Rigorous analysis of diffraction gratings of arbitrary profiles using virtual photonic crystals

A new approach is developed to calculate diffraction efficiency for a dielectric grating with an arbitrary refractive index profile. By treating a one-dimensional grating as a segment of a virtual two-dimensional (2D) photonic crystal, we exploit a rigorous theory of photonic crystal refraction and calculate the diffraction efficiencies. We expand, analytically in many cases, the dielectric function of the grating into 2D Fourier series. We find the eigenmodes for the virtual photonic crystal, and then use these eigenmodes to match the boundary conditions by solving a set of linear equations. In two such simple steps, the diffraction efficiencies can be computed rigorously without slicing the grating into thin layers.     

Design of transmission blazed binary gratings for optical limiting with the form-birefringence theory

The structure of transmission blazed binary gratings for optical limiting is designed with the form-birefringence theory. This kind of grating has subwavelength features, can imitate the transmission blazed grating effectively, and has higher efficiencies than a transmission blazed grating with a subwavelength structure. The diffraction efficiencies are calculated and analyzed. For the normal incident light with 10.6 microm wavelength, the transmissivities for the designed grating at 0 degrees deviation angle for TE and TM polarizations are 0.05% and 5.09%, respectively, which are basically identical to the results of the finite-difference time-domain method. The diffraction efficiencies of the first transmitted order for TE and TM polarizations are 93.95% and 83.88%, respectively.     

Temporal superresolution: An application of frequency filtering by a grating in the resonance domain

Abstract

A diffraction grating in the resonance domain is known to exhibit significant change in diffraction efficiencies with a small change of the grating parameters. It is proposed that this property can be utilized for frequency filtering, when polychromatic light illuminates the grating. As an example, compression of a femtosecond optical pulse is numerically demonstrated with the concept of superresolution. Suppression of zeroth diffraction order by suitably optimized grating structure induces the pulse width to narrow. This scheme considerably simplifies existing optical pulse shaping systems.     

Wavelength multiplexing and demultiplexing with one single volume hologram in photorefractive crystal

Based on anisotropic diffraction of a volume phase grating in a photorefractive crystal, we theoretically discuss an optical multi- and demultiplexing scheme implemented by one single grating in photorefractive LiNbO₃ crystal. It shows that our scheme can simultaneously demultiplex 93 channels in the telecommunication wavelength around 1550?nm. Using only one grating to realize WDM can avoid the multiple exposure problems encountered by multiple hologram scheme. Moreover, in our scheme, the transmitted and diffracted beams are orthogonal to each other, thus we don't need to use a normal recording and readout structure. Our theoretical results can be used in the design of a WDM device.     

Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.     

聚合物网络稳定液晶光栅的制备与特性研究

将光敏预聚物单体与向列相液晶按一定比例混合,注入液晶盒;采用光掩模法,在紫外灯照射下,使混合物产生定域光聚合反应,形成聚合物网络稳定液晶光栅。利用光学显微镜和He-Ne激光器进行测试,实验检测结果表明,该光栅具有周期性的栅结构,且衍射效率具有先增大后减小电场调制特性,并利用折射率调制机理对该现象进行分析。     

Extraordinary magneto-optical effect of transmitted wave phase change in periodic diffraction structures

Based on the results of electromagnetic simulations for a dielectric structure comprising a grating over a homogeneous layer, a new magnetooptical effect is predicted according to which the phase of the transmitted zeroth order of diffraction must exhibit resonant variation during a change in the magnetization of the material. The structure is magnetized in the plane of the grating, in a direction perpendicular to its grooves. Since the magnitude of this effect is greater by several orders than that of the analogous effect for a homogeneous magnetized layer, the new effect is called extraordinary. The phenomenon is given a theoretical explanation based on a resonance excitation of an eigenmodes in the structure and the dependence of the mode frequency on the magnetization. It is shown that a large change in the phase of the transmitted order of diffraction is achieved at a certain ratio of the resonant and nonresonant diffraction processes.     

