The Properties of Holographic Overlap Gratings

The analysis of a holographic beam expander which can, under perfect lossless conditions, convert a plane input beam into a plane diffracted beam, with a specified diffraction efficiency and beam width expansion ratio, is presented. Using solutions of the coupled-wave differential equations of [2], the effects of average loss, and both constant and spatially dependent dephasing are studied. These solutions are also used to compare the properties of overlap gratings with Kogelnik's [1] results for infinite gratings, and to extend the analysis of [4] to lossy, dephased cases. The maximum possible diffraction efficiency of an absorption overlap grating is shown to depend on its shape and also to lie between the values for Kogelnik's reflection and transmission cases.     

The influence of the procedure on the dynamic range of bleached silver halide emulsions

Abstract

Bleached holograms are one of the most interesting techniques used to produce phase holograms of high quality on photographic emulsions. Of particular interest is the method of fixation-free rehalogenating bleaching. Using Kogelnik's coupled-wave theory we shall obtain information about the characteristics of the final holograms recorded in bleaching procedures. In this way, it is possible to analyse the particular mechanisms involved in the formation of the holograms. In this paper we study the influence of the different experimental conditions on the refractive index modulation created inside the hologram. It will be demonstrated that it is possible to maintain the values of diffraction efficiency over a wide range of exposures if the correct experimental conditions are chosen. On the other hand, it will also be demonstrated that the use of fixation-free rehalogenating bleaching techniques allows high-refractive-index modulations to be obtained. Moreover, it is possible to attain a theoretical diffraction efficiency of 100%, which is only limited by absorption and scattering.     

High-efficiency volume holograms recording on acrylamide and N,N′methylene-bis-acrylamide photopolymer with pulsed laser

In order to achieve a better understanding of the mechanisms of hologram formation and higher diffraction efficiencies in volume gratings stored in acrylamide based photopolymers, a crosslinker (N,N′methylene-bis-acrylamide) has been incorporated in the photopolymer to record holograms by pulsed laser exposure. The presence of this component increases the polymerization rate and refractive index modulation. The recording was performed using a holographic copying process. The original was a grating of 1000?lines/mm processed using silver halide sensitized gelatin. First, the effect of the pulse fluence was investigated. When the pulse fluence was optimized, the results obtained using the new composition of material were compared with those using the composition without a crosslinker. Using a pulsed laser at 532?nm the photopolymer without crosslinker presented diffraction efficiencies slightly less than 60%. On the other hand, when the crosslinker was introduced in the photopolymer composition, the diffraction efficiencies achieved were higher than 85%. The non-linearity of the material's response was also studied comparing the energetic sensitivity, diffraction efficiencies and index modulation of gratings recorded with pulsed and continuous laser exposure. This study was performed fitting the angular scan of each grating using Kogelnik's theory.     

A treatment of the general volume holographic grating as an array of parallel stacked mirrors

An alternative model to Kogelnik's coupled wave theory of the volume holographic grating is developed in terms of an infinite array of parallel stacked mirrors. The model is based on summing the individual Fresnel reflections from an infinite number of infinitesimal discontinuities in the permittivity profile. The resulting first-order coupled partial differential equations are solved in a rotated frame of reference in order to derive analytical expressions for the diffraction efficiency of the general slanted grating at an arbitrary angle of incidence. The model has been tested using computational solutions of the Helmholtz equation for the unslanted reflection grating. For index modulations characteristic of modern silver halide and photopolymer materials used in display and optical element holography the new model shows excellent agreement with the numerical results. Kogelnik's model also provides good agreement as long as the dephasing parameter is not too large. The model has been tested against Kogelnik's theory for a variety of cases with finite fringe slant with good agreement for typical index modulations. A further advantage of the new model is that colour holographic gratings may be treated at and away from Bragg resonance. Numerical and analytical results are presented concerning the diffractive efficiency of two- and three-colour holographic gratings.     

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Abstract

High spatial frequency lamellar gratings are shown to function as phase compensators, quarter-wave and half-wave retarders, and polarization rotators that operate on specularly reflected (zeroth-order) beams. These gratings are designed using rigorous coupled-wave and modal grating diffraction theories. Controlling the geometrical parameters of these gratings allows for engineering the phase retardation and polarization conversion introduced to a reflected beam. Fabrication and operational tolerances for these elements are discussed. Wavelength and polar angle of incidence variation affect the performance of these elements more strongly than variations in other geometrical and operational parameters.     

