Thick grating analysis of interferometrically produced waveguides

The thin grating decomposition method of thick grating analysis is used to analyze guiding effects in thick phase gratings having sinusoidal refractive index modulation.     

The multiwave regime of light diffraction and focusing effect in volume phase gratings

Some pecularities of multiwave light diffraction in optically thin and thick phase unslanted gratings have been considered. An approximate solution of the wave equation is derived by the eiconal method. The solution is valid for gratings which are both optically thin and thick. This is verified by comparison of approximate solutions with numerical calculations. A range of parameters is found where the solution gives a reliable result. It has been found that the phase grating has the property of focusing light in planes with a maximum value of refractive index if the grating thickness is close to the focal distance introduced.     

声表面波在厚金属栅阵中的耦合模参数

提出了一种研究声表面波在压电晶体厚金属栅阵中传播特性的理论方法。将有限元和声表面波在周期栅阵中的变分原理分析方法相结合,在陈东培和H.A.Haus理论基础上、用有限元分析金属短路栅对声表面波传输特性的影响,将力学负载贡献的耦合模参数用有限元矩阵表示,使其适用于声表面波在厚金属或任意形状栅条中传输情况,给出了具体理论分析方法和相应的理论表达式。最后,具体研究了几种压电晶体上金、铝或银栅阵中声表面波的传输特性,通过数值计算给出了声表面波的耦合模参数。      

Microphotometric investigations of thick refractive index gratings in photorefractive crystals

Transmission microphotometry is used as a new tool for the investigation of the holographic writing process of thick refractive index gratings. Theoretical results on the origin of the contrast formation are discussed. They are experimentally confirmed by rocking curves of thick refractive index gratings in doped LiNbO₃ crystals.     

利用傅里叶模方法分析厚层光刻胶内衍射光场

建立了描述厚层光刻胶内衍射光场形成过程的物理模型,并利用傅里叶模方法模拟计算和分析了其内部衍射光场分布。该方法考虑了其界面反射、透射及光刻胶复折射率在空间上的缓慢变化对衍射光场的影响,采用该方法模拟光刻胶内衍射光场具有数值计算结果准确、计算速度快的优点。对厚层光刻胶折射率在几种特殊分布情况下衍射光场分布的数值模拟表明,衍射光场与其复折射率的空间分布有关。由于厚层光刻胶折射率在空间上呈缓慢变化的特点,为降低其数值计算量和编程难度,可以将厚层光刻胶近似为折射率随曝光时间变化的光栅。     

Extension of Reflectance and Transmission Coefficient Matrix to C-method for study of periodic multilayer system

The C-method is one of the most efficient and versatile method designed for diffraction gratings. The boundary conditions of the grating can be greatly simplified when the coordinate systems coincide with the surfaces of the grating. Reflectance and Transmission Coefficient Matrix (RTCM) with clearly physical concept is a powerful propagation algorithm proposed for steady and fast calculation of multilayer gratings. In this paper, the C-method is extended to treat the multilayer diffraction grating with the identical or nonidentical surface shapes. Numerical examples including diffraction efficiencies of both dielectric and metallic grating are presented. In addition, the excellent convergence for various adjacent-heights and diffracted orders of our propagation algorithm for TE and TM polarizations is also included.     

A heuristic method to simulate the pulse propagation in nonlinear fiber bragg gratings

In this paper we simulated the pulse propagation and the switching effects in nonlinear fiber Bragg gratings using a combination of Fourier series analysis technique and Jacobi iterative method. The effects of nonlinearity and dispersion on the pulse propagation have been studied extensively. An all optical self switch was designed by this simulation. This switch is operated based on the input power.     

Nearly-analogue blazed phase grating using high birefringence liquid crystal

Diffraction of liquid crystal gratings has been thoroughly studied for many applications such as diffraction optics, optical processing, and spectral analysis. In pure optical processing one varies the direction of propagation of light beam without any mechanical adjustment. In this work we propose a beam steering device using highly birefringent liquid crystal material. Using a highly birefringent material one can reduce the LC layer thickness needed to achieve 2π of phase modulation and thus reduce the fringing effect caused by deformation of the electric field at the edge of the pixel. Here, we present 1.5-μm thick, high-resolution diffraction grating with non-detectable fringing.     

Accurate calculation of reflectance spectra for thick one-dimensional inhomogeneous optical structures and media: stable propagation matrix method

Numerical instability is usually observed when the propagation matrix method is used to calculate the reflectance and transmittance spectra for the thick one-dimensional inhomogeneous optical structures and media. To remove this numerical instability we applied two procedures, the normalization and the singular-value decomposition, for the propagation matrix and the matrix involved in calculating the matrix of reflection coefficients, respectively. Examples of a cholesteric liquid crystal and a helical structure of ferroelectric liquid crystals with a twist defect show that the modified propagation matrix method is able to accurately calculate the reflectance spectra for thick structures.     

