A complex image method is presented for the analysis of a subwavelength circular aperture in a perfectly conducting screen of infinitesimal thickness illuminated by a plane wave. The method is based on the Bethe-Bouwkamp quasi static model of the aperture field and uses the spectral domain formulation as the point of departure. Closed-form expressions are obtained for the electromagnetic fields valid for all observation points. Sample numerical results demonstrate the accuracy and efficiency of the method for both normal and oblique illuminations, including an evanescent wave. In the latter case, the results show a circulating power flux and enhanced field confinement near the aperture.
2. Ducourtieux, S., S. Grésillon, J. C. Rivoal, C. Vannier, C. Bainier, D. Courjon, and H. Cory, "Imaging subwavelength holes in chromium films in scanning near-field optical microscopy. Comparison between experiments and calculation," Eur. Phys. J. Appl. Phys., Vol. 26, 35-43, 2004.
doi:10.1051/epjap:2004014
3. Lin, Y., M. H. Hong, W. J. Wang, Z. B. Wang, G. X. Chen, Q. Xie, L. S. Tan, and T. C. Chong, "Surface nanostructuring by femtosecond laser irradiation through near-field scanning optical microscopy," Sens. Actuators A, Vol. 133, 311-316, 2007.
doi:10.1016/j.sna.2006.05.047
4. Bethe, H. A., "Theory of diffraction by small holes," Phys. Rev., Vol. 66, 163-182, Oct. 1944.
doi:10.1103/PhysRev.66.163
5. Bouwkamp, C. J., "On Bethe's theory of diffraction by small holes," Philips Res. Rep., Vol. 5, 321-332, Oct. 1950.
6. Bouwkamp, C. J., "Diffraction theory. A critique of some recent developments,", Math. Res. Group, Res. Rep. No. EM-50, New York University, Washington Sq. College of Arts and Science, New York, Apr. 1953.
7. Bouwkamp, C. J., "Diffraction theory," Rep. Progr. Phys., Vol. 17, 35-100, 1954.
doi:10.1088/0034-4885/17/1/302
8. Dunn, R. C., "Near-field scanning optical microscopy," Chem. Rev., Vol. 99, 2891-2927, 1999.
doi:10.1021/cr980130e
9. Leviatan, Y., "Study of near-zone fields of a small aperture," Appl. Phys., Vol. 60, No. 5, 1577-1583, 1986.
10. Dürig, U., D. W. Pohl, and F. Rohner, "Near-field optical-scanning microscopy," J. Appl. Phys., Vol. 59, No. 10, 3318-3327, 1986.
doi:10.1063/1.336848
11. Nakano, T. and S. Kawata, "Numerical analysis of the near-field diffraction pattern of a small aperture," J. Mod. Opt., Vol. 39, No. 3, 645-661, 1992.
doi:10.1080/09500349214550611
12. Van Labeke, D., D. Barchiesi, and F. Baida, "Optical characterization of nanosources used in scanning near-field optical microscropy," J. Opt. Soc. Am. A, Vol. 12, No. 4, 695-703, 1995.
doi:10.1364/JOSAA.12.000695
13. Van Labeke, D., F. I. Baida, and J. Vigoureux, "A theoretical study of near-field detection and excitation of surface plasmons," Ultramicroscopy, Vol. 71, 351-359, 1998.
doi:10.1016/S0304-3991(97)00067-3
14. Baida, F. I. and D. Van Labeke, "Propagation and diffraction of locally excited surface plasmons," J. Opt. Soc. Am. A, Vol. 18, 1552-1561, July 2001.
15. Grober, R. D., T. Rutherford, and T. D. Harris, "Modal approximation for the electromagnetic field of a near-field optical probe," Appl. Opt., Vol. 35, 3488-3494, July 1996.
16. Stevenson, R. and D. Richards, "The use of a near-field probe for the study of semiconductor heterostructures," Semicond. Sci. Technol., Vol. 13, 882-886, 1998.
doi:10.1088/0268-1242/13/8/009
17. Petersson, L. E. R. and G. S. Smith, "Transmission of an inhomogeneous plane wave through an electrically small aperture in a perfectly conducting plane screen," J. Opt. Soc. Am. A, Vol. 21, No. 6, 975-980, 2004.
doi:10.1364/JOSAA.21.000975
18. Harrington, R. F., Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961.
19. Lin, C., K. M. Leung, and T. Tamir, "Modal transmission-line theory of three-dimensional periodic structures with arbitrary lattice configurations," J. Opt. Soc. Am. A, Vol. 19, 2005-2017, Oct. 2002.
20. Michalski, K. A., "Extrapolation methods for Sommerfeld integral tails (Invited review paper)," IEEE Trans. Antennas Propagat., Vol. 46, 1405-1418, Oct. 1998.
21. Aksun, M. I., "A robust approach for the derivation of closed-form Green's functions," IEEE Trans. Microwave Theory Tech., Vol. 44, 651-658, May 1996.
doi:10.1109/22.493917
22. Li, Y. L. and M. J. White, "Near-field computation for sound propagation above ground --- Using complex image theory," J. Acoust. Soc. Am., Vol. 99, 755-760, Feb. 1996.
doi:10.1121/1.414652
23. Alparslan, A., M. I. Aksun, and K. A. Michalski, "Closed-form Green's functions in planar layered media for all ranges and materials," IEEE Trans. Microwave Theory Tech., Vol. 58, 602-613, Mar. 2010.
doi:10.1109/TMTT.2010.2040354
24. Sarkar, T. K. and O. Pereira, "Using the matrix pencil method to estimate the parameters of a sum of complex exponentials," IEEE Antennas Propagat. Magaz., Vol. 37, 48-55, Feb. 1995.
doi:10.1109/74.370583
25. Rahmat-Samii, Y. and R. Mittra, "Electromagnetic coupling through small apertures in a conducting screen," IEEE Trans. Antennas Propagat., Vol. 25, 180-187, Mar. 1977.
doi:10.1109/TAP.1977.1141554
26. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.
Submit