Analysis of the diffractional properties of dual-period apodizing gratings: theoretical and experimental results

We present an analysis of the diffractional properties of dual-period apodizing gratings. In a previous paper we used these components to obtain single-lateral-mode and dual-longitudinal-mode emission from a broad-area diode laser. We now calculate the diffracted field for a monochromatic beam incident on the grating by using an analytical model. Predictions of the model are compared with experimental measurements made with several dual-period gratings. We also discuss the situation in which a dual-period grating is used as an external coupler of a diode laser in a two-wavelength emission regime.     

基于激光诱导表面周期结构的微纳防伪结构色

激光诱导表面周期结构由于其周期相关的光栅衍射特性在明场下显示出鲜艳的结构色,备受研究人员的广泛关注,而微纳结构在显微镜暗场显示的颜色通常容易被忽略.本文报道通过飞秒激光对氧化铟锡薄膜加工形成双周期光栅结构,利用其在明场和暗场的观察下具有不同的颜色特性实现图像加密应用.通过控制飞秒激光的偏振、脉冲能量和扫描速度在氧化铟锡...     

Simple measuring technique for the diffraction efficiency of slanted volume gratings at various wavelengths

To measure diffraction efficiencies of gratings as a function of wavelength, it is necessary to have quasi-monochromatic light sources of various wavelengths. We propose a method to measure the wavelength dependence of the grating diffraction efficiency by using a quasi-monochromatic light source. This method of estimating the real diffraction characteristics of the gratings for various wavelengths is very useful and simple. First the diffraction efficiency of the grating as a function of various incident-beam angles of monochromatic light is measured, then, using these data, we can obtain the diffraction efficiencies for various wavelengths of the same incident angle of light by virtue of a mathematical-conversion method. The mathematical-conversion results for two laminated differently slanted angle gratings of the same volume grating period are in good agreement with the experimental ones.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.     

A non-contact technique for determining the depth of zero-order gratings

Abstract

In this work we present a simple, non-contact method for characterizing the depth of deep zero-order diffraction gratings using standard visible optics. Form birefringence exhibited by zero-order structures alters the polarization state of light transmitted through them. The amount of change is dependent on several factors including the depth of the grating grooves. By recording the polarization changes of laser light transmitted through the sample we demonstrate how the depth of any grating with a known pitch may be determined. Results for many different gratings have been analysed and show good agreement with groove depths measured from scanning electron micrographs. From these results a universal relationship between the amount of polarization change and the depth of the grating grooves has been determined.     

Nonparaxial scalar treatment of sinusoidal phase gratings

Scalar diffraction theory is frequently considered inadequate for predicting diffraction efficiencies for grating applications where lambda/d>0.1. It has also been stated that scalar theory imposes energy upon the evanescent diffracted orders. These notions, as well as several other common misconceptions, are driven more by an unnecessary paraxial approximation in the traditional Fourier treatment of scalar diffraction theory than by the scalar limitation. By scaling the spatial variables by the wavelength, we have previously shown that diffracted radiance is shift invariant in direction cosine space. Thus simple Fourier techniques can now be used to predict a variety of wide-angle (nonparaxial) diffraction grating effects. These include (1) the redistribution of energy from the evanescent orders to the propagating ones, (2) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (3) nonparaxial diffraction efficiencies predicted with an accuracy usually thought to require rigorous electromagnetic theory.     

Pulse shaping properties of volume holographic gratings in anisotropic media

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO(3) crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications.     

Dynamic holographic gratings with photoresist

The theoretical development of dynamic holographic gratings with piezoelectric crystals is presented. A thin layer of photoresist is applied over the surface of the piezoelectric crystal. A holographic grating was recorded over the photoresist-piezo device in such a way that when it is activated the changes in its dimensions produce a geometrical change in the grooves of the grating. Hence the initial diffraction pattern created may be dynamically modified.     