Off-Bragg analysis of the diffraction efficiency of transmission photorefractive holograms

Formulas for calculating the diffraction efficiency of gratings recorded in a photorefractive medium are given. The analysis uses coupled-wave theory for photorefractive hologram gratings and takes into account the photorefractive phase shift and fringe-bending effect. General solutions for diffracted (signal) and undiffracted (reference) waves are derived in a closed-form expression. By use of the derived formulas the diffraction efficiency for angle mismatch from the Bragg condition can easily be evaluated as compared with numerical-analysis methods. The diffraction efficiency is also quantified in terms of medium parameters and recording and reconstruction conditions.     

Rigorous coupled-wave analysis for practical planar dielectric gratings: 2. Diffraction by a surface-eroded hologram layer

The diffraction efficiencies of practical dielectric holograms are evaluated with rigorous coupled-wave analysis. The cases of the hologram surfaces eroded in several shapes are treated and compared with those in which the surfaces are not eroded and with those in which there are only surface gratings. Eroding the surface will increase the higher-order reflection diffraction efficiencies and the transmissions, thus reducing the first reflection and the zeroth transmission. However, sealing the hologram with a cover plate, as is done in manufacturing many holograms, extinguishes the erosion effect.     

Off-Bragg analysis of the diffraction efficiency of reflection photorefractive holograms

Formulas are given for the calculation of diffraction efficiency of reflection-type gratings recorded in a photorefractive medium. The analysis incorporates the coupled-wave theory that was developed for photorefractive hologram gratings. This analysis takes into account grating slant with respect to the medium surface, light absorption during reconstruction, any incident angle of the reference beam, and any photorefractive phase shift. General solutions for signal and reference wave functions are given in a closed-form expression by use of a hypergeometric function. The optimum media parameters and recording conditions for high diffraction efficiency are obtained by the derived formulas. The diffraction properties for off-Bragg conditions are also discussed.     

Study of the dynamic formation of transmission gratings recorded in photopolymers and holographic polymer-dispersed liquid crystals

Local and nonlocal models for the diffusion of photopolymers are applied to the dynamic formation of transmission gratings recorded in photopolymers and holographic polymer-dispersed liquid crystals (H-PDLCs). We retrieve the main parameters of H-PDLCs (refractive-index modulation and diffusion coefficient) by combining a solution of the one-dimensional diffusion equation and the rigorous coupled-wave theory applied to transmission gratings. The rigorous coupled-wave theory method provides us with information on higher harmonics of the refractive profile (not only on the first harmonic as when the classical Kogelnik theory is applied). Measurements concerning the second harmonic validate the modeling.     

Multiplexed holographic transmission gratings recorded in holographic polymer-dispersed liquid crystals: static and dynamic studies

The optimization of the experimental parameters of two multiplexed holographic transmission gratings recorded in holographic polymer-dispersed liquid crystals is investigated. Two methods are used to record the holograms: simultaneous and sequential multiplexing. These two processes are optimized to produce two multiplexed Bragg gratings that have the same and the highest possible diffraction efficiencies in the first order. The two methods show similar results when suitable recording parameters are used. The parameters of the recorded gratings (mainly the refractive-index modulation) are retrieved by use of an extension of the rigorous coupled-wave theory to multiplexed gratings. Finally, the response of the holograms to an electric field is studied. We demonstrate few coupling effects between the behavior of both gratings, and we expect a possibility of switching from one grating to the other.     

非相干组束中反射体布拉格光栅的衍射潜力(英文)

基于耦合波理论,提出了一种推导反射体布拉格光栅衍射效率方程的新方法.在被推导的衍射效率方程基础上,获得了平面单色和高斯光束反射体布拉格光栅衍射的详细理论模型,分析了平面单色、发散单色和多色光束的衍射效率.结果表明:平面单色波的角和谱选择性随光栅厚度和空间频率而变化,角选择性的范围从低于0.01mrad到超过100mrad,谱选择性的范围从低于0.1nm到超过100nm;当光束的角发散或谱宽等于光栅的角选择或谱选择性时,光栅能提供超过88%的衍射效率;当光束的角发散或谱宽远小于光栅的角选择或谱选择性时,光栅衍射效率下降不明显,不到平面单色波的1%.     

