COMPLEX RAYS AND APPLICATIONS

Elman Hasanoğlu

COMPLEX RAYS AND APPLICATIONS

Abstract

Complex rays are a fascinating aspect of modern diffraction theory, typically sought as complex solutions to the eikonal equation. Traditionally, these solutions are obtained by analytically continuing real rays into the complex domain. However, this approach demands the analyticity of initial data, significantly limiting its applicability to many practical problems. Additionally, unlike real rays, complex rays cannot be visualized in space, presenting another drawback. In this paper, we present an alternative interpretation of complex rays, as introduced in [1], and describe a novel approach to two model diffraction problems and Gaussian beams.

Keywords

References

Hasanov (Hasanoglu) E. A New Theory of Complex Rays, IMA Journal of Applied Mathematics. 69, 2004,
Luneburg R.K., (1964), Mathematical Theory of Optics, University of California Press.
Born M., Wolf E. Principles of Optics (Seventh edition), (1999), Cambridge University Press
V.M., Buldyrev V. S., (1991), Short-Wavelength Diffraction Theory Asymptotic Methods, Springer Ser. Wave Phenomena 4, Springer-Verlag, Berlin.
Babiç V.M., Kirpiçnikova N. Y. (1979) The Boundary Layer Method in Diffraction Problems, Springer-Verlag, Berlin.
Keller J. B. Semiclassical mechanics, (1985), SIAM Rev., 27, pp. 485-504.
Keller J. B., Streifer W. (1971), Complex rays with an application to Gaussian beams, J. Opt. Soc. Amer., 61, pp. 40-43.
Katsav M., Heyman E., Klinkenbusch L., (2014), Beam Diffraction by a Wedge: Exact and Complex Ray Solutions, IEEE AP, 62, No. 7.

Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Elman Hasanoğlu ^*
0000-0001-8471-7575
Türkiye

Publication Date

December 6, 2025

Submission Date

September 12, 2024

Acceptance Date

May 25, 2025

Published in Issue

Year 2025 Volume: 15 Number: 12

IZ

https://izlik.org/JA64YA23XL

Cite

RIS / Bibtex

APA

Hasanoğlu, E. (2025). COMPLEX RAYS AND APPLICATIONS. TWMS Journal of Applied and Engineering Mathematics, 15(12), 2798-2808. https://izlik.org/JA64YA23XL

AMA

1.Hasanoğlu E. COMPLEX RAYS AND APPLICATIONS. JAEM. 2025;15(12):2798-2808. https://izlik.org/JA64YA23XL

Chicago

Hasanoğlu, Elman. 2025. “COMPLEX RAYS AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics 15 (12): 2798-2808. https://izlik.org/JA64YA23XL.

EndNote

Hasanoğlu E (December 1, 2025) COMPLEX RAYS AND APPLICATIONS. TWMS Journal of Applied and Engineering Mathematics 15 12 2798–2808.

IEEE

[1]E. Hasanoğlu, “COMPLEX RAYS AND APPLICATIONS”, JAEM, vol. 15, no. 12, pp. 2798–2808, Dec. 2025, [Online]. Available: https://izlik.org/JA64YA23XL

ISNAD

Hasanoğlu, Elman. “COMPLEX RAYS AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics 15/12 (December 1, 2025): 2798-2808. https://izlik.org/JA64YA23XL.

JAMA

1.Hasanoğlu E. COMPLEX RAYS AND APPLICATIONS. JAEM. 2025;15:2798–2808.

MLA

Hasanoğlu, Elman. “COMPLEX RAYS AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 12, Dec. 2025, pp. 2798-0, https://izlik.org/JA64YA23XL.

Vancouver

1.Elman Hasanoğlu. COMPLEX RAYS AND APPLICATIONS. JAEM [Internet]. 2025 Dec. 1;15(12):2798-80. Available from: https://izlik.org/JA64YA23XL