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.     

Attenuated thick hologram gratings. Part I: Diffraction efficiency

In this paper volume hologram reconstruction is considered as an electromagnetic scattering problem that leads to a characteristic integral equation. Our main attempt is the calculation of diffraction efficiency for attenuated gratings, that is compared with those of unattenuated gratings, to point out the influence of grating attenuation. In this respect the solution in the first Born approximation is found to be sufficient for diffraction efficiency calculations of attenuated gratings.     

光折变光栅在超短脉冲光照射下衍射的研究

利用Kogelnik单色光在体光栅中衍射效率公式推导出超短脉冲光读出稳态光折变体光栅时的衍射光频谱表达式,并在此基础上导出了脉冲光读出时的总衍射光强及总光强衍射效率.研究发现衍射光的频谱分布、总光强及衍射效率与光栅周期Λ、光栅厚度d和读出光脉冲宽度Δτ有密切的关系.通过调整这些参量,光折变光栅可以对入射的超短脉冲光实现不同程度的滤波作用.该结论可用于超短脉冲的整形研究.     

体全息成像系统中非周期体光栅的深度选择性研究

由一束球面波和一束平面波或者两束球面波干涉所形成的体全息光栅,由于其光栅矢量在全息图体积内是随位置的变化而变化的,所以被称为非周期型的体光栅。主要研究了用于体全息三维成像系统的非周期体光栅的深度选择特性。根据叠加的原理,将非周期体光栅看作多个固定周期的基元体光栅的叠加,结合耦合波理论分析非周期体光栅的衍射特性。采用这一方法,利用Matlab软件模拟,研究了两束记录光夹角对所记录的非周期体光栅深度选择性的影响和在两束记录光夹角相同时,球面参考光体全息成像系统及平面参考光体全息成像系统深度选择性的差别,最后在光折变晶体材料中进行非周期型和周期型体光栅的记录和再现,对模拟结果进行了实验验证。     

Diffraction from angular multiplexing slanted volume hologram gratings

The diffraction characteristics of the volume holographic gratings made by multiexposures with angular multiplexing during its construction is investigated. Because of the reflection by the interface between the emulsion and the substrate or the air there is an extra unslanted periodic structure inside a slanted grating, it will affect properties of the slanted volume holographic gratings. When the angle between the surface of the substrate and the grating plane of the slanted grating is less than a certain value, an extra peak accompanying the main peak will appear in the diffraction spectrum. But, when the angle is larger than the certain value, one designed and expected main peak will disappeared while the extra peak is kept and observed. This phenomenon limits the capacity of the volume hologram for the application in wavelength-division multiplexing (WDM).     

Two-dimensional non-spatial filtering based on holographic Bragg gratings

The filter made up of two gratings performs as a two-dimensional non-spatial filtering. This paper reports that the volume Bragg gratings are fabricated by interfering two collimated coherent laser beams in photopolymer. Diffraction efficiency of a single grating is up to 78% in Bragg's condition, then a two-dimensional non-spatial filter, which consists of two volume Bragg gratings and a half-wave plate, enables the laser beam filtered in two dimensions with the diffraction efficiency of 54%. The Bragg's condition and effect of polarisation on performances of the two-dimension filter are also discussed.     

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.     

Profiled hologram diffraction gratings based on As2Se3 inorganic photoresist

We devised a method of producing blaze hologram diffraction gratings by transforming symmetric grooves of the original grating into asymmetric ones using an additional oblique irradiation by monochromatic or polychromatic light and a repeated chemical etching of the additionally irradiated grating. Photosensitive As₂Se₃ film layers are used as a photoconductive material for recording gratings. A numerical computer modeling of the formation of asymmetric grooves is conducted. The calculated shape of the groove profile is in good agreement with experimental data. The manifestation of asymmetry of the profile shape of the produced gratings in angular and spectral relations for their diffraction efficiency is considered. It is shown that by varying the parameters of producing the original gratings and the conditions of their additional treatment it is possible to obtain hologram gratings with the required profile shape and blaze angle. To whom correspondence should be addressed. Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 45, Nauka Ave., Kiev, 252028, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 4, pp. 587–590, July–August, 1999.     

