On energy conditions for electromagnetic diffraction by apertures. (English) Zbl 1247.78012
Authors’ abstract: The diffraction of light is considered for a plane screen with an open bounded aperture. The corresponding solution behind the screen is given explicitly in terms of the Fourier transforms of the tangential components of the electric boundary field in the aperture. All components of the electric as well as the magnetic field vector are considered. We introduce solutions with global finite energy behind the screen and describe them in terms of two boundary potential functions. This new approach leads to a decoupling of the vectorial boundary equations in the aperture in the case of global finite energy. For the physically admissible solutions, that is, the solutions with local finite energy, we derive a characterisation in terms of the electric boundary fields.
Reviewer: Johannes Elschner (Berlin)
References:
| [1] | M. Kunik and P. Skrzypacz, “Diffraction of light revisited,” Mathematical Methods in the Applied Sciences, vol. 31, no. 7, pp. 793-820, 2008. · Zbl 1138.78006 · doi:10.1002/mma.945 |
| [2] | N. Gorenflo and M. Kunik, “A new and self-contained presentation of the theory of boundary operators for slit diffraction and their logarithmic approximations,” Mathematische Nachrichten, vol. 285, no. 1, pp. 74-102, 2012. · Zbl 1230.78008 · doi:10.1002/mana.200910203 |
| [3] | W. Rudin, Functional Analysis, Tata/McGraw-Hill, New Delhi, India, 1979. · Zbl 0867.46001 |
| [4] | M. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, UK, 2000. · Zbl 0948.35001 |
| [5] | G. I. Eskin, Boundary Value Problems for Elliptic Pseudo-Differential Operators, American Mathematical Society, Providence, RI, USA, 1981. · Zbl 0458.35002 |
| [6] | N. Gorenflo, “A characterization of the range of a finite convolution operator with a Hankel kernel,” Integral Transforms and Special Functions, vol. 12, no. 1, pp. 27-36, 2001. · Zbl 1035.47023 · doi:10.1080/10652460108819331 |
| [7] | N. Gorenflo, “Transformation of an axialsymmetric disk problem for the Helmholtz equation into an ordinary differential equation,” Integral Equations and Operator Theory, vol. 32, no. 2, pp. 180-198, 1998. · Zbl 0915.45005 · doi:10.1007/BF01196517 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
