Characteristics of a concave diffraction grating on which a spherical wave is incident

Kulakova, N. A.; Mirumyants, S. O.; Bugaenko, A. G.

doi:10.1364/jot.73.000682

Cited by 3 publications

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“…The results reported in [14] using the derived scalar analytical expression for a concave grating were compared to the numerical efficiency calculus obtained using the vector electromagnetic theory for a plane perfectly conducting grating. In [15], the analysis of the distribution of incidence waves and variablespace grooves on a concave grating surface was performed. The authors calculated the diffraction efficiency in the principal section using both the scalar and the vector methods for a spherical wave incident.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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

Goray¹

2022

J. Opt.

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“…Analytic expressions of diffraction energy distribution were derived by utilizing the geometrical relation between incident rays of arbitrary grooves and principle one. Kulakova et al [13] set up the mathematic model on a concave grating when the spherical wave was incident. The analysis on the distribution as well as variable spacing of grooves was added, and then the diffraction efficiency distribution in the principal section was discussed by both the scalar and vector method.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the diffraction efficiency on concave gratings based on Fresnel–Kirchhoff’s diffraction formula

Huang

et al. 2013

Appl. Opt.

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Fraunhofer diffraction formula cannot be applied to calculate the diffraction wave energy distribution of concave gratings like plane gratings because their grooves are distributed on a concave spherical surface. In this paper, a method based on the Kirchhoff diffraction theory is proposed to calculate the diffraction efficiency on concave gratings by considering the curvature of the whole concave spherical surface. According to this approach, each groove surface is divided into several limited small planes, on which the Kirchhoff diffraction field distribution is calculated, and then the diffraction field of whole concave grating can be obtained by superimposition. Formulas to calculate the diffraction efficiency of Rowland-type and flat-field concave gratings are deduced from practical applications. Experimental results showed strong agreement with theoretical computations. With the proposed method, light energy can be optimized to the expected diffraction wave range while implementing aberration-corrected design of concave gratings, particularly for the concave blazed gratings.

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Diffraction on non-plane gratings irradiated by non-planar waves

Goray

2022

2022 Days on Diffraction (DD)

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Characteristics of a concave diffraction grating on which a spherical wave is incident

Cited by 3 publications

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

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

Calculation of the diffraction efficiency on concave gratings based on Fresnel–Kirchhoff’s diffraction formula

Diffraction on non-plane gratings irradiated by non-planar waves

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