The Diffraction of the Bessel Beams from a Half Screen with Boundary Diffraction Wave Theory

Abstract

In this study, the behavior of Bessel beams diffracted from the edge of a black half-plane was examined using the Boundary Diffraction Wave Theory (BDWT). Firstly, the vector potential was rearranged in relation to Helmholtz-Kirchoff integral for the diffraction of Bessel beams from the black half-plane. By using this vector potential, the BDWT diffraction integral was obtained and the diffracted fields were calculated. Then, the related coordinate transformations were made and the diffracted fields were obtained in spherical coordinates. Additionally, the behavior of the diffracted fields and Bessel beams was evaluated by interpreting the numerically derived graphs.

Keywords

• Boundary Diffraction Wave Theory,Bessel beams,Helmholtz-Kirchoff integral,Diffracted fields

SINIR KIRINIM DALGASI TEORİSİ İLE YARIM DÜZLEMDEN BESSEL IŞINLARININ KIRINIMI

Abstract

Bu çalışmada, Sınır Kırınım Dalgası Teorisi (SKDT) yaklaşımı kullanılarak yutucu bir yarım düzlemin kenarından kırınan Bessel ışınlarının davranışı incelenmiştir. İlk olarak, vektör potansiyeli, Bessel ışınlarının yutucu yarım düzlemden kırınımı için, Helmholtz-Kirchoff integraliyle bağlantılı olarak yeniden düzenlenmiştir. Bu vektör potansiyelinden yola çıkılarak SKDT kırınım integrali elde edilmiş ve kırınan alanlar hesaplanmıştır. Daha sonra, ilgili koordinat dönüşümleri yapılarak kırınan alanlar küresel koordinatlarda elde edilmiştir. Ayrıca, Bessel ışınlarının ve hesaplanan kırınan alanların davranışı sayısal olarak elde edilen grafikler değerlendirilerek yorumlanmıştır.

Keywords

• : Sınır Kırınım Dalgası Teorisi,Bessel ışınları,Helmholtz-Kirchoff integrali,Kırınan Alanlar

References

1. 1. McGloin, D., ve Dholakia, K. (2005) Bessel Beams: Diffraction in a New Light, Contemporary Physics, 46, 15-28. https://doi.org/10.1080/0010751042000275259
2. 2. Yu, Y. Z. ve Dou, W. B. (2008) Vector Analyses of Nondiffracting Bessel Beams, Progress in Electromagnetics Research Letters (PIER L), 5, 57-71. doi:10.2528/PIERL08110906
3. 3. Young, T. (1802) The Theory of Light and Colours, Phill. Trans. R. Soc., 20, 12-48. doi: 10.1098/rstl.1802.0004
4. 4. Marchand, E. W. ve Wolf, E. (1962) Boudary Diffraction Wave in the Domain of the Raygleigh-Kirchoff Diffraction Theory, Journal of the Optical Society of America, 52, 761-767. https://doi.org/10.1364/JOSA.52.000761
5. 5. Miyamoto, K. ve Wolf, E. (1962a) Generalization of the Maggi-Rubinowicz theory of the Boundary Diffraction Wave-Part I, Journal of the Optical Society of America, 52, 615-625. https://doi.org/10.1364/JOSA.52.000615
6. 6. Miyamoto, K. ve Wolf, E. (1962b) Generalization of the Maggi-Rubinowicz theory of the Boundary Diffraction Wave-Part II, Journal of the Optical Society of America, 52, 626-637. https://doi.org/10.1364/JOSA.52.000626
7. 7. Yalçın, U. (2009a), Uniform Scattered Fields of the Extended Theory of Boundary Diffraction Wave for PEC Surfaces, Progress in Electromagnetics Research M (PIER M), 7, 29-39. doi:10.2528/PIERM09031201
8. 8. Yalçın, U. (2009b) Scattering from Perfectly Magnetic Conducting Surfaces: The Extended Theory of Boundary Diffraction Wave Approach, Progress in Electromagnetics Research M (PIER M), 7, 123-133. doi:10.2528/PIERM09042210

9. 9. Yalçın, U. (2011) Analysis of Diffracted Fields with the Extended Theory of the Boundary Diffraction Wave for Impedance Surfaces, Applied Optics, 50(3), 296-301. https://doi.org/10.1364/AO.50.000296
10. 10. Yalçın, U. (2009) Yutucu Yarım Düzlemin Kenarından Kırınan Üniform Alanların Sınır Kırınım Dalgası Teorisi İle Hesabı, 2. Mühendislik ve Teknoloji Sempozyumu, Çankaya/Ankara, 82-88.
11. 11. Otis, G. ve Lit, J.W.Y. (1975) Edge-On Diffraction of a Gaussian Laser Beam by a Semi-Infinite Plane, Applied Optics, 14, 1156-1160. https://doi.org/10.1364/AO.14.001156
12. 12. Durnin, J. (1987) Exact solutions for nondiffracting beams. I. The scalar theory, Journal of the Optical Society of America, 4, 651-654. https://doi.org/10.1364/JOSAA.4.000651
13. 13. Altıngöz C. ve Yalçın, U. (2013) Yutucu Kesik Silindirin Kenarından Kırınan Üniform Alanların Sınır Kırınım Dalgası Teorisi ile Hesabı, Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 28(1), 85-90.
14. 14. Yalçın U. ve Altıngöz C. (2017) Uniform Scattered Fields from a Parabolic Surface with the Boundary Diffraction Wave Theory, Photonics Letters of Poland, 9(4), 125-127. doi: 10.4302/plp.v9i4.753