Study on tapered crossed subwavelength gratings by Fourier modal method (original) (raw)
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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.
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.
Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit
Journal of the Optical Society of America A, 1998
Effective medium theory is useful for designing optical elements with a form-birefringent subwavelength structure. We describe a way to determine the effective refractive indices and the directions of their principal axes for two-dimensional (2-D) subwavelength gratings in the normal incidence case. The effective indices and the directions are calculated from finite coupled-coefficient equations that are used in 2-D rigorous coupled-wave analysis. We use the effective medium theory to calculate transmittance of several kinds of 2-D periodic subwavelength gratings. These results are compared with results of rigorous grating analysis to confirm the predictions of the effective medium theory for 2-D subwavelength gratings.
Antennas and Propagation Society …, 2005
Due to the filtering and diffractive effects of their periodic structures, dielectric gratings have found different applications in controlling the propagation of electromagnetic waves. Different numerical and semi-analytical techniques, such as method of moments, modal analysis and transverse resonance method, were proposed for solving dielectric grating structures [1]-[3]. The main advantage of semi-analytical techniques compared with the numerical techniques is the less computational effort to obtain the characteristics of the grating structure. Modal analysis showed significant advantage over the transverse resonance approach for modeling one-dimensional grating structure where the complexity of the former does not increase with the number of dielectric slabs present in the unit cell as it is usually happens in the later approach [1]. Another important advantage of modal analysis compared with the transverse resonance method is that it can be extended to two-dimensional structure as it is used for solving a waveguide filled with inhomogeneous materials [4]. The present work extends the modal analysis of one-dimensional dielectric grating to the case of two-dimensional dielectric grating.
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.
Gratings: Theory and Numeric Applications, Second Revisited Edition
2014
The second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11)
Use of grating theories in integrated optics
Journal of the Optical Society of America A, 2001
], two of the present authors proposed extending the domain of applicability of grating theories to aperiodic structures, especially the diffraction structures that are encountered in integrated optics. This extension was achieved by introduction of virtual periodicity and incorporation of artificial absorbers at the boundaries of the elementary cells of periodic structures. Refinements and extensions of that previous research are presented. Included is a thorough discussion of the effect of the absorber quality on the accuracy of the computational results, with highly accurate computational results being achieved with perfectly matched layer absorbers. The extensions are concerned with the diversity of diffraction waveguide problems to which the method is applied. These problems include two-dimensional classical problems such as those involving Bragg mirrors and grating couplers that may be difficult to model because of the length of the components and three-dimensional problems such as those involving integrated diffraction gratings, photonic crystal waveguides, and waveguide airbridge microcavities. Rigorous coupled-wave analysis (also called the Fourier modal method) is used to support the analysis, but we believe that the approach is applicable to other grating theories. The method is tested both against available numerical data obtained with finite-difference techniques and against experimental data. Excellent agreement is obtained. A comparison in terms of convergence speed with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach. Consequently, a simple, efficient, and stable method that may also be applied to waveguide and grating diffraction problems is proposed.
An All-Purpose Full-Vectorial Finite Element Model for Arbitrarily Shaped Crossed-Gratings
2009
We demonstrate the accuracy of the Finite Element Method (FEM) to characterize an arbitrarily shaped crossed-grating in a multilayered stack illuminated by an arbitrarily polarized plane wave under oblique incidence. To our knowledge, this is the first time that 3D diffraction efficiencies are calculated using the FEM. The method has been validated using classical cases found in the literature. Finally, to illustrate the independence of our method towards the shape of the diffractive object, we present the global energy balance resulting of the diffraction of a plane wave by a lossy thin torus crossed-grating.
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.
Subwavelength diffraction gratings in the visible spectral range
Quantum Electronics, 2018
We report the results of computer calculations and measurements of subwavelength diffraction gratings in the visible range of the radiation spectrum. The influence of various grating parameters (duty cycle, microrelief shape and depth, material, angle of incidence, wavelength, and radiation polarisation) on the diffraction efficiency is studied. A distinctive feature of the subwavelength gratings in question is that the entire diffracted energy of the beam is redistributed into the zero and-1st orders. It is found that the zero order can be suppressed by choosing the depth and shape of the grating relief. The subwavelength gratings with a period of 400 nm are fabricated and measurements are performed using lasers and laser diodes emitting in the visible wavelength range. High diffraction efficiency into the-1st order (more than 70 %) is observed in a wide spectral range of 450-650 nm with an increase in the grating relief depth (at a depth of h = 80 nm). It is experimentally demonstrated that under certain conditions, the plasmon resonance effect arises, in which total absorption of incident radiation takes place. The optical elements considered can be used in image processing systems, projection displays, in the development of various sensors, etc.