Characterization of Total Fields Radiated from a Circular Aperture: A Comparative Analysis for Opaque, PEC, and PMC Surfaces

Öz

This study comparatively investigates the behavior of total fields radiated from a circular aperture on opaque, Perfect Electric Conductor (PEC), and Perfect Magnetic Conductor (PMC) surfaces. The total field calculations were performed using the Boundary Diffraction Wave Theory (BDWT) and the Generalized BDWT (GBDWT), and the analyses were based on the vector potential formulation introduced by Miyamoto and Wolf. The obtained non-uniform total field expressions were transformed into a uniform form by employing the detour parameter and the asymptotic properties of the Fresnel function. For opaque surfaces, only the incident wave was considered, while for PEC and PMC surfaces, both incident and reflected waves were included. The spatial distribution of the total field was graphically compared for various aperture radii and observation distances, and the influence of surface type on the field was analyzed in detail. The results show that the amplitude and phase characteristics of the total field vary significantly depending on surface type; in particular, high-frequency interference patterns appear on PEC surfaces, whereas amplitude distributions are smoother and lower on opaque surfaces. The findings reveal, both qualitatively and quantitatively, the significant role of surface properties in determining the total field behavior. Furthermore, this study provides a useful reference for surface selection and optimization in engineering applications such as antenna design, electromagnetic shielding, and radar cross-section (RCS) reduction. 

Anahtar Kelimeler

• Circular Aperture
• Extended Boundary Diffraction Wave Theory (EBDWT)
• Characterization
• Opaque Surface
• PEC/PMC
• Total Field

DAİRESEL AÇIKLIKTAN OLUŞAN TOPLAM ALANLARIN KARAKTERİZASYONU: OPAK, PEC VE PMC YÜZEYLER İÇİN KARŞILAŞTIRMALI ANALİZ

Öz

Bu çalışma, dairesel bir açıklıktan yayılan toplam alanların Opak, Mükemmel Elektrik İletken (PEC) ve Mükemmel Manyetik İletken (PMC) yüzeylerdeki davranışlarını karşılaştırmalı olarak incelemektedir. Toplam alan hesaplamalarında Sınır Kırınım Dalgası Teorisi (SKDT) ile Genelleştirilmiş SKDT (GSKDT) yöntemleri kullanılmış, analizler, Miyamoto ve Wolf tarafından tanımlanan vektör potansiyeli temeline dayandırılmıştır. Elde edilen non-uniform toplam alan ifadeleri, Detour parametresi ve Fresnel fonksiyonunun asimptotik özellikleri kullanılarak uniform forma dönüştürülmüştür. Opak yüzeylerde yalnızca gelen dalga dikkate alınırken, PEC ve PMC yüzeylerde hem gelen hem de yansıyan dalgalar hesaba katılmıştır. Farklı açıklık yarıçapları ve gözlem mesafeleri için toplam alanın uzaysal dağılımı grafiksel olarak karşılaştırılmış, yüzey tiplerinin alan üzerindeki etkileri ayrıntılı biçimde analiz edilmiştir. Sonuçlar, toplam alanın genlik ve faz karakteristiğinin yüzey tipine bağlı olarak belirgin biçimde değiştiğini göstermekte; özellikle PEC yüzeylerde yüksek frekanslı girişim desenleri, opak yüzeylerde ise daha düşük genlikli ve düzgün bir dağılım gözlenmektedir. Elde edilen bulgular, yüzey özelliklerinin toplam alan davranışı üzerindeki rolünü hem nitel hem de nicel olarak ortaya koymakta; anten tasarımı, elektromanyetik kalkanlama ve radar kesit alanı (RCS) azaltımı gibi mühendislik uygulamalarında yüzey seçimi ve optimizasyonu için yol gösterici bir referans sunmaktadır. 

Anahtar Kelimeler

• Dairesel Açıklık
• Genelleştirilmiş Sınır Kırınım Dalgası Teorisi (GSKDT)
• Karakterizasyon
• Opak Yüzey
• PEC/PMC
• Toplam Alan

