Noninvasive characterization of continuous-profile blazed diffraction gratings

Smooth, continuous-profile diffractive optical elements and other regular microstructures demand advanced characterization methods. Here the problem of reconstructing the profiles with optical scatterometry is addressed for the first time to our knowledge. We represent the profile of a blazed grating with an analytic Chebyshev series. The coefficients of the series are inferred from the far-field diffraction pattern, when the grating profile is illuminated with coherent light. An advanced neural-network model is used as a nonlinear statistical estimator. The reconstruction error is found to be less than 4% as normalized to the depth of the profile, even with realistic measurement errors included in the simulations.     

Effect of fabrication errors in channel waveguide Bragg gratings

The spectral performances of nonideal rectangular Bragg gratings, integrated in a rib waveguide, are analyzed by a multilayer approach based on the effective-index method. The effects of errors on the photolithographic definition of the grating, that is, period and shape, and of errors on the control of etching depth are investigated. Also the influence of the stitching error, which is unavoidable when the grating is realized by means of electron-beam photolithography, is addressed. A novel analytical approach that extends coupled-mode theory to the analysis of real gratings is also presented.     

Transmittance analysis of diffraction phase grating

In order to accurately analyze and design the transmittance characteristic of a diffraction phase grating, the validity of both the scalar diffraction theory and the effective medium theory is quantitatively evaluated by the comparison of diffraction efficiencies predicted from both simplified theories to exact results calculated by the rigorous vector electromagnetic theory. The effect of surface profile parameters, including the normalized period, the normalized depth, and the fill factor for the precision of the simplified methods is determined at normal incidence. It is found that, in general, when the normalized period is more than four wavelengths of the incident light, the scalar diffraction theory is useful to estimate the transmittance of the phase grating. When the fill factor approaches 0.5, the error of the scalar method is minimized, and the scalar theory is accurate even at the grating period of two wavelengths. The transmittance characteristic as a function of the normalized period is strongly influenced by the grating duty cycle, but the diffraction performance on the normalized depth is independent of the fill factor of the grating. Additionally, the effective medium theory is accurate for evaluating the diffraction efficiency within an error of less than around 1% when no higher-order diffraction waves appear and only the zero-order waves exist. The precision of the effective medium theory for calculating transmittance properties as a function of the normalized period, the normalized groove depth, and the polarization state of incident light is insensitive to the fill factor of the phase grating.     

远红外光光栅光谱仪测量误差分析

采用平面闪耀光栅作为光谱元件的远红外光谱测量原理,分析了四种主要的重复性误差:光栅常数制造误差、零点标定误差、转角测量误差、入射光束与衍射光束的夹角测量误差。 并分别以112.5mm、40.05mm、25mm和12mm的四种闪耀波长为例,计算出了它们的误差传递系数曲线,根据误差传递系数对光谱仪进行误差分配,分析和计算表明:当光栅转角测量精度为1,光栅常数误差为0.5mm时,光谱仪可以满足l/100的波长测量误差要求和l/200的波长重复性测量误差要求。     

用于分频的闪耀光栅设计及衍射行为研究

详细地介绍了用于分频的闪耀光栅设计方法 ;推导了影响元件性能的衍射效率公式 ;并研究了纵横向工艺误差对其衍射行为的影响。模拟结果显示在 8%和 5%纵横向相对误差范围内 ,该闪耀光栅具有良好的分色效果。     

Analysis and design of a concave diffraction grating with total-internal-reflection facets by a hybrid diffraction method

A novel hybrid diffraction method is introduced to simulate the diffraction and imaging of a planar-integrated concave grating that has total internal reflection (TIR) facets. The Kirchhoff-Huygens diffraction formula is adopted to simulate the propagation of the lightwave field in the free-propagation region, and a rigorous coupled-wave analysis is used to calculate the polarization-dependent diffraction by the grating. The hybrid diffraction method can be used to analyze accurately the imaging properties as well as the polarization-dependent diffraction characteristics of a concave grating. The dependence of several merit parameters of a concave grating with TIR facets on its basic geometric parameters is studied. Compared with one with metallic echelle facets, a concave grating with TIR facets shows a much lower polarization-dependent loss. Since more performance specifications can be considered in the design of a concave grating than with the conventional scalar method, design error can be reduced greatly with the present hybrid diffraction method.     

