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We theoretically present and experimentally validate a method to overlay the interference field (for making straight-line holographic gratings) with a real grating and a derived method to measure the lateral shift between two real gratings. The methods rely only on the real gratings' profile symmetry, and they are robust against variations of the real gratings' profile parameters and functional form.

The work started 20 years ago [Appl. Opt.42, 6255 (2003)APOPAI0003-693510.1364/AO.42.006255] investigating the physical mechanism of multilayer dielectric reflection gratings to achieve 100% diffraction efficiency is completed to offer much deeper insight than before. How different scattering matrix elements of the top periodic surface corrugation contribute to the -1st-order efficiency of such a compound grating is unveiled analytically using a minimum set of real parameters. The two diffraction amplitudes transmitted through the top corrugation play a dominant role in enabling 100% diffraction efficiency. Simple necessary and sufficient conditions for 100% efficiency are derived. Moreover, the role of the reflection phase of the perfect reflector, including the contribution of the optical path between the top corrugation and the reflector, is emphasized.

A detailed review of the theory of effective permittivity for one- and two-dimensional periodic structures shows its limited validity for metal-dielectric structures in the visible and near infra-red if the feature dimensions are comparable with the metal skin depth. We propose a phenomenological correction to the static formulae using a realistic assumption for the electric field behavior inside the metal features. This approach allows us to obtain analytical expressions for the effective permittivity in the case when the electric field is not sufficiently homogeneous within the unit cell of the gratings. A comparison with the numerical results of the Fourier modal method demonstrates the validity of the analytical formulae. Additional study is made on the impedance approximation at the outer boundaries of the periodical structure in order to propose analytical formulae for the reflection coefficient that permits better correspondence with the numerical results. The link between the values of effective permittivity and permeability defined as the ratios between the averaged fields, and the metamaterial permittivity and permeability is discussed.

The translational coordinate transformation method (the C method) in grating theory is studied numerically and analytically. We first study the convergence characteristics of the C method by numerical computations in high floating-point data precisions. Guided by insights gained from this numerical study we analytically studied condition numbers of the most important eigenvalues of the eigenvalue problem of the C method. Asymptotic estimates of condition numbers of these eigenvalues and estimates of convergence rate of the error in satisfying the Helmholtz equation by the eigenvectors are derived. These theoretical results explain well many observed numerical phenomena of the C method. Using the first-order perturbation theory of simple eigenvalues we analyze the effects of round-off errors on eigenvalue distribution and condition numbers. This leads to an extremely simple perturbative preconditioning technique that significantly improves the numerical stability of the C method with as little as just one line of code modification. The performance of the perturbatively preconditioned C method is not inferior to the C method preconditioned by the multilinear parameterization technique. We recommend it as the preferred method for modeling deep and smooth gratings.

We present an in situ duty cycle control method that relies on monitoring the TM/TE diffraction efficiency ratio of the -1st transmitted order during photoresist development. Owing to the anisotropic structure of a binary grating, at an appropriately chosen angle of incidence, diffraction efficiencies in TE and TM polarizations vary with groove depth proportionately, while they vary with duty cycle differently. Thus, measuring the TM/TE diffraction efficiency ratio can help estimate the duty cycle during development while eliminating the effect of photoresist thickness uncertainty. We experimentally verified the feasibility of this idea by fabricating photoresist gratings with different photoresist thicknesses. The experimental results were in good agreement with theoretical predictions.

This article reviews the state of the art in optical design, modeling and characterization of solar central receiver systems.

An efficient modal method for numerically modeling slanted lamellar gratings of isotropic dielectric or metallic media in conical mounting is presented. No restrictions are imposed on the slant angle and the length of the lamellae. The end surface of the lamellae can be arbitrary, subject to certain restrictions. An oblique coordinate system that is adapted to the slanted lamella sidewalls allows the most efficient way of representing and manipulating the electromagnetic fields. A translational coordinate system that is based on the oblique Cartesian coordinate system adapts to the end-surface profile of the lamellae, so that the latter can be handled simply and easily. Moreover, two matrix eigenvalue problems of size 2N × 2N, one for each fundamental polarization of the electromagnetic fields in the periodic lamellar structure, where N is the matrix truncation number, are derived to replace the 4N × 4N eigenvalue problem that has been used in the literature. The core idea leading to this success is the polarization decomposition of the electromagnetic fields inside the periodic lamellar region when the fields are expressed in the oblique translational coordinate system.

A simple variable transformation that consists of two joined straight-line segments per grating period is proposed for the parameterized coordinate transformation method (the C method). With this bilinear parameterization, the C method can produce convergent numerical results for gratings of deep and smooth profiles with a groove depth-to-period ratio as high as 10, which to date has been far out of reach of the C method. The danger of getting divergent results due to inadvertently using an overly large truncation number is also practically eliminated.

In the recent Letter [Opt. Lett.39, 781 (2014)10.1364/OL.39.000781OPLEDP0146-9592] that proposes a method to design slanted parallelogram gratings based on the simplified modal method, the analysis of the modal field in the grating layer is incorrect; therefore, the validity of the equivalence between slanted parallelogram gratings and upright rectangular gratings that the authors thereby have deduced is questionable or at least in need of substantial modifications.

It is insufficient to consider that hypersingularity is unphysical solely based on energy considerations. With a proper combination of the two degenerate hypersingular modes, the energy-flux edge condition is satisfied. A hyperbolic wedge model is presented that is much simpler than the previous model for the purpose of studying singular characteristics of the edge fields. This model not only reproduces the sharp edge model as the wedge becomes infinitely sharp but also naturally shows how the two degenerate hypersingular modes of the sharp edge model should be combined. In an incidental study of the effect of rounding edges on numerical computation, I show that the converged results for rounded edges do not converge to a fixed value when the radius of curvature tends to zero, if the corresponding sharp edge supports hypersingularity. I also prove that introducing a small amount of absorption loss for the purpose of improving numerical convergence is effective only when the ratio of the real parts of the permittivities of the two media forming the wedge is close to -1. Finally I remark on the possible illposedness of the hypersingularity problem without imposition of the edge condition.

We present a specialized scatterometry method to measure the groove profiles of highly asymmetric triangular gratings. Compared with the conventional scatterometry working in a specular way, this method utilizes diffraction spectra of the reflected ±1st orders and is good at measuring this kind of asymmetric grating with a higher sensitivity. In our work, diffraction efficiency angular spectra at a single wavelength are measured and passed on to a parameter optimization process to retrieve three profile defining parameters. Final results are compared with the ones from an atomic force microscope and discrepancies are discussed and explained.

I extend a previous work [J. Opt. Soc. Am. A, 738 (2011)] on field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings to the case of arbitrary metallic wedge angles. Simple criteria are given that allow one knowing the lossless permittivities and the arbitrary wedge angles to determine if the electric field at the edges is nonsingular, can be regularly singular, or can be irregularly singular without calculating the singularity exponent. Furthermore, the knowledge of the singularity type enables one to predict immediately if a numerical method that uses Fourier expansions of the transverse electric field components at the edges will converge or not without making any numerical tests. All conclusions of the previous work about the general relationships between field singularities, Fourier representation of singular fields, and convergence of numerical methods for modeling lossless metal-dielectric gratings have been reconfirmed.