Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals

We present a numerical study of bidimensional photonic crystals with an emphasis on the behavior of the gaps versus the polarization and the conicity of the incident plane wave. We use a rigorous modal theory of diffraction at oblique incidence by a set of arbitrarily shaped parallel fibers. This theory allows the study of the refractive properties of bidimensional photonic crystals. We develop a heuristic method of homogenization that allows us to predict the position of the gaps and their behavior with respect to the polarization and the conicity angle. With this homogenization scheme, we also present some important elements for obtaining full gaps.     

Range-finding method using diffraction gratings

A model in geometric optics, along with some preliminary experimental results for a new range-finding method that exploits near-field diffraction phenomena found with plane gratings, is presented. Among the characteristics investigated is a magnification effect applicable to three-dimensional microscopy. A variety of embodiments of the method is disclosed, including an off-axis illumination model and a method of near-field focus compensation that takes advantage of the Scheimpflug condition.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization

Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered. The far-field diffraction patterns, the transmission coefficient tau, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E=Ntau/lambda, valid in the scalar region, is extended to the TM polarization case in the vectorial region, lambda being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength lambda. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.     

Rigorous coupled-wave analysis for practical planar dielectric gratings: 1. Thickness-changed holograms and some characteristics of diffraction efficiency

A new and useful method for obtaining diffraction efficiencies from holograms manufactured practically is presented. Applying the rigorous coupled-wave analysis, we express each difference between the practical and the ideal as a mathematical component that can be easily integrated. In Part 1 the effects due to thickness change in the hologram layer (observed frequently after the development process) are treated. Although uniform swelling or shrinking causes a simple reconstruction wavelength or incidence-angle shift, nonuniform thickness extends the capacity of the Bragg condition matching, creating a diffraction efficiency curve in the asymmetric profile. Other characteristics of diffraction are also maintained. A refractive-index change has an effect that is similar to the thickness change. Higher-order terms in permittivity modulation create negligible effects in general holograms when used at or near the simple first-order Bragg condition.     

Frequency selective characteristics of gratings with arbitrary profiles composed of left-handed materials

The frequency selective surface (FSS) of gratings with arbitrary profiles composed of left-handed materials is systematically analysed by a method that combines the staircase approximation and the multimode network theory with the rigorous mode matching procedure. The effects of different periodic groove profiles, such as rectangle, ellipse and trapezoid on the reflection characteristics of the FSS are carefully studied and compared with each other. The variations of the frequency selective characteristics with dielectric loss and the comparisons between left-handed and right-handed gratings are also presented with the physical explanations of the related phenomena.     

Rigorous coupled-wave analysis for practical planar dielectric gratings: 3. Increase of higher-order lights owing to degenerated complex diffraction

The diffraction efficiencies by practical dielectric holograms are evaluated with the rigorous coupled-wave analysis. As discussed in Parts 1 and 2, only the first reflection light can be diffracted by general sealed volume reflection holograms. Here we discuss the possibility that complex diffraction, which occurs in multiple-grating-storage holograms, makes diffraction efficiencies of higher-order lights increase drastically, i.e., the degenerated complex diffraction. Although evident in special cases only, they appear frequently in actual holographic use.     

Enhancement of nonlinear effects using photonic crystals

The quest for all-optical signal processing is generally deemed to be impractical because optical nonlinearities are usually weak. The emerging field of nonlinear photonic crystals seems destined to change this view dramatically. Theoretical considerations show that all-optical devices using photonic crystal designs promise to be smaller than the wavelength of light, and to operate with bandwidths that are very difficult to achieve electronically. When created in commonly used materials, these devices could operate at powers of only a few milliwatts. Moreover, if these designs are combined with materials and systems that support electromagnetically induced transparency, operation at single-photon power levels could be feasible.     

Analysis of arbitrary defects in photonic crystals by use of the source-model technique

A novel method derived from the source-model technique is presented to solve the problem of scattering of an electromagnetic plane wave by a two-dimensional photonic crystal slab that contains an arbitrary defect (perturbation). In this method, the electromagnetic fields in the perturbed problem are expressed in terms of the field due to the periodic currents obtained from a solution of the corresponding unperturbed problem plus the field due to yet-to-be-determined correction current sources placed in the vicinity of the perturbation. Appropriate error measures are suggested, and a few representative structures are presented and analyzed to demonstrate the versatility of the proposed method and to provide physical insight into waveguiding and defect coupling mechanisms typical of finite-thickness photonic crystal slabs.     

Equal-frequency surface analysis of two-dimensional photonic crystals

This paper presents an analytical treatment of equal-frequency surface analysis of a two-dimensional photonic crystal. We first define the equal-frequency surface in terms of plane waves, which can be numerically evaluated. Then one- and two-plane-wave approximations are proposed, which consequently lead to analytical expressions of the equal-frequency surface. The approach presented is well suited to two-dimensional photonic crystals of weak dielectric modulation. For photonic crystals with a large modulation, the approach can be used to gain a general idea of the shape of the bands.     

