Geodesic
Skattering of a~highfrequency electromagnetic wave fieldskattered by the vertex of a~perfectly conducting cone. (Singular directions.)
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 5-14

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An analitic exspression for electromagnetic wave field scattering by the vertex of a perfectly conducting cone in the singular directions is considered. The approach is a generalisation of the approach of the papers [1–3]. The spherical front of the wave, propagating from the vertex of the cone tangents the front of the wave, reflected by the cone surface in this “singular” directions. The wave field is expressed in the terms of the parabolic cylinder functions. 
@article{ZNSL_2002_285_a0,
     author = {V. M. Babich and D. B. Dement'ev and B. A. Samokish and V. P. Smyshlyaev},
     title = {Skattering of a~highfrequency electromagnetic wave fieldskattered by the vertex of a~perfectly conducting cone. {(Singular} directions.)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--14},
     publisher = {mathdoc},
     volume = {285},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a0/}
}
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V. M. Babich; D. B. Dement'ev; B. A. Samokish; V. P. Smyshlyaev. Skattering of a~highfrequency electromagnetic wave fieldskattered by the vertex of a~perfectly conducting cone. (Singular directions.). Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 5-14. http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a0/