Singularities of Wave Fields and Numerical Methods of Solving the Boundary-Value Problems for Helmholtz Equation

Kyurkchan, A. G.; Sukov, A. I.; Kleev, A. I.

doi:10.1016/b978-044450282-7/50017-8

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…As mentioned in Section 2, the location of the multipole expansions should in principle depend on (1) the exciting field ⌽ exc D i (for the sake of simplicity in this description, we consider that the exciting field is acting only in domain D i ), (2) the geometry of the domains (which in the 2D case is given by the interface curve ⌫ ij ϵ ‫ץ‬D ij ), and (3) their material properties i , j . Some authors 55,56 working with the GMT do indeed use the information about ⌽ exc D i to find the position of the sources. They compute the analytical continuation of the exciting field in the domain D j (the so-called nonphysical domain).…”

Section: Automatic Multipole Setting For Cylindrical Structuresmentioning

confidence: 99%

Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures

et al. 2002

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Highly accurate computations of surface plasmons in metallic nanostructures with various geometries are presented. Calculations for cylinders with irregular cross section, coupled structures, and periodic gratings are shown. These systems exhibit a resonant behavior with complex field distribution and strong field enhancement, and therefore their computation requires a very accurate numerical method. It is shown that the multiple multipole (MMP) method, together with an automatic multipole setting (AMS) procedure, is well suited for these computations. An AMS technique for the two-dimensional MMP method is presented. It relies on the global topology of each domain boundary to generate a distribution of numerically independent multipole expansions. This technique greatly facilitates the MMP modeling.

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Section: Automatic Multipole Setting For Cylindrical Structuresmentioning

confidence: 99%

Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures

et al. 2002

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“…Как показано в работе [5], предлагаемый подход, который можно назвать модифицированным МПГУ, базируется на более аккуратном учете физических свойств реальной структуры и позволяет существенно увеличить точность расчетов. Действительно, результаты работ [14][15][16] убедительно демонстрируют, что учет априорной информации дает возможность значительно повысить эффективность алгоритма решения задачи дифракции.…”

Section: основные соотношенияunclassified

Расчет Омических Потерь В Открытых Резонаторах

2012

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Приведены результаты решения задачи о собственных колебаниях открытого двумерного резонатора, зеркала которого имеют конечную проводимость. При расчетах использовали модифицированный метод продолженных граничных условий. Результаты сопоставлены с асимптотическим решением, полученным методом параболического уравнения.Ключевые слова: Открытые резонаторы, метод интегральных уравнений, метод адаптивной коллокации, эквивалентные граничные условия, аналитическое продолжение поля.

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“…2D boundary-value problems of this theory are studied, as a rule, using several popular methods, such as the Rayleigh method and its modern versions [13][14][15][16], the Fourier modal method and the C-method [6,8,10,17], rigorous coupled-wave methods and cross-section methods (differential methods) [8,9], finite-element methods [18], and analytical regularization methods [6,[10][11][12]. The advantages and disadvantages of these frequency-domain methods are well known.…”

Section: Introductionmentioning

confidence: 99%

Time-and-frequency domains approach to data processing in multiwavelength optical scatterometry of dielectric gratings

et al. 2013

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This paper focuses on scatterometry problems arising in lithography production of periodic gratings. Namely, the paper introduces a theoretical and numerical-modeling-oriented approach to scatterometry problems and discusses its capabilities. The approach allows for reliable detection of deviations in gratings' critical dimensions (CDs) during the manufacturing process. The core of the approach is the one-to-one correspondence between the electromagnetic (EM) characteristics and the geometric/material properties of gratings. The approach is based on highly accurate solutions of initial boundary-value problems describing EM waves' interaction on periodic gratings. The advantage of the approach is the ability to perform simultaneously and interactively both in frequency and time domains under conditions of possible resonant scattering of EM waves by infinite or finite gratings. This allows a detection of CDs for a wide range of gratings, and, thus is beneficial for the applied scatterometry.

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Singularities of Wave Fields and Numerical Methods of Solving the Boundary-Value Problems for Helmholtz Equation

Cited by 5 publications

References 10 publications

Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures

Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures

Расчет Омических Потерь В Открытых Резонаторах

Time-and-frequency domains approach to data processing in multiwavelength optical scatterometry of dielectric gratings

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