Analysis of diffraction gratings by using an edge element method

Typically the grating problem is formulated for TE and TM polarizations by using, respectively, the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence, and this leads to a one-field-component problem. For some grating profiles such as metallic gratings with a triangular profile, the prediction of TM polarization by using a standard finite-element method experiences a slower convergence rate, and this reduces the accuracy of the computed results and also introduces a numerical polarization effect. This discrepancy cannot be seen as a simple numerical issue, since it has been observed for different types of numerical methods based on the classical formulation. Hence an alternative formulation is proposed, where the grating problem is modeled by taking the electric field as unknown for TM polarization. The application of this idea to both TE and TM polarizations leads to a two-field-component problem. The purpose of the paper is to propose an edge finite-element method to solve this wave problem. A comparison of the results of the proposed formulation and the classical formulation shows improvement and robustness in the new approach.     

Rigorous and approximate analysis of metallic gratings in soft X-ray and EUV regions

Abstract

In deep ultraviolet and soft X-ray regions the complex refractive indices of metals differ substantially from their values in the visible region of the spectrum. The implications of this fact are analysed for metallic gratings illuminated by electromagnetic fields with wavelengths ranging from soft X‐rays to near infrared, concentrating on short wavelengths. In particular, we study metal-stripe gratings (linear polarizers for visible light) by rigorous diffraction theory to determine the short-wavelength region in which a combination of the geometrical thin-element approximation and the theory of single-layer films can be applied. Then we study inductive grid filters for protection of X-ray detectors from infrared radiation in space applications.     

Design of binary diffraction gratings of liquid crystals in a linearly graded phase model

We report on a linearly graded phase model for the design of binary diffraction gratings of liquid crystals (LCs) associated with the periodic interfacial effect. The binary nature of the LC grating is produced by use of periodic striped domains in an alternating homeotropic and hybrid geometry. In our graded phase model the diffraction patterns and the diffracted intensities of the LC binary grating is primarily governed by three length scales: the cell thickness and two distortion parameters scaled by the grating period at two domain boundaries. The experimental data agree well with theoretical predictions made in our linearly graded phase model as well as the elastic continuum theory.     

SU-8光刻胶制作三维光子晶体

针对SU-8光刻胶应用于三维光子晶体的制作研究,本文提出并实现了对SU-8光刻胶的重要成分SU-8环氧树脂采用柱层析和高压液相色谱-尺寸排阻色谱法进行分离,分离结果表明SU-8环氧树脂分子量分布范围很大,从大约100～100000,包括SU-1、SU-2、SU-4、SU-6、SU-8多种组分及其混合物.采用分离后的SU-8和SU-6纯组分配制了性能优化的SU-8光刻胶,并总结了其最佳光刻工艺,结合干涉光刻技术制作了晶格常数为922nm的三维面心立方光子晶体结构.     

Scattered-light properties of diffraction gratings

One of the many calibrations performed for a scientific-quality spectrometer is the characterization of its scattered-light properties. The scattered light can arise from any optical surface, and light leaks or scattering from baffles can also contribute to the instrumental stray-light level. For a diffraction-grating spectrometer the primary contribution to instrumental scattered light has been found to be the scattered light from the grating. The results from measuring the scattered-light properties of 10 diffraction gratings are discussed along with the application of these results in analyzing the total scattered light measured for three spectrometers. It has been found from these measurements that there are two components of the grating scattered light: a Lorentzian-type component and a constant background component. The Lorentzian component is predicted from the diffraction theory for a grating, and the constant background component is consistent with Rayleigh scattering from the microscopic surface im erfections. It was also discovered that multiple replicas of gratings from the same master grating exhibit significantly more scattered light than the preceding replica by factors of 1.1-2.     

Evolution of complete photonic band gap in anisotropic photonic quasicrystals using liquid crystals

Abstract

In this study, we analyse the evolution of complete photonic band gap in two-dimensional photonic structures by arranging the 12-fold symmetric quasicrystalline unit cells on square and triangular lattices. The unit cells composed of circular air holes in anisotropic tellurium background and the air holes are infiltrated with liquid crystal. Using the supercell method based on plane wave expansion, we study the variation of complete band gap by changing the optical axis orientation of liquid crystals.     

Hybrid-matrix algorithm for rigorous coupled-wave analysis of multilayered diffraction gratings

This paper presents an alternative approach called the hybrid-matrix or H-matrix algorithm for the stable and efficient implementation of the rigorous coupled-wave analysis of multilayered diffraction gratings. The H matrix is superior to both the T and R matrices because of its numerical stability across the whole range of large and small layer thicknesses. It is also more concise and simple than the S matrix in obviating the need to invoke auxiliary reference layers or two consecutive layers. For high efficiency, the stack H-matrix recursive algorithm is derived in terms of eigen-submatrices directly without any auxiliary layer matrix. Compared with the enhanced transmittance matrix (partial-solution) approach, the enhanced H-submatrix approach achieves 30% higher computation efficiency and requires less memory.     

Spectral dependence of the diffraction efficiency of light-induced gratings in YAlO3:Mn crystals

The results of measurements of spectral dependence of diffraction efficiency of light-induced holographic gratings in YAlO₃:Mn(0.5%) crystal are reported. The experimental data are interpreted as an effect of interaction of both refractive index changes and light-induced absorption associated with optical transition within photo-induced Mn⁵⁺ ions and intrinsic defect centers. Nature of the intrinsic traps involved in the process is discussed.