Method for designing phase-calculation algorithms for two-dimensional grating phase-shifting interferometry

We propose a design method of phase-analysis algorithms based on two-dimensional grating phase shifting for Talbot interferometry, Talbot-Lau imaging, or the Ronchi test. These algorithms are designed to separate the two orthogonal shearing wavefronts and eliminate error effects of unwanted diffraction orders, simultaneously. Taking the effect of multidiffraction into account, moving the two-dimensional grating along a certain pass leads to a series of phase-shifted interfrograms, from which two orthogonal shearing wavefronts are derived, for the tested wavefront to be retrieved. The designing process is demonstrated, and the residual errors are analyzed via simulation works and experimental comparison.     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

LWIR亚波长铝/硒化锌光栅偏振器设计

为提高长波红外偏振成像系统中偏振器件性能,本文通过分析光栅材料及结构参数对光栅偏振性能的影响,设计并优化了一种双层材料构成的亚波长光栅。该光栅为矩形形貌,光栅区由铝与硒化锌构成,两种材料的厚度分别为0.6 μm和0.4 μm,光栅周期1 μm,占空比50%。利用严格耦合波理论分析并计算该结构光栅的衍射效率,7~15 μm波段的光以0~60°入射后其0级横磁模透射率达到87.54%以上,消光比超过47 dB。该光栅在10.6 μm的测试波长下,TM透射率高达90.80%且具有50 dB以上的消光比,相比槽深相同的单层铝光栅,偏振透过率明显提高。仿真结果显示,该光栅在整个宽长波红外波段具有良好的偏振性能。     

衍射频谱法测光栅膜层厚度

根据傅立叶光学理论从光栅的衍射频谱中可以反推光栅本身的多种信息,包括其形貌特征。 利用矩形相位光栅的傅立叶变换,推导出零级和一级衍射光强和矩形相位光栅膜层厚度之间的函数关系,据此可在测得零级和一级次光强后,推算出光栅膜层厚度。以台阶仪作为标准,该方法的测量误差在4%以内。     

Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.     

Crossed phase gratings with diffractive optical elements

Orienting two identical or complementary diffractive gratings with a small angle between the grating grooves allows a new crossed-grating device to be constructed. This device has an effective profile that varies locally. For understanding the effects of this variation and the diffraction efficiency of the gratings, the local profiles were correlated with the moiré period of the crossed-grating system by use of various techniques. Asymmetric intensity behavior in the first order of the crossed gratings was seen. Effectively, the diffraction efficiency of the crossed gratings yielded a response equivalent to that of a grating with variable blaze that could be useful in optical computing as a passive optical switching device. One of several models is described that creates greater asymmetric behavior.     

Diffraction patterns of binary liquid crystal gratings in homeotropic and hybrid geometries

We report on the diffraction properties of the binary liquid crystal (LC) gratings consisting of alternating homeotropic and hybrid domains. The measured diffraction patterns agree well with theoretical results in a comprehensive model with a linearly approximated phase profile around the domain boundary. It is found that the linearly distorted length is independent of the grating period and depends only on the cell thickness, the surface anchoring energy, and the elastic constants of the LC material. For the LC cell thickness of 5.9 μm, the linearly distorted length is determined as 2.12 μm. The binary LC grating devices are expected to play an important role in the area of optical data storage and optical information processing.     

Efficient detour-phase encoding of one-dimensional multilevel phase diffractive elements

We show that detour-phase encoding with a multilevel blaze structure as a carrier grating is especially suited to the implementation of diffractive elements with relatively high complexity in one axis. For our proposal the carrier grating is aligned perpendicularly to this axis. In this way the element can be encoded with a high space-bandwidth product and a high phase resolution by use of a moderate carrier frequency. Moreover, this frequency can be adjusted to isolate the reconstructed field from the noise resulting from high diffraction orders of the carrier grating or caused by etching errors during fabrication.     

High-efficiency diffractive waveguide lenses by parametric optimization

The first-order diffraction efficiency of a waveguide diffraction grating is maximized, for a wide range of grating periods, by optimization of the effective-index modulation profile. Three different values of effective-index modulation in the range of 0.02-0.11 are considered. The analysis is performed with the thin-grating-decomposition method. The results are verified by electromagnetic grating theory and applied to the construction of diffractive waveguide lenses with an improved overall efficiency. In the neighborhood of the optical axis, the optimized lens structure is a close approximation of a gradient-thickness Fresnel lens. Significant deviations from this shape appear when the local grating period reduces below ~ 15-25λ, where ~ is the wavelength of the guided mode. Near the edges of a high-numerical-aperture lens, where the local period is ~ 3-6λ, an approximate Bragg grating structure is obtained.     

