On the Fresnel diffraction pattern of phase holographic gratings

The Fresnel diffraction pattern of phase diffraction gratings is studied on the example of idealized sinusoidal relief-phase plane holographic thermoplastic gratings. It is shown that, in the region of low spatial frequencies, which are more than two times lower than the inverse wavelength of the reading coherent radiation, the intensities of the main diffraction maxima, the diffraction efficiency, and the light-scattering power are independent of the spatial frequency of the phase gratings under investigation, which are characterized by a sinusoidal law of modulation of the reading-radiation phase. It is established that the range of spatial frequencies at which a plateau is observed in these dependences increases with decreasing amplitude of the phase modulation of the reading light. These dependences are also observed to have similar character for the thermoplastic holographic gratings under study. Calculations were performed to analyze the influence of real profiles of thermoplastic strain on the diffraction efficiency and light-scattering power of such gratings. On the basis of analysis of the results obtained, recommendations on using holographic and raster techniques of recording data on phase carriers are given that make it possible to improve the quality of the restored optical image.     

Fresnel formulation for multi-element lamellar diffraction gratings in conical mountings

A formulation of the modal method for multi-element dielectric lamellar diffraction gratings is presented. It combines the conventional semi-analytic Kronig-Penny formulation with a Fresnel scattering matrix approach to the solution of the diffraction problem. The theory is intuitive, applicable to complex geometries, and provides insight into diffraction grating physics. With the Fresnel matrix extensions the method potentially has greater generality than other formulations, and is applicable to non-trivial waveguide problems, such as characterizing the coupling between 1D photonic crystal waveguides. A numerically stable way of using the modal method for multilayer stacks of lamellar gratings is described.     

Fresnel formulation for multi-element lamellar diffraction gratings in conical mountings

A formulation of the modal method for multi-element dielectric lamellar diffraction gratings is presented. It combines the conventional semi-analytic Kronig–Penny formulation with a Fresnel scattering matrix approach to the solution of the diffraction problem. The theory is intuitive, applicable to complex geometries, and provides insight into diffraction grating physics. With the Fresnel matrix extensions the method potentially has greater generality than other formulations, and is applicable to non-trivial waveguide problems, such as characterizing the coupling between 1D photonic crystal waveguides. A numerically stable way of using the modal method for multilayer stacks of lamellar gratings is described.     

Optical testing of ultrasonic phase gratings using a Fresnel diffraction method

A simple optical method is proposed for studying the Raman-Nath parameter of plane, sinusoidal, ultrasonic beams. The Fresnel diffraction field of a continuous ultrasonic grating illuminated by a collimated laser beam is measured by a photodetector placed mid-way between the self-image planes of the grating. Measurement of the amplitude of the fundamental of the output signal enables the absolute determination of the depth of phase modulation. A comparison of the proposed method with the techniques discussed in the literature is presented.     

An indirect algorithm of Fresnel diffraction

An indirect algorithm for Fresnel diffraction calculation at any distance is presented in this paper. Using this indirect algorithm, the Fresnel diffraction on a near plane can be realized in two steps, the first is to acquire the diffractive field on a far field and the second is to obtain the diffractive field on a near plane using an inverse Fresnel integral. Compared with conventional algorithms, this algorithm is valid at any range of distance. The sampling theorem, as the basis of this indirect algorithm, is discussed in detail. Theoretical calculations show good agreements with experimental results.     

An experimental study on the validity of diffraction theories for off-Bragg replay of volume holographic gratings

We perform experiments on the direction of the diffracted beam in off-Bragg replay for volume holographic gratings. The obtained results clearly verify the assumptions made by the first-order two-wave coupling theory for one dimensional lossless unslanted planar volume gratings using the beta-value method rather than Kogelnik??s K-vector closure method.     

Partially coherent Fresnel diffraction by a slit aperture. III. Fresnel diffraction patterns

The intensity distribution in the Fresnel diffraction pattern of a slit aperture illuminated with partially coherent light is obtained, as a function of the coherence condition across the aperture, by evaluating the formula developed in a previous paper. It is shown that the Fresnel diffraction pattern is affected by the coherence condition of illumination across the aperture and its form.     

圆孔的菲涅耳衍射

得到了圆孔菲涅耳衍射光强分布的表达式,此式由贝塞尔函数的数列(或Lommel函数)给出,因此很容易利用普及的数学软件算出结果.并且利用CCD照相机量度了衍射光强分布,与运算的结果作了比较,也与Burch在1985报导的结果作了比较.     