Crystal diffraction grating in LiNbO3:Fe derived from interferometric volume holography

A 90° two-beam coupling configuration was used to store an image of an extended object in a 0.032 %wt iron-doped LiNbO₃ crystal. A volume hologram was thus generated, via the photorefractive effect, within the microstructure of the crystal. The time evolution of partial spatial erasure of the hologram under illumination was studied by capturing its reconstructed image on a digital camera and performing a two-dimensional inverse Fourier transform. This produced the refractive index grating created through interference of object and reference beams. The nature, intensity distribution and dimensions of the diffraction grating were derived in order to throw light upon the movement and mechanisms of charges, which create the index grating.     

光折变多重体光栅的制作及应用

根据光折变多重体光栅的滤波原理,在10×10×10 mm3的LiNbO3∶Fe晶体中利用循环曝光法写入了光栅波矢夹角为0.037°且衍射效率均衡的8重体光栅,实验上证实了光写入多重光折变体光栅应用于波分复用系统的可行性.利用LiNbO3∶Fe晶体制作了一个原理性双通道波分复用器,成功地实现了对相同方向入射的波长分别为635 nm和650 nm的两束光的有效分离,并根据布喇格条件,将光折变体光栅应用于光波波长的测量,测量精度可达10 pm量级.     

Volume holograms as frequency-selective elements

In this paper we investigate the possibility of using thick holograms as diffraction gratings. We compare the well-known parameters of the plane diffraction grating such as dispersion, efficiency, resolution, and others, with those for volume holograms. The calculations for the case of volume holograms are based on the theory of coupled waves. Experiments were performed with volume-phase holograms in transmission, stored in dichromated gelatine layers. The investigations show that the volume hologram fulfills two functions simultaneously. It acts as a spectral predecomposer and also as a high-resolving spectral apparatus.     

Diffraction properties of ultrashort pulsed beams with arbitrary temporal profiles by a reflection volume holographic grating

The diffraction properties of reflection volume holographic gratings are studied when the gratings are illuminated by an ultrashort beam with arbitrary temporal profiles. The modified Kogelnik's theory of coupled waves is used. Simple analytical expressions for spectral and temporal distribution of the transmitted and diffracted are obtained. The dependences of the diffraction bandwidth, the Bragg selectivity bandwidth and the total diffraction efficiency of the reflection volume grating on the temporal profiles of the input ultrashort pulse are investigated. Study shows that the bandwidth of the reflection volume holographic gratings varies with the grating parameters more slowly than the transmitting volume holographic gratings. For three different temporal profiles, numerical results about diffraction properties of the reflection volume holographic gratings are given and compared with the transmitting volume holographic gratings.     

体全息光栅线性记录折射率分布的修正

在讨论非线性记录体全息光栅的光谱特性时,发现一些文献在线性记录时折射率分布的表达式有些不妥.重新讨论了线性记录情况下折射率分布的表达式,引入了光束比和总光强折射率调制系数,用耦合波理论计算讨论了不同光束比和总光强折射率调制系数对光栅衍射光谱特性的影响.计算结果表明,光栅衍射光谱主峰峰值随总光强调制系数的减小而略有降低,主峰峰值随光束比减小下降得不大,带宽随总光强调制系数和光束比的减小而明显变窄,次峰峰值随总光强调制系数和光束比的减小而明显减小.     

Bragg diffraction of light by a set of parallel phase gratings: Analysis and applications

Bragg diffraction of light by a set of parallel phase gratings is considered, utilizing two-dimensional coupled-wave theory. The diffraction characteristics of a Bragg-type spatial light modulator are presented. It is shown that the resolution limit and the accuracy of spatial light modulation are determined by the geometry parameter of the grating. The results obtained are used for the choice of the design parameters of various optical Bragg processors.     