Deformation of the modulation profile in phase holographic gratings

Among all the parameters that characterize a phase grating, the most difficult to control is the modulation profile of the refractive index. In fact, it covers many scalar parameters that are the Fourier coefficients of the profile. To study the influence of processing baths on the modulation profile, in phase holographic gratings made of dichromated gelatin, we have observed that the shape of the profiles obtained sometimes presents a slight concavity or a convexity in the middle, leading to an increase or a decrease in the diffraction efficiency. We present the experimental results and a numerical study in the form of a theoretical prediction, which confirms the experimental observations.     

Grating mosaic based on image processing of far-field diffraction intensity patterns in two wavelengths

A practical grating mosaic method is proposed based on quantitative image processing of three far-field diffraction intensity patterns in two wavelengths. This method aims at making a perfect mosaic of two planar gratings that can substitute for a single and larger grating without introducing wavefront aberration at any wavelength. The zeroth-order and first-order far-field patterns of one wavelength are analyzed for separating and eliminating the angular mosaic errors. The first-order far-field patterns of two wavelengths are applied for separation of the lateral and longitudinal phase errors. Then the three patterns are considered together to enlarge the target range of coarse adjustment required for further fine adjustment in longitudinal position. Experimentally, angular and positional detection sensitivities of less than 6 microrad and 14 nm were achieved, respectively, and the periodicity in positional adjustment was checked, which departed less than 1.8% from the theoretical period. The performance of the perfect mosaic grating was diagnosed with the far-field diffraction intensity pattern in a third wavelength, and the necessity for a perfect mosaic was verified.     

基于球杆仪和光栅尺的工作台精度调整

用球杆仪和光栅尺同时测量了两轴联动精密工作台的走圆运动．结果显示,光栅尺的主要误差源是测量噪声和定位误差,球杆仪的主要误差源是定位误差．尽管对于单轴实时位置反馈来说,光栅尺的测量精度已经足够,但是两个方向光栅尺的测量数据不能反映两轴间的相对精度．通过对光栅尺和球杆仪测量的工作台走圆运动测量数据的分析,建立了测量系统的数学模型,在此基础上解耦并识别出了球杆仪和光栅尺的定位误差．提出了根据光栅尺倾角误差实现工作台精度调整的策略．     

Optimization of diffraction grating profiles in fabrication by electron-beam lithography

We propose a new design method for periodic diffraction gratings to be fabricated with direct-writing electron-beam lithography. When the grating has a small period, the proximity effect of electron scattering restricts the grating profile after developing. Our design method optimizes the electron-dose profile and grating profile simultaneously to obtain the desired diffraction efficiency under the restriction of the proximity effect. The optimization is made with rigorous electromagnetic grating analysis and the resist development simulator. When we designed the diffraction grating with a period of 1.0 microm to obtain the highest efficiency of the first-order diffracted light of a 633-nm wavelength, the calculated grating profile was really different from the profile optimized only with rigorous electromagnetic grating analysis. Moreover, the diffraction grating of the electron-beam resist was fabricated according to the simulation result. The estimated diffraction efficiency was 82%, and the measured efficiency was 70%.     

Relation between optical Fresnel transformation and quantum tomography in two-mode entangled case

In many applications of phase-shifting interferometry (PSI) the actually recorded object wave is the diffraction field of an object surface. In this case not only the phase error but also the amplitude error in the retrieval process have effects on the object wave reconstruction in its original plane. In this paper, for the first time that we know, the amplitude errors in wave reconstruction in PSI are discussed systematically. Some general relations between the amplitude errors and the phase errors for three commonly encountered error sources, namely the phase shift error, the light source intensity fluctuation and the detector nonlinearity, are revealed. The analytical expressions of the amplitude and phase errors for six frequently used algorithms in PSI are derived. The statistical variances of the two kinds of error are introduced to describe the overall performance of these algorithms and are quantitatively calculated. A series of computer simulations are also given as a verification of our analyses. These results can be used for evaluating the complete wave errors in PSI and developing new methods for their correction.