Sensitivity analysis of 2D photonic band gaps of any rod shape and conductivity using a very fast conical integral equation method

The conical boundary integral equation method has been proposed to calculate the sensitive optical response of 2D photonic band gaps (PBGs), including dielectric, absorbing, and highconductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2×2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equations system and the factorization of the discrete matrices, which takes the major computing time, are carried out only once for a boundary. It turned out that a small number of collocation points per boundary combined with a high convergence rate can provide adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs. array cell geometry parameters was found to vary from a few percent up to a few hundred percent. The influence of other types of anomalies (i.e. waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc), conductivity, and polarization states on the optical response has been demonstrated

Solving conical diffraction with integral equations

Off-plane scattering of time-harmonic plane waves by a diffraction grating with arbitrary conductivity and general border profile is considered in a rigorous electromagnetic formulation. The integral equations for conical diffraction were obtained using the boundary integrals of the single and double layer potentials including the tangential derivative of single layer potentials interpreted as singular integrals. We derive an important formula for the calculation of the absorption in conical diffraction. Some rules which are expedient for the numerical implementation of the theory are presented. The efficiencies and polarization angles compared with those obtained by Lifeng Li for transmission and reflection gratings are in a good agreement. The code developed and tested is found to be accurate and efficient for solving off-plane diffraction problems including high-conductive surfaces, borders with edges, real border profiles, and gratings working at short wavelengths

Sensitivity analysis of 2D photonic band gaps of any rod shape and conductivity using a very fast conical integral equation method

The conical boundary integral equation method has been proposedto calculate the sensitive optical response of 2D photonic band gaps (PBGs),including dielectric, absorbing, and high-conductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any gratingboundary profile. The computation of the matrices is based on the solution of a 2 x 2system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equations system and the factorization of the discrete matrices, which takes the major computing time, are carried out only oncefor a boundary. It turned out that a small number of collocation points per boundary combined with a high convergence rate can provide adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. Thenumerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high fillingratios. The diffracted energy response calculated vs. array cell geometry parameters was found to vary from a few percent up to a few hundred percent. The influence of other types of anomalies (i.e. waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc), conductivity, and polarization states on the optical response has been demonstrated

Electronic states in a quantum well - nanobridge - quantum dot structure

Using the finite volume method we compute within effective mass approximation the single-particle eigenstates for electrons and holes in a InGaAs/GaAs quantum well - nanobridge - quantum dot structure. It is shown that hybrid states appear in this complex system. The interaction between the eigenvalues may be an explanation for the additional photoluminescence peak measured for inverted structures with smaller nanobridge lengths

Electronic states in a quantum well -- nanobridge -- quantum dot structure

Using the finite volume method we compute within effective mass approximation the single-particle eigenstates for electrons and holes in a InGaAs/GaAs quantum well -- nanobridge -- quantum dot structure. It is shown that hybrid states appear in this complex system. The interaction between the eigenvalues may be an explanation for the additional photoluminescence peak measured for inverted structures with smaller nanobridge lengths

Diffraction Grating Groove Metrology Using AFM & STM

AFM & STM metrology has been around for a long time, and especially intense since it has been awarded by the Nobel Prize in Physics in 1986. Since then, many AFM & STM groove profile measurements on surface relief diffraction gratings have been presented. However, a wide review of the results of the use of AFM & STM methods for groove metrology of various surface relief gratings has not really been undertaken. The following problems are discussed in this chapter: the cantilever tip deconvolution, geometry, and radius; groove shapes and abrupt groove slopes; roughness; PSD functions; etc. Also, the author demonstrates comparisons with other widely-used metrology techniques and examples of AFM & STM data of bulk, coated, and multilayer-coated ruled, or holographic, or lithographic gratings having realistic groove profiles. These gratings were chosen because high quality efficiency data exists, in particular, for space gratings or/and X-ray gratings characterized by synchrotron radiation sources; and their groove profiles, together with random nanoroughness, were measured by AFM or STM to be included in rigorous efficiency and scattered light intensity calculus. In the present chapter, both the earlier published results and the recent, non-published yet results are described and discussed

Gratings: Theory and Numeric Applications, Second Revisited Edition

International audienceThe 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

Solving conical diffraction grating problems with integral equations

Off-plane scattering of time-harmonic plane waves by a plane diffraction grating with arbitrary conductivity and general surface profile is considered in a rigorous electromagnetic formulation. Integral equations for conical diffraction are obtained involving, besides the boundary integrals of the single and double layer potentials, singular integrals, the tangential derivative of single-layer potentials. We derive an explicit formula for the calculation of the absorption in conical diffraction. Some rules that are expedient for the numerical implementation of the theory are presented. The efficiencies and polarization angles compared with those obtained by Lifeng Li for transmission and reflection gratings are in a good agreement. The code developed and tested is found to be accurate and efficient for solving off-plane diffraction problems including high-conductive gratings, surfaces with edges, real profiles, and gratings working at short wavelengths

Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method

The conical-boundary-integral-equation method has been proposed for calculation of the sensitive optical response of two-dimensional photonic band gaps (PBGs), including dielectric, absorbing, and high-conductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2×2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equation system and the factorization of the discrete matrices, which takes the majority of the computing time, are carried out only once for a boundary. It turns out that a small number of collocation points per boundary combined with a high convergence rate can provide an adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs the array cell geometry parameters was found to vary from a few up to a few hundred percent. The influence of other types of anomalies (i.e., waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc.), conductivity, and polarization states on the optical response is demonstrated