The dipole impedance of an aperture in a plane conductor is obtained by modifying the general network formulation of electromagnetic apertures presented by Mautz and Harrington. The derived dipole impedances are combined in parallel to form an effective circuit description of low frequency aperture diffraction. Power transmitted into the aperture by an incident wave is determined by incorporating standard techniques for the transfer of wave power at an impedance mismatch. This transmitted power is divided into forward and backward scattered fields based upon the behavior of image currents surrounding the aperture, leading to a peak in forward scattered power above unity, consistent with known aperture behavior. The presented aperture circuit maintains an excellent correspondence with measurements of radiated power for an aperture excited by high energy electrons and with the numerically calculated impedance of a circular aperture using the finite element method.
2. Harrington, R. F. and J. R. Mautz, "A generalized network formulation for aperture problems," IEEE Transactions on Antennas and Propagation, 870-873, 1976.
doi:10.1109/TAP.1976.1141420
3. Harrington, R. F. and D. T. Auckland, "Electromagnetic transmission through narrow slots in thick conducting screens," IEEE Transactions on Antennas and Propagation, Vol. 28, No. 5, 616-622, 1980.
doi:10.1109/TAP.1980.1142382
4. Harrington, R. F., "Resonant behavior of a small aperture backed by a conducting body," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 2, 205-212, 1982.
doi:10.1109/TAP.1982.1142761
5. Mautz, J. R. and R. F. Harrington, "An admittance solution for electromagnetic coupling through a small aperture," Appl. Scien. Res., Vol. 40, 36-69, 1983.
6. Harrington, R. F. and J. R. Mautz, "Characteristic modes for aperture problems," IEEE Transactions on Microwave Theory and Techniques, Vol. 33, No. 6, 500-505, 1985.
doi:10.1109/TMTT.1985.1133105
7. Harrington, R. F. and J. R. Mautz, "Electromagnetic coupling through apertures by the generalized admittance approach," Comput. Phys. Comm., Vol. 68, 19-42, 1991.
doi:10.1016/0010-4655(91)90192-N
8. Wang, T., R. F. Harrington, and J. R. Mautz, "Electromagnetic scattering from and transmission through arbitrary apertures in conducting bodies," IEEE Transactions on Antennas and Propagation, Vol. 38, No. 11, 1805-1814, 1990.
doi:10.1109/8.102743
9. Leviatan, L., R. F. Harrington, and J. R. Mautz, "Electromagnetic transmission through apertures in a cavity in a thick conductor," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 6, 1153-1165, 1982.
doi:10.1109/TAP.1982.1142926
10. Liang, C. and D. K. Cheng, "Generalized network representations for small-aperture coupling between dissimilar regions," IEEE Transactions on Antennas and Propagation, Vol. 31, No. 1, 177-182, 1983.
doi:10.1109/TAP.1983.1143007
11. Hsi, S., R. F. Harrington, and J. R. Mautz, "Electromagnetic coupling to a conducting wire behind an aperture of arbitrary size and shape," IEEE Transactions on Antennas and Propagation, Vol. 33, No. 6, 581-587, 1985.
doi:10.1109/TAP.1985.1143628
12. Jeng, S. K., "Scattering from a cavity-backed slit in a ground plane-TE case," IEEE Transactions on Antennas and Propagation, Vol. 38, 1523-1529, 1990.
doi:10.1109/8.59763
13. Bethe, H., "Theory of diffraction by small holes," Phys. Rev., Vol. 66, No. 7--8, 163-182, 1944.
doi:10.1103/PhysRev.66.163
14. Bouwkamp, C. J., "Diffraction theory," Rep. on Prog. in Phys., Vol. 17, 35-100, 1954.
doi:10.1088/0034-4885/17/1/302
15. Garcia de Abajo, F. J., "Light transmission through a single cylindrical hole in a metallic film," Opt. Exp., Vol. 10, No. 25, 1475-1484, 2002.
16. Roberts, A., "Electromagnetic theory of diffraction by a circular aperture in a thick, perfectly conducting screen," J. Opt. Soc. Am., Vol. 4, No. 10, 1970-1983, 1987.
doi:10.1364/JOSAA.4.001970
17. Degiron, A., H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Comm., Vol. 239, No. 1--3, 61-66, 2004.
doi:10.1016/j.optcom.2004.05.058
18. Rayleigh, L., Theory of Sound, Dover Publications, New York, 1945.
19. Blackstock, D. T., Fundamentals of Physical Acoustics, Wiley-Interscience, New York, 2000.
20. Chang, C., A. K. Sarychev, and V. M Shalaev, "Light diffraction by a subwavelength circular aperture," Laser Phys. Lett., Vol. 2, 351-355, 2005.
doi:10.1002/lapl.200510006
21. Ebbesen, T. W., H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature, Vol. 391, 667-669, 1998.
doi:10.1038/35570
22. Genet, C. and T. W. Ebbesen, "Light in tiny holes," Nature, Vol. 445, No. 7123, 39-46, 2007.
doi:10.1038/nature05350
23. Harrington, R. F., Time-Harmonic Electromagnetic Fields, IEEE Press, 2004.
24. Gluckstern, R. L. and R. K. Cooper, "Electric polarizability and magnetic susceptibility of small holes in a thin screen," IEEE Transactions on Microwave Theory and Techniques, Vol. 38, No. 2, 186-192, 1990.
doi:10.1109/22.46429
25. De Meulenaere, F. D. and J. Van Bladel, "Polarizability of some small apertures," IEEE Transactions on Antennas and Propagation, Vol. 25, No. 25, 198-205, 1977.
doi:10.1109/TAP.1977.1141568
26. Jackson, J. D., Classical Electrodynamics, John Wiley and Sons, New York, 1999.
27. Bortchagovsky, E., G. Colas Des Francs, D. Molenda, A. Naber, and U. C. Fisher, "Transmission of an obliquely incident beam of light though small apertures in a metal film," Appl. Phys. B, Vol. 85, No. 1--2, 49-53, 2006.
doi:10.1007/s00340-006-2296-9