarimeter and the phase shift, the ellipticity and the azimuth orientation are compared with those calculated from Fresnel formulae. At large angles of incidence, an initially right circularly polarized (RCP) beam becomes elliptically polarized with an azimuth of nearly +45°. From these results, holographic diffraction gratings are recorded on an azobenzene-containing polymer thin film using (i) co- and contra-circularly polarized beams and (ii) a right circularly polarized beam interfering with a +45° linearly polarized light beam. Using Jones-matrix formalism, the polarization states of the diffracted orders from the birefringence (Δn) and the surface-relief (2Δd) gratings are derived and compared with experimental measurements. Finally, the induced local birefringences and surface-relief amplitudes are discussed in connection with atomic force microscopy measurements. The diffraction efficiencies obtained under the (+45°+RCP) and (LCP + RCP) (where LCP = left circularly polarized) configurations are thus compared and discussed. Received: 5 October 2001 / Revised version: 26 November 2001 / Published online: 17 January 2002     

Direct fabrication of surface-relief grating by interferometric technique using femtosecond laser

A surface-relief grating is a key element in optical communication and opto-electronic integrated devices. To date, many techniques for fabricating surface-relief gratings have been reported, but the present techniques still have many limitations and disadvantages. In this paper we present a new optical configuration to imprint a surface-relief grating by two-beam interferometry using a femtosecond laser. A relatively simple set-up is proposed in order to generate two parallel laser beams and then focus them by a common focusing lens to obtain an interference pattern. With the use of the common focusing lens, the two parallel beams will interfere exactly at the focal plane. This new optical set-up not only facilitates the alignment but also enhances the tunability to obtain different grating periods. Experimental results on solid copper targets are presented. The grating surface morphologies are studied by a scanning electron microscope and the grating relief profiles are characterized by an atomic force microscope. The prominent experimental results obtained have verified the feasibility of the new technique. In addition, the influence of laser fluence and pulse number on the surface morphology is presented. PACS 42.15.Eq; 42.25.Hz; 42.62.Cf     

Holographic grating based Ebert spectrograph

In this paper we discuss the aberration properties and design procedure of in-plane Ebert spectrograph using conventional as well as holographic diffraction gratings. In both cases the gratings are situated at the well-known √3-position so that the spectrum can be recorded on a flat surface. It has been found that the holographic grating system has better resolution than the conventional grating system. The design parameters of a medium sized holographic grating spectrograph in which a concave spherical mirror is mounted in the off-axis configuration have been specified. The performance of the spectrograph has been evaluated by plotting spot diagram.