An examination of the theories for the calculation of diffraction by square wave gratings. II, Angular variation (original) (raw)
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Optik, 1990
Various approximate models for diffraction by a grating structure are proposed, based on Fresnel-Huygens reflection coefficients. These approximate models are used to predict the volume diffraction orders produced by TE polarized light, incident on square-wave surface-relief gratings. Approximation to the diffraction orders from two forms of dielectric structure are examined for variation of the thickness, period and the angle of incidence of the input light. The results from the approximate theories are compared to those from the rigorous modal method and to one another.
Modelling of images of square-wave gratings and isolated edges using rigorous diffraction theory
Optics Communications, 1994
The angular spectrum approach, using a rigorous electromagnetic calculation for the scatter function of a grating, is used to calculate images of dielectric surface-relief square-wave gratings. Coherent bright field, dark field, and confocal images are calculated and presented, tbe rigorous Modal Method being used to calculate the scatter function of the specimen. The superior metrological information available from a confocal imaging system over the others is clearly demonstrated, as is the sectioning characteristic of the system. The periods of the gratings have been chosen so that tbe images approximate to those from isolated edges.
Proceedings of SPIE - The International Society for Optical Engineering, 2012
In this work a set of simplified theories for predicting diffraction efficiencies of diffraction phase and triangular gratings are considered. The simplified theories applied are the scalar diffraction and the effective medium theories. These theories are used in a wide range of the value Λ/λ and for different angles of incidence. However, when 1 ≤ Λ/λ ≤ 10, the behaviour of the diffraction light is difficult to understand intuitively and the simplified theories are not accurate. The accuracy of these formalisms is compared with both rigorous coupled wave theory and the finite-difference time domain method. Regarding the RCWT, the influence of the number of harmonics considered in the Fourier basis in the accuracy of the model is analyzed for different surface-relief gratings. In all cases the FDTD method is used for validating the results of the rest of theories. The FDTD method permits to visualize the interaction between the electromagnetic fields within the whole structure providing reliable information in real time. The drawbacks related with the spatial and time resolution of the finite-difference methods has been avoided by means of massive parallel implementation based on graphics processing units. Furthermore, analysis of the performance of the parallel method is shown obtaining a severe improvement respect to the classical version of the FDTD method.
Modelling of relief of phase reflection diffraction grating
Applied Mathematical Modelling, 2003
This article describes theoretical and experimental results on phase reflection diffraction gratings. Based on Fourier optics the mathematical formulation describing diffraction dispersion of light from a relief grating of the trapezium profile is derived. We propose a method that lets us estimate the gratingÕs geometric parameters in a versatile modelling system. We have designed an original programme that estimates diffraction intensities and calculates diffraction efficiency. The estimated intensities are used to reconstruct the gratingÕs geometrical properties using our mathematical model. The precision of the method is evaluated as the deviation of obtained results from microscopy data.
Gratings: Theory and Numeric Applications
2012
A typical question that almost all of us (the authors' team and other colleagues) has been asked not only once has in general the meaning (although usually being shorter): "What is the best method for modeling of light diffraction by periodic structures?" Unfortunately for the grating codes users, and quite fortunately for the theoreticians and code developers, the answer is quite short, there is no such a bird like the best method.
A modal model for diffraction gratings
Journal of Modern Optics, 2003
A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from subgratings are allowed, as are coatings on the sidewalls of lines, and arbitrary complex structure. Conical angles and good conductors are supported.
Angular responses of the first diffracted order in over-modulated volume diffraction gratings
Journal of Modern Optics, 2004
Kogelnik's Coupled Wave Theory has been used for decades to predict the diffraction efficiency of volume diffraction gratings. Although this theory has been applied with success to volume diffraction gratings recorded under a great variety of experimental conditions, its predictions deviate from the actual behaviour whenever the hologram is thin or the refractive index is high. In these cases, it is necessary to use a more general Coupled Wave Theory (CW) or the Rigorous Coupled Wave Theory (RCW). Both of these theories allow for more than two orders propagating inside the hologram. The difference between them is that in the CW theory the second derivatives that appear in the coupled equations are disregarded. The RCW doesn't incorporate any approximation and thus, since it is rigorous, permits judging the accuracy of the approximations included in Kogelnik's and CW theories. In this article a comparison between the predictions of the three theories for phase transmission diffraction gratings is carried put. Over-modulated diffraction gratings are also recorded in photographic emulsions in order to study the applicability of Kogelnik's Theory in this case. Good agreement between theory and experiment is found for both Kogelnik's and Rigorous Coupled Wave Theory formulations in the particular experimental cases studied.
A new theoretical method for diffraction gratings and its numerical application
Journal of Optics, 1980
Une nouvelle mbthode d'ktude theorique des reseaux de diffraction et son application numkrique RESUME : Nous presentons un nouveau formalisme de la diffraction par un reseau, tres different de ceux actuellement utilises. I1 se caracterise par I'utilisation d'un systeme d e coordonnees de translation qui permet, apres emploi des equations de Maxwell en coordonnees curvilignes, d'aboutir a un systeme d'equations differentielles a coefficients constants. L'application numerique est fondee sur le calcul matriciel elementaire. Le programme est teste a l'aide de criteres numeriques et par comparaison des resultats avec ceux issus de la methode integrale.
Rigorous coupled-wave analysis of planar-grating diffraction
A rigorous coupled-wave approach is used to analyze diffraction by general planar gratings bounded by two different media. The grating fringes may have any orientation (slanted or unslanted) with respect to the grating surfaces. The analysis is based on a state-variables representation and results in a unifying, easily computer-implementable matrix formulation of the general planar-grating diffraction problem. Accurate diffraction characteristics are presented for the first time to the authors' knowledge for general slanted gratings. This present rigorous formulation is compared with rigorous modal theory, approximate two-wave modal theory, approximate multiwave coupled-wave theory, and approximate two-wave coupled-wave theory. Typical errors in the diffraction characteristics introduced by these various approximate theories are evaluated for transmission, slanted, and reflection gratings. Inclusion of higher-order waves in a theory is important for obtaining accurate predictions when forward-diffracted orders are dominant (transmission-grating behavior). Conversely, when backward-diffracted orders dominate (reflection-grating behavior), second derivatives of the field amplitudes and boundary diffraction need to be included to produce accurate results.