A holographic method for studying absorptivity modulation in transparent media

A dual-beam holographic method is described that can be used for measuring small induced absorptivity modulation in a transparent medium. The proposed method is based on a diffraction-interference scheme in which the interference field inducing an amplitude grating is shifted by a quarter of period relative to a reference volume phase grating. The induced amplitude grating introduces a nonequivalent energy exchange between the transmitted beams, which is proportional to changes in the absorption coefficient of the medium. The new dual-beam holographic method of measuring small absorptivity modulation is compared to the well-known single-beam diffraction technique.     

Efficiencies of master, replica, and multilayer gratings for the soft-x-ray-extreme-ultraviolet range: modeling based on the modified integral method and comparisons with measurements

The near-normal-incidence efficiencies of a 2400-groove/mm holographic master grating, a replica grating, and a multilayer grating are modeled in the soft-x-ray-extreme-ultraviolet (EUV) regions and are compared with efficiencies that are measured with synchrotron radiation. The efficiencies are calculated by the computer program PCGrate, which is based on a rigorous modified integral method. The theory of our integral method is described both for monolayer and multilayer gratings designated for the soft-x-ray-EUV-wavelength range. The calculations account for the groove profile as determined from atomic force microscopy with a depth scaling in the case of the multilayer grating and an average random microroughness (0.7 nm) for the short wavelengths. The refractive indices of the grating substrate and coatings have been taken from different sources because of the wide range of the wavelengths (4.5-50 nm). The measured peak absolute efficiency of 10.4% in the second diffraction order at a wavelength of 11.4 nm is achieved for the multilayer grating and is in good agreement with a computed value of approximately 11.5%. Rigorous modeling of the efficiencies of three similar gratings is in good overall agreement with the measured efficiency over a wide wavelength region. Additional calculations have indicated that relatively high normal incidence efficiency (of at least several percent) and large angular dispersion in the higher orders can be achieved in the 4.5-10.5-nm range by application of various multilayer coatings.     

The Diffraction Efficiency of Double-grating Holographic Fan-out Elements

Abstract

An analytical expression is derived for the diffraction efficiency of a holographic fan-out element containing two superimposed gratings separated by a small angle. In addition to the usual zero and first orders an infinite set of the significant spurious waves is considered. In deriving the expression all these spurious waves are assumed to satisfy the Bragg condition exactly. The results are compared with a direct numerical solution and give very good agreement for angles up to 1°. Furthermore the analysis provides useful information for angles up to 5°. An analogy is drawn with a hybrid hologram consisting of a thick ‘carrier’ grating and a thin ‘modulation’ grating. Using this model the diffraction efficiencies can be calculated using the standard grating formulae. For fan-out applications the spurious waves around the first orders are considered the most important. From this analysis it can be seen that they can be made negligibly small but at the cost of a reduction in total diffraction efficiency.     

Characteristics of short-period blazed fiber Bragg gratings for use as macro-bending sensors

The characteristics of short-period blazed fiber Bragg gratings for use as macro-bending sensors are discussed. This sensor is able to detect macro bending with the transmitted power variation of the first side mode in the blazed fiber Bragg grating. Since an incident ray experiences different variations of tilt angles with respect to bending direction, the blazed fiber Bragg grating has different coupling efficiencies of the first side mode, which can be reduced considerably in the case of twisted blazed fiber Bragg gratings.     

光刻法制备聚合物/液晶光栅

将明胶涂覆在表面经过取向处理的带有ITO电极的玻璃基板上，以紫外灯为光源，通过光掩模法，使明胶在光场的引发下发生光化学反应，样品显影刻蚀处理后呈栅状，将液晶注入光栅盒中，形成聚合物／液晶光栅。该光栅衍射效率可利用电场调控。采用He—Ne激光器对所制样品进行测试，结果表明，所制样品的栅结构较好。避免了液晶与聚合物相分离的不完全性和栅条边缘不整齐的现象。制得的光栅其第一衍射级次的开关比为87：1，显示了较好的开关能力。