Grazing-angle scattering (GAS) is a type of Bragg scattering of waves in slanted non-uniform periodic gratings, when the diffracted order satisfying the Bragg condition propagates at a grazing angle with respect to the boundaries of a slab-like grating. Rigorous analysis of GAS of bulk TE electromagnetic waves is undertaken in holographic gratings by means of the enhanced T-matrix algorithm. A comparison of the rigorous and the previously developed approximate theories of GAS is carried out. A complex pattern of numerous previously unknown resonances is discovered and analysed in detail for gratings with large amplitude, for which the approximate theory fails. These resonances are associated not only with the geometry of GAS, but are also typical for wide transmitting gratings. Their dependence on grating amplitude, angles of incidence and scattering, and grating width is investigated numerically. Physical interpretation of the predicted resonances is linked to the existence and the resonant generation of special new eigenmodes of slanted gratings. Main properties of these modes and their field structure are discussed.
A highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the surrounding media. This pattern is shown to exist in the geometry of grazing-angle scattering (GAS), that is when the scattered wave (+1 diffracted order) in the slab propagates almost parallel to the slab (grating) boundaries. The predicted resonances are demonstrated to be unrelated to resonant generation of the conventional guided modes of the slab. Their physica…
The diffraction of electromagnetic waves at the surface periodic structures accompanied by strong anomalous effects in different diffraction orders is considered in great detail for high-contrast interfaces. We restrict our discussion to the TM polarization of the incident wave (the magnetic field is orthogonal to the plane of incidence) and the simplest geometry when the plane of incidence is orthogonal to the grating grooves. The most attention is focused on the strong maxima and minima of the energy flux density accompanying specific grazing propagation of some diffraction order. Relation t…
We report on the observation of emerging beam resonances, well known as Rayleigh-Wood anomalies and threshold resonances in photon and electron diffraction, respectively, in an atom-optical diffraction experiment. Diffraction of He atom beams reflected from a blazed ruled grating at grazing incidence has been investigated. The total reflectivity of the grating as well as the intensities of the diffracted beams reveal anomalies at the Rayleigh angles of incidence, i.e., when another diffracted beam merges parallel to the grating surface. The observed anomalies are discussed in terms of the clas…
We provide rigorous numerical calculations (using the rigorous coupled-wave analysis) of transmission spectra of various metallic and metamaterial one-dimensional gratings and identify plasmonic resonances responsible for enhanced transmission. We argue that the most important mechanism which influences the resonant transmission is the coupling of incident electromagnetic wave with two plasmonic waves: lengthwise plasmons, which propagates along the grating, and crosswise plasmons excited in air gaps.
Extremely asymmetrical scattering (EAS) is a new type of Bragg scattering in thick, slanted, periodic gratings. It is realised when the scattered wave propagates parallel to the front boundary of the grating. Its most important feature is the strong resonant increase in the scattered wave amplitude compared to the amplitude of the incident wave: the smaller the grating amplitude, the larger the amplitude of the scattered wave. In this paper, rigorous numerical analysis of EAS is carried out by means of the enhanced T-matrix algorithm. This includes investigation of harmonic generation inside a…
Extremely asymmetrical scattering (EAS) is an unusual type of Bragg scattering in slanted periodic gratings with the scattered wave (the +1 diffracted order) propagating parallel to the grating boundaries. Here, a unique and strong sensitivity of EAS to small stepwise variations of mean structural parameters at the grating boundaries is predicted theoretically (by means of approximate and rigorous analyses) for bulk TE electromagnetic waves and slab optical modes of arbitrary polarization in holographic (for bulk waves) and corrugation (for slab modes) gratings. The predicted effects are expla…
A multi-reflection model of grating diffraction based on the simplified modal method is proposed. Simulation results for a guided mode resonance Brewster grating using our method and rigorous coupled wave analysis are presented to verify our model. The solution of our method is in good agreement with that of rigorous coupled wave analysis. Benefiting from its clear physical view, this model helps us to better understand the diffraction process inside subwavelength gratings. On the basis of the multi-reflection model, we developed a matrix Fabry-Perot (FP) resonance condition and a single-mode …
The modified rigorous coupled-wave analysis technique is developed to describe the optical characteristics of the plasmonic structures with the grating-gated delta-thin conductive channel in the far- and near-field zones of electromagnetic waves. The technique was applied for analysis of the resonant properties of AlGaN/GaN heterostructures combined with deeply-subwavelength metallic grating which facilitates the excitation of the two-dimensional plasmons in the THz frequency range. The convergence of the calculations at the frequencies near the plasmon resonances is discussed. The impact of t…
We use a rigorous electromagnetic approach to analyze the fundamental limit of light-trapping enhancement in grating structures. This limit can exceed the bulk limit of 4n^2, but has significant angular dependency. We explicitly show that 2D gratings provide more enhancement than 1D gratings. We also show the effects of the grating profile's symmetry on the absorption enhancement limit. Numerical simulations are applied to support the theory. Our findings provide general guidance for the design of grating structures for light-trapping solar cells.