Kaynakça

1. Aime C., Prunet S., Theys C., Ferrari A. ve Lantéri H. (2024). A new approach for the numerical calculation of diffraction patterns using starshades. Astronomy & Astrophysics, 686, A240. doi:10.1051/0004-6361/202449589
2. Altınel M. ve Yalçın U. (2021). Opak bir yüzey üzerindeki dairesel açıklıktan saçılan alanların hesabı. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 26(2), 433–446. doi:10.17482/uumfd.883713
3. Altınel M. ve Yalçın U. (2024). Uniform diffracted fields of the extended theory of BDW from the circular aperture on a perfectly magnetic conductive surface. COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 43(2), 269–281. doi:10.1108/compel-06-2023-0223
4. Apaydın G. ve Sevgi L. (2020). Scattering from a strip with mixed boundary conditions. Radio Science, 55(12), e2020RS007092. doi:10.1029/2020RS007092
5. Barnett A. H. (2020). Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform FFT. arXiv preprint, arXiv:2010.05978
6. Basdemir H. D. (2024). Diffraction of a pseudo nondiffracting Bessel beam by a perfect electromagnetic conductor (PEMC) circular disk. Journal of the Optical Society of America A, 41(4), 700–709. doi:10.1364/josaa.516314
7. Batoroev A. S. (2021). Fresnel diffraction from sector apertures. Optics Express, 29(19), 30419–30425. doi:10.1364/oe.430724
8. Borghi R. (2015). Uniform asymptotics of paraxial boundary diffraction waves. Journal of the Optical Society of America A, 32(4), 685–696. doi:10.1364/josaa.32.000685

9. Born M. ve Wolf E. (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press. doi:10.1017/cbo9781139644181
10. El-Din A. S. ve Mohamed R. A. (2021). Electromagnetic plane-wave diffraction by a cylindrical arc with edges in a PEC environment: A hybrid analytical–numerical method. International Journal of Applied Electromagnetics and Mechanics, 65 (3–4), 237–246. doi:10.3233/JAE-210018
11. Ganci S. (2008). Diffracted wavefield by an arbitrary aperture from Maggi–Rubinowicz transformation: Fraunhofer approximation. Optik, 119(1), 41–45. doi:10.1016/j.ijleo.2006.06.007
12. Gao Y., Wei S., Wang Z. ve Zhai G. (2021). Information-theoretical resolution limit of a far-field subwavelength-aperture system. Physical Review A, 103, 033519. doi:10.1103/physreva.103.033519
13. Glückstad J. ve Madsen A. E. G. (2023). New analytical diffraction expressions for the Fresnel–Fraunhofer transition regime. Optik, 285, 170950. doi:10.1016/j.ijleo.2023.170950
14. Keller J. B. (1962). Geometrical theory of diffraction. Journal of the Optical Society of America, 52(2), 116–130. doi:10.1364/josa.52.000116
15. Lovat G., Burghignoli P., Araneo R. ve Celozzi S. (2021). Magnetic field penetration through a circular aperture in a perfectly conducting plate excited by a coaxial loop. IET Microwaves, Antennas & Propagation, 15(10), 1147–1158. doi:10.1049/mia2.12105
16. Lucido M., Chirico G., Migliore M. D., Pinchera D. ve Schettino F. (2023). Plane-wave diffraction from a resistive-filled circular hole in infinite resistive plane: An analytically regularizing approach. Applied Sciences, 13(13), 7465. doi:10.3390/app13137465
17. Miyamoto K. ve Wolf E. (1962). Generalization of the Maggi–Rubinowicz theory of the boundary diffraction wave—Part I. Journal of the Optical Society of America, 52(6), 615–625. doi:10.1364/josa.52.000615
18. Patel M. R. ve Sengupta D. L. (2021). Diffraction from composite boundaries using hybrid analytic–numerical approaches. IEEE Transactions on Antennas and Propagation, 69(3), 1345–1356. doi:10.1109/tap.2020.3034567
19. Serdyuk V. M. (2023). Diffraction of a plane electromagnetic wave by a circular aperture in a conducting screen of finite thickness. Progress In Electromagnetics Research B, 102, 99–114. doi:10.2528/pierb23061503
20. Sheppard C. J. R. (2024). The Fresnel approximation and diffraction of focused waves. Photonics, 11(4), 346. doi:10.3390/photonics11040346
21. Umul Y. Z. (2010). Uniform boundary diffraction wave theory of Rubinowicz. Journal of the Optical Society of America A, 27(7), 1613–1619. doi:10.1364/josaa.27.001613
22. Wang Z., Kapsalidis F., Wang R., Beck M. ve Faist J. (2022). Ultra-low threshold lasing through phase front engineering via a metallic circular aperture. Nature Communications, 13, 230. doi:10.1038/s41467-021-27927-9
23. Yalçın U. (2009). Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces. Progress In Electromagnetics Research M, 7, 29–39. doi:10.2528/pierm09031201
24. Zhou F., Wu Y., Zhang Z., Bai X. ve Jiao C. (2022). Loop-to-loop magnetic coupling through a circular aperture in a planar PEC screen of finite thickness. IEEE Access, 10, 116635. doi:10.1109/access.2022.3219473