Simulation of diffraction from volume holograms

Coupled wave equations that consider two-dimensional distribution and phases of gratings are derived by using weak grating and slow varying approximation. The result of angular selectivity on rand binary data page shows that each minimum is nonzero and each maximum that is not the middle maximum is a little bit smaller than that on plane wave volume hologram. Angular multiplexing is also modeled using the same method, and the middle page is read out in two different angular spacings. The relationship about PSNR versus angular spacing at different multiplexing pages is analyzed to reflect crosstalk between pages. All simulative results show this method is effective for volume holograms simulation.     

A method for the evaluation of the grating envelope in volume holographic media

A novel method for measuring the three-dimensional spatial distribution of gratings in a volume holographic medium is described. In this method, the diffraction of a uniform probe light wave is measured as a function of the deviation (either in angle or wavelength) from the Bragg condition. The envelope function of the grating is obtained by solving the coupled wave equations inversely. Not only the amplitude but also the phase of the envelope function is obtained. This method allows for the depletion of the probe light wave in the hologram and is applicable to both dielectric (refractive index) and absorption gratings. The resolution and the maximum measurable depth in this method are discussed.     

Boundary effects in the diffraction of light by volume gratings: II. Phase transmission gratings

The two-wave approximation of the method of characteristics modes is used to analyze theoretically the diffraction of light by volume phase transmission gratings for arbitrary proportions between the average refractive index of the grating and the refractive indices of the ambient media. Simple expressions are derived for calculating the amplitudes of the diffracted waves in the case where the angle of incidence of the primary wave coincides with the Bragg angle. The roles of the front and back boundaries of the grating are discussed separately, and a new method for separating the contribution of the boundary diffraction, which is due to the periodic inhomogeneity of the grating boundaries, is proposed. The experimental possibility of selecting partial Bloch waves in the measurements of the diffraction efficiency of gratings that have high reflection coefficients of both boundaries is demonstrated.     

Diffraction patterns for a transmission volume hologram under Bragg mismatch

We have presented simulations and experiments for 2-dimensional diffraction distributions of a transmission volume hologram. We sample the input pattern with a few elementary points and calculate the diffraction of the corresponding elementary grating. The simulations can describe well the diffraction pattern obtained in the experiment and can be used to predict the tolerance for angular deviation of the reading beam. The tolerance for angular deviation depends on its direction. It is affected by the Bragg degeneracy. The simulation results provide a clear picture of the spatial tolerance for reading a transmission volume hologram.     

Contribution of Absorptive and Refractive Gratings to Mixed Holograms Using Xanthene-Dye-Doped Films

The contribution of absorptive and refractive gratings to a mixed hologram is investigated by means of two-wave coupling technique by moving a hologram. Polyvinyl alcohol films doped with xanthene-dyes such as erythrosin B,eosin Y, uranin and fluorescein which absorb an argon-ion laser light of 488 nm and 515 nm are used as hologram recording materials in our experiment. A simple model of the two-level one-step photo-bleaching well explains the growth of an absorptive grating and the refractive index and also the working wavelength dependence of growth of the refractive grating in the xanthene-dye-doped films.     

Phase diffraction gratings based on a Si(400) crystal

The X-ray optical properties of diffraction gratings fabricated on the basis of a Si(400) crystal with a period of D = 1 μm are studied by triple-crystal X-ray diffractometry. The diffraction gratings are manufactured both by silicon profiling during the process of plasma chemical etching and by forming a phase-shift grating on the surface of a Si crystal. The principal difference in the diffraction properties of these gratings is demonstrated. The presence of an Au phase-shift grating is shown to lead to the formation of a two-dimensional diffraction pattern, whereas Si profiling leads to the formation of only a one-dimensional diffraction pattern.