部分相干同步辐射照射下光栅分数塔尔博特效应

基于高斯谢尔光束的相干模式分解理论和波动光学,建立了部分相干同步辐射硬X射线光束通过光学器件的传播模型。模拟了微聚焦X射线光束照射下光栅的分数塔尔博特效应,得到了聚焦光束的光强分布和相干特性变化,并分析了散焦光束入射下的光栅自成像。然后通过模拟准直光束入射下的光栅塔尔博特效应,得到了不同传播距离处自成像条纹的变化情况,分析了影响光栅自成像条纹形状的因素。通过光栅衍射条纹测量同步辐射相干度,发现对矩形相位光栅来说,应该对衍射图样进行傅里叶分解,求出各级傅里叶系数随传播距离的变化曲线,从而得到入射光束相干特性。     

Formation of pores in the optical fiber exposed to intense pulsed UV radiation

A new method of forming refractive index gratings (type-IIA Bragg gratings) in the optical fiber by exposing it to intense UF laser radiation is suggested. Central in this method is the generation and propagation of micropores in the parts of the fiber where mechanical stresses are localized. It is shown that such parts are the center of the core and the core-cladding interface. The temperature of the radiation-heated germaniumdoped core is found experimentally and theoretically. Thermal stresses arising in the heated fiber are calculated. A theory of cracking and pore formation in the fiber exposed to intense laser pulses is worked out. The pore size distribution, pore formation and growth rate, and pore density versus time of laser action are estimated.     

Electrical characteristics of the waveguide grating system

Electromagnetic wave propagation is conside-red through a waveguide system consisting of arbitrary number of short-period gratings (i.e. whose period is much shorter than the wave-length). We assume that gratings are formed by ideal conductors having arbitrary cross-section. In order to "stitch" together the fields on gratings, equivalent boundary conditions are used.We have analyzed and studied experimentally the electrical characteristics of an adjustable frequency filter. The filter consists of three short-period gratings formed by conductors with circular cross-section.Experimental results are in good agreement with theory.     

Thick grating focussing-device-design using poynting-vector-optics

Novel thick grating focussing and de-focussing devices are described which employ uniform phase gratings with special boundary shapes. The analysis used is based upon an eigenmodal approach to Kogelnik's coupled-wave equations, akin to the dynamical theory of x-ray diffraction. The relationship between the direction of phase progression of the coupled-waves at Bragg incidence, and the direction of the Poynting vector is carefully delineated. As a consequence, a new technique-Poynting Vector Optics — is suggested as potentially an important means of designing thick gratings to fulfil certain beam processing roles, especially in integrated optics applications. The two-dimensional coupled-wave equations are briefly employed to illustrate the effectiveness of a particular focussing device.     

Frequency Selective Properties of Two-Dimensional Dielectric Gratings: TE- and TM-Polarizations

This work analyzes the propagation characteristics of electromagnetic waves and the frequency selectivity of dielectric gratings with periodicity in two dimensions, having in mind their application as dichroic surfaces in the millimeter wave band. The moment method and the Green's functions, along with the volume equivalence theorem are used. Particular cases were analyzed to compare with results available in the specialized literature and agreement was observed. This work gives evidence that the inclusion of the periodicity along a second dimension allows an additional adjusting parameter of the frequency selective characteristics for the design requirements of dielectric gratings.     

共振域矩形介质光栅的逆向设计

采用模态法研究了共振域光栅分束器及闪耀光栅等光学器件的设计原理及逆向设计方法,给出了-1级非偏振闪耀光栅的典型设计示例。研究表明,自准直角入射时,光束在光栅内传输将激发产生离散模,通过调节离散模透过光栅传输时的累积相位差,可对衍射光进行调控,实现偏振(非偏振)分束、偏振(非偏振)闪耀等功能。采用严格耦合波法对基于模态法逆向设计的-1级非偏振石英闪耀光栅的几何参数进行验证,计算结果显示两者非常吻合,证明了该方法的正确性。     

Application of the beam propagation method to diffused transmission gratings

In this paper results for the diffraction characteristics of phase gratings calculated by the beam propagation method and by a rigorous integral equation method are presented, with the latter results serving as a reference. The configurations under consideration have refractive index changes which are realistic for ion exchange processes in glass. Thus, multiple reflections have only little influence which makes the beam propagation method applicable to the problem. Typically, the diffraction efficiencies computed by both methods differ by less than 2%. In contrast to the integral equation method, the beam propagation method works with a definable lateral field profile, enabling the modelling of a grating within a complete device design including the near field pattern. This revised version was published online in November 2006 with corrections to the Cover Date.     

Ray picture of diffraction gratings

We elaborate on a geometrical picture of diffraction gratings. Exact paraxial propagation including coherence effects is obtained by allowing the geometrical rays to transport Wigner function instead of simply specific intensity. We apply this formalism to perfect and less than perfect gratings, illuminated by plane and Gaussian waves.     

Analysis of multiplexed holograms stored in a thick PVA/AA photopolymer

Multiplexing many holograms in photopolymers over 500 μm thick poses many problems associated with Beer’s law. In fact, the commercial holographic films (Aprilis and Inphase for example) are around 300 μm thick. For this range of thickness of absorbent photopolymeric materials, the gratings are recorded using all the thickness of the layer. Since the optical thicknesses of the multiplexed gratings are similar, it is easy to obtain an optimized time schedule to maximize the capacity of the material. For large thicknesses, the different effective optical thickness of each hologram requires an accurate prediction of each effective optical thickness in order to determine the minimum separation necessary between two consecutive multiplexed holograms. In this study, we have checked the experimental utility of the schedule model presented in a previous study to predict the multiplexing process of many gratings in a PVA/acrylamide photopolymer.     

Numerical study of perfectly conducting wire gratings in the resonance domain

Using the Hamiltonian method that we have recently proposed [1, 2] and which is described in the IEEE transactions on antennas and propagation [3], we give some theoretical data related to perfectly conductor wire gratings. Phase-shift and efficiency are given for several diffraction orders, for four shapes of cross-section, and for both fundamental cases of polarization.