Integral equation method with parametrization of grating profile theory and experiments

Abstract

Theories and their numerical implementations to rigorously solve Maxwell's equations are fundamental in diffractive optics. Various rigorous methods have been developed in the past which allow the analysis and synthesis of diffraction gratings. The basis of the great majority of rigorous methods is the Fourier series expansion of the permittivity function. Unfortunately the Fourier expansion can easily give poor results for the TM mode. By using an integral method with parametrization of the grating profile this problem can be overcome for surface modulated gratings. The theory and a comparison of theoretical and experimental results are presented.     

Diffraction analysis of blazed transmission gratings with a modified extended scalar theory

An alternative interpretation of the diffraction of blazed transmission gratings with moderate structure period is proposed according to a modified extended scalar theory (MEST). The diffraction field on the bottom facet of the grating is considered to be the interference of four subfields investigated in the problem of diffraction of a plane wave by an infinite half-plane. It is observed that MEST gives the total field that agrees with rigorous coupled-wave analysis (RCWA), and the result is more reliable than that of extended scalar theory (EST). The MEST is still a ray-optical-based approximation approach, and the region of validity is compared with EST and RCWA.     

Non-uniformities in Thick Dichromated Gelatin Transmission Gratings

Abstract

The angular characteristics of transmission gratings are studied for the case when three parameters, namely the dielectric-constant modulation, the average dielectric constant and the grating vector vary with distance in the grating. The diffraction efficiency is worked out with the aid of a coupled-wave theory for linear and quadratic variation of the parameters. Gratings recorded in thick (≈ 60 µm) dichromated gelatin plates are measured. The spatial variations of the parameters are deduced by comparing the experimental and theoretical results.     

Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization

Abstract

In this paper, an accurate method for computing the elecromagnetic field distribution in lamellar gratings is proposed. The method that relies on the rigorous coupled-wave analysis provides accurate numerical results and avoids possible sources of artefacts due to permittivity discontinuities. Its performance is analysed through various lamellar grating cases, including dielectric and metallic materials, the visible and near-infrared (1–10 μm) regions of the spectrum. Special attention is placed on field singularities which are in general present at the grating wedges for transverse magnetic polarization.     

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.     

Effect of Slab Interfaces on Diffraction of Visible Light by a Thick Volume Grating

Abstract

A theory of visible light diffraction by a volume grating is given for the case when reflection at slab interfaces cannot be neglected. A method of approximate solution of the second-order coupled-wave equations, applicable over a wide range of the grating vector orientation, is proposed. An appropriate boundary-value problem is discussed and solved in the two-wave approximation. The results are analytical and expressed in matrix notation suitable for both transmission and reflection diffraction gratings. Particular attention is given to the diffraction regime that arises in a slanted grating under the total internal reflection of the diffracted wave (TIRDW). Strong transmission anomalies occurring in the vicinity of the TIRDW threshold are established and analysed.     

Efficiency of Thick Phase Holograms in the Presence of Shear-type Effects Due to Processing

Abstract

Based on the results of the coupled-wave theory the diffraction efficiency is calculated for thick phase transmission holographic gratings taking into account the chemical processing of the recording material. Three effects of processing are considered: variations in the average refractive index, changes in thickness and shear-type effects. The comparison of experimental and theoretical results demonstrates the validity of the expression obtained and the important influence of the shearing effects on the efficiency and angular responses of transmission holographic gratings.     

On the effective medium theory of subwavelength periodic structures

Abstract

The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelength ratios. It is shown that for large period-to-wavelength ratios near the cutoff value, no analogy between 2-D periodic structures and homogeneous media holds for highly modulated lamellar gratings.     

General solution of the coupled-wave equations of acousto-optics

The basic problem of the diffraction of an optical plane wave by an acoustic plane wave in an anisotropic homogeneous medium is considered. The acousto-optical interaction is considered indifferently of the isotropic or of the birefringent type. Coupled-wave equations are obtained rigorously and cast into an eigenvalue value problem. A general solution is obtained for the diffraction efficiency of diffracted orders, for any interaction length and diffraction regime. The theory includes the Bragg regime, the Raman-Nath regime, and all intermediate situations in the same formulation. The method of solution is both exact and computationally efficient. It is similar in character to the rigorous coupled-wave analysis of Moharam and Gaylord but differs by the choice of basis functions adapted to propagating rather than static gratings. Examples are given for acousto-optical interaction in paratellurite, TeO2.