Correlation and fractal properties of speckles in the extremely deep Fresnel diffraction region

Based on the Kirchhoff approximation and the theoretical analysis of the random light fields,the speckle intensity distributions in the extremely deep Fresnel diffraction region are simulated.The fractal property of the speckles as well as the relation between the speckle intensity distribution and the corresponding random surface is investigated.We design a microscope system to detect experimentally the speckles in the extremely deep Fresnel diffraction region,and the experimental results prove the conclusions drawn from our simulations.     

An image deblurring method using diffraction gratings

A method of image deblurring is described, in which the restoration filter is derived from Ronchi rulings. Although two-dimensional spatial filtering is used, the method employs a line source, resulting in significant noise reduction. Experimental results are given.     

用菲涅耳理论研究衍射光路可逆性

 用菲涅耳衍射理论研究了光栅及双光栅成像系统衍射光路的可逆性。首先用菲涅耳衍射理论分析单片光栅衍射光的复振幅分布,根据其复振幅分布的相位关系研究其可逆性;再根据单片光栅衍射光路所具有的结论来分析双光栅衍射成像效应的衍射光路可逆性,得到了光栅衍射光路及双光栅成像系统光路具有部分可逆性;应用衍射光路的部分可逆性诠释了双光栅成像效应的本质及光栅的汇合光谱特性是色散光谱特性的逆效应,并根据衍射光路具有部分可逆性的特性实现了图像处理。     

树状分形结构形成过程的实验研究

对大量金属小球在强电场作用下运动形态的演化全过程用联机摄像装置进行了实时拍摄,通过用Sandbox方法计算其稳定状态的分维数,系统地研究了分维数随电压的变化关系.结果表明：在一定电压范围内金属小球聚集体通过自组织过程形成稳定的树状分形结构,其分维数随外加电压的增加而减小.该结果对研究耗散结构的形成机理和外界动力对耗散结构的形貌影响具有参考价值. 关键词： 分形生长 自组织过程 树状结构 分维数     

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.     

Protecting MRI rooms by dielectric diffraction gratings

Nowadays in order to protect against the waves available in surrounding MRI rooms we use mu-metal. We suggest to use 1D dielectric gratings to protect MRI rooms from surrounding mobile waves. Hence, we present a grating with maximum reflection by RCWA method.     

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.     

亚微米光栅零级衍射特性的数值研究

用耦合波理论分析了亚微米光栅对光波场的衍射作用,给出了在TE和TM偏振入射条件下矩阵形式的耦合波方程,研究了光栅在TE偏振入射条件下可见光波段内的反射和透射零级衍射特性。亚微米光栅零级衍射效率是波长、偏振和入射角的函数,在不同照明、观察和光栅参数条件下,光栅零级衍射具有非常复杂的光谱结构,经过适当的优化光栅参数,零级衍射具有许多独特的衍射特性,在许多应用领域具有广泛的应用前景。     

圆形余弦光栅菲涅耳衍射场的研究

基于波前相因子判断法并考虑到圆光栅孔径的影响,揭示了圆形余弦光栅的衍射场含有3种成分,它们是均受限于圆形孔径的平面衍射波、发散球面衍射波和会聚球面衍射波;分别给出了这3种衍射场的积分表达式,进而导出了沿轴的衍射场复振幅分布的3个公式,并显示了相应的沿轴衍射场实振幅分布曲线,得到了实焦斑的横向半值线宽和轴向半值线宽公式.本研究为圆形余弦光栅用于聚焦和成像技术进一步提供了一个理论基础.     

Determination of refractive indices of liquids by Fresnel diffraction

We demonstrate an easy, reliable, applicable, and sensitive method to measure refractive index of liquids by using Fresnel diffraction. In this method a cylindrical glass rod, in general, or an optical fiber in special case, is immersed into a liquid. Physical parameters of the rod, like radius and refractive index, should be well known. Then, the normalized intensity distribution on the Fresnel diffraction pattern of a plane wave diffracted from the immersed fiber is measured. Thereafter, refractive index of the liquid is evolved by the least-square method. This method applied to determine the refractive index of four liquids; pure water, 2-propanol (isopropanol), acetone and methanol. Index of refraction of each one has been acquired for four visible wavelengths. A theoretical approach and experimental results is presented.     

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.