Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction

Schmidt, G.; Kleemann, Bernd H.

doi:10.1080/09500340.2010.538734

Cited by 11 publications

(6 citation statements)

References 52 publications

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“…ux k ; 0w 0 t k e −iα j x k ; (28) where ux k ; 0 for 0 ≤ k < N 0 , which are given in u 0 . Similarly, the expansion coefficients of the reflected wave can be constructed from u m after a subtraction by the incident wave.…”

Section: Top and Bottom Boundary Conditionsmentioning

confidence: 99%

“…Efficient numerical methods are needed to analyze the diffraction and scattering of light by these periodic structures. Existing numerical methods for diffraction gratings include general-purpose methods such as the finitedifference time-domain (FDTD) method and the finite element method (FEM) [3], and more special methods such as the analytic modal method [4][5][6][7], numerical modal methods [8][9][10][11][12][13][14][15][16][17][18], the boundary integral equation (BIE) methods [19][20][21][22][23][24][25][26][27][28], etc. Although FDTD and FEM are extremely versatile, they are typically less efficient than the special methods.…”

Section: Introductionmentioning

confidence: 99%

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High order integral equation method for diffraction gratings

2012

J. Opt. Soc. Am. A

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Conventional integral equation methods for diffraction gratings require lattice sum techniques to evaluate quasi-periodic Green's functions. The boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method in Wu and Lu [J. Opt. Soc. Am. A 26, 2444 (2009)], [J. Opt. Soc. Am. A 28, 1191 (2011)] is a recently developed integral equation method that avoids the quasi-periodic Green's functions and is relatively easy to implement. In this paper, we present a number of improvements for this method, including a revised formulation that is more stable numerically, and more accurate methods for computing tangential derivatives along material interfaces and for matching boundary conditions with the homogeneous top and bottom regions. Numerical examples indicate that the improved BIE-NtD map method achieves a high order of accuracy for in-plane and conical diffractions of dielectric gratings.

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Section: Top and Bottom Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High order integral equation method for diffraction gratings

2012

J. Opt. Soc. Am. A

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“…Nowadays, the method of boundary integral equations [22,23,31,32] is universally recognised as one of the most developed and flexible methods of the accurate numerical solution of diffraction problems. The integral approach and the similar finite-element method generally implies 2D integration.…”

Section: Modified Boundary Integral Equation Methods (Mim)mentioning

confidence: 99%

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

Goray¹

2022

J. Opt.

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The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

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“…A large variety of rigorous electromagnetic methods to obtain the optical response of a given photonic structure are available in the literature. Among these methods, we can mention the modal method [20,21,22,23,24], coordinate-transformation methods [25,26] and the integral method [27,28,29]. These approaches are very efficient for the accurate determination of the optical response of corrugated interfaces and periodic gratings of canonical shapes.…”

Section: Introductionmentioning

confidence: 99%

Enhanced method for determining the optical response of highly complex biological photonic structures

Dolinko

Skigin

2013

J. Opt. Soc. Am. A

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We present a set of techniques that enhances a previously developed time domain simulation of wave propagation and allows the study of the optical response of a broad range of dielectric photonic structures. This method is particularly suitable for dealing with complex biological structures, especially due to the simple and intuitive way of defining the setup and the photonic structure to be simulated, which can be done via a digital image of the structure. The presented techniques include a direction filter that permits the decoupling of waves traveling simultaneously in different directions, a dynamic differential absorber to cancel the waves reflected at the edges of the simulation space, and a multifrequency excitation scheme. We also show how the simulation can be adapted to apply a near to far field method in order to evaluate the resulting wavefield outside the simulation domain. We validate these techniques, and, as an example, we apply the method to the complex structure of a microorganism called Diachea leucopoda, which exhibits a multicolor iridescent appearance.

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Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction

Cited by 11 publications

References 52 publications

High order integral equation method for diffraction gratings

High order integral equation method for diffraction gratings

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

Enhanced method for determining the optical response of highly complex biological photonic structures

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