What we believe to be a new type of resonant coupling of an incident bulk wave into guided modes of a slab with a thick holographic grating is shown to occur in the presence of strong frequency detunings of the Bragg condition. This happens through the reflection of the strongly noneigen +1 diffracted order with the slab-grating boundaries, the resultant reflected waves forming a guided slab mode. Rigorous coupled-wave analysis is used for the numerical analysis of the predicted resonant effects. Possible applications include enhanced options for the design of multiplexing and demultiplexing s…
Extremely asymmetrical scattering (EAS) is a highly resonant type of Bragg scattering with a strong resonant increase of the scattered wave amplitude inside and outside the grating. EAS is realized when the scattered wave propagates parallel to the grating boundaries. We present a rigorous algorithm for the analysis of non-steady-state EAS, and investigate the relaxation of the incident and scattered wave amplitudes to their steady-state values. Non-steady-state EAS of bulk TE electromagnetic waves is analyzed in narrow and wide, slanted, holographic gratings. Typical relaxation times are dete…
We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in 1D-periodic guided-mode resonant gratings (GMRGs) consisting of a slab waveguide layer with a binary grating attached to one or both of its interfaces. Using these models, we obtain simple closed-form expressions predicting the locations of the BICs and quasi-BICs in the $ω$-$k_x$ parameter space. We study two mechanisms of the BIC formation: coupling between two counter-propagating guided modes and coupling between a guided mode and a Fabry-Pérot mode. The BIC condi…
The excitation of multiple surface-plasmon-polariton (SPP) waves of different linear polarization states and phase speeds by a surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied theoretically, using rigorous coupled-wave-analysis. The incident plane wave can be either p or s polarized. The excitation of SPP waves is indicated by the presence of those peaks in the plots of absorbance vs. the incidence angle that are independent of the thickness of the rugate filter. The absorbance peaks representing the excitation of s-polarized SPP waves are nar…
A rigorous coupled-wave analysis of birefringent holographic gratings with periodically-modulated dielectric tensor along an in-plane direction and tensor variations in the thickness direction
The phenomenon of filtering in zero-diffraction order is studied for transmission through 1D-periodic structures on a silicon wafer. Our study combines FTIR spectrometry in the range from 2.5 to 25 microns, and a rigorous full-vector simulation. The phenomenon exhibits itself as 'bright' and 'dark' bands in the spectra of normal transmission through grating samples, which replace each other quasi-periodically with respect to wave number, at wavelengths smaller than the grating period. The transmission modulation ratio is extremely high for two-side polished samples. Good agreement between the …
The rigorous coupled-wave analysis (RCWA) is one of the most successful and widely used methods for modeling periodic optical structures. It yields fast convergence of the electromagnetic far-field and has been adapted to model various optical devices and wave configurations. In this article, we investigate the accuracy with which the electromagnetic near-field can be calculated by using RCWA and explain the observed slow convergence and numerical artifacts from which it suffers, namely unphysical oscillations at material boundaries due to the Gibb's phenomenon. In order to alleviate these sho…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack lightened by a plane wave of arbitrary incidence and polarization angle. It relies on a rigorous treatment of the plane wave sources problem through an equivalent radiation problem with localized sources. Bloch conditions and a new Adaptative Perfectly Matched Layer have been implemented in order to truncate the computational domain. We derive this formulati…
We present a concept for an ultra-thin solar fuel device with a nanostructured back contact. Using rigorous simulations we show that the nanostructuring significantly increases the absorption in the semiconductor, CuBi$_2$O$_4$ in this case, by 47\% (5.2~mAcm$^{-2}$) through the excitation of plasmonic modes. We are able to attribute the resonances in the device to metal-insulator-metal plasmons coupled to either localised surface plasmon resonances or surface plasmon polaritons. Rounding applied to the metallic corners leads to a blueshift in the resonance wavelength while maintaining absorpt…
A periodic arrangement of one-dimensional slits carved in perfect electric conductor is investigated and an equivalent model based on the effective medium theory is derived. The proposed model is no longer fully homogeneous and features periodic surface conductivity on its upper and lower interfaces. Therefore, and in sheer contrast to all the previous attempts that were successful in mimicking only the zeroth-order diffracted waves, it is capable of emulating both specular and non-specular diffraction orders. The parameters of the equivalent model are found by comparing the scattered waves of…
This paper provides a method based on rigorous coupled wave analysis for the calculation of the radiative thermal capacitance between a layer that is patterned with arbitrary, periodically repeating features and a planar one. This method is applied to study binary gratings and arrays of beams with a rectangular cross section. The effects of the structure size and spacing on the thermal capacitance are investigated. In all of these calculations, a comparison is made with an effective medium theory which becomes increasingly accurate as the structure sizes fall well below the relevant resonance …
