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Progress In Electromagnetics Research Letters
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By Y. Zhang, S. Li, Y. Zhu, Y. Zhuang, T. Suyama, C. Zheng, and Y. Okuno

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Based on the scattering theory and the Green function method, a dynamical theory is given for calculating the diffraction of deeply-etched gratings with a stratified structure substrate. The key of our method is that the patterned grating structure is considered as a perturbation to the unpatterned stratified structure rather than to vacuum. Using the first-order Born approximation and in the Fresnel diffraction region, we obtain a simple analytical expression, which can be used to calculating the scattering intensity of deeply-etched circular binary Fresnel zone plates with a stratified substrate (MDECBFZPs). The numerical results show that the focusing intensity at the foci of the MDCBFZP changes periodically with the etching depth and the thickness of the substrate film. Our results are in good agreement with FDTD simulations.

Y. Zhang, S. Li, Y. Zhu, Y. Zhuang, T. Suyama, C. Zheng, and Y. Okuno, "Periodic Transmission of Circular Binary Fresnel Zone Plates with Etching Depth and Substrate," Progress In Electromagnetics Research Letters, Vol. 40, 93-105, 2013.

1. Baez, A. V., "Fresnel zone plate for optical image formatting using extreme ultraviolet and soft X radiation," J. Opt. Soc. Am., Vol. 51, 405-412, 1961.

2. Schmahl, G., B. Niemann, D. Rudolph, M. Diehl, J. Thieme, W. Neff, R. Holz, R. Lebert, F. Richter, and G. Herziger, "A laboratory X-ray microscope with a plasma X-ray source," X-Ray Microscopy III, A. G. Michette, G. R. Morrison, and C. J. Buckley, Eds., Springer-Verlag, Berlin, 1992.

3. Fu, Y., W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, "Plasmonic microzone plate: Superfocusing at visible regime," Appl. Phys. Lett., Vol. 91, 2007.

4. Mote, R. G., S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, "Near-field focusing properties of zone plates in visible regime --- New insights," Opt. Express, Vol. 16, 9554-9564, 2008.

5. Kim, H. C., H. Ko, and M. S. Cheng, "High efficient optical focusing of a zone plate composed of metal/dielectric multilayer," Opt. Express, Vol. 17, 3078-3083, 2009.

6. Carretero, L., M. Perez-Molina, S. Blaya, P. Acebal, A. Fimia, R. Madrigal, and A. Murciano, "Near-field electromagnetic analysis of perfect black Fresnel zone pates using radial polarization," J. Lightwave Technolgy, Vol. 29, 2585-2591, 2011.

7. Wood, R. W., Physical Optics, 3rd Ed., Macmillan, New York, 1934.

8. Cao, Q. and J. Jahns, "Comprehensive focusing analysis of various Fresnel zone plates," J. Opt. Soc. Am. A, Vol. 21, 561-571, 2004.

9. Zhang, Y., C. Zheng, and H. Xiao, "Improving the resolution of a solid immersion lens optical system using a multiphase Fresnel zone plate," Opt. & Laser Techn., Vol. 37, 444-449, 2005.

10. Zhang, B. and D. Zhao, "Focusing properties of Fresnel zone plates with spiral phase," Opt. Express, Vol. 18, 12818-12823, 2010.

11. Lu, P., C. Zhou, J. Feng, and H. Cao, "Unified design of wavelength-independent deep-etched fused-silica gratings," Opt. Commun., Vol. 283, 4135-4140, 2010.

12. Wang, B., C. Zhou, J. Feng, H. Ru, and J. Zheng, "Wideband two-port beam splitter of a binary fused-silica phase grating," Appl. Opt., Vol. 47, 4004-4008, 2008.

13. Djabery, R., S. Nikmehr, and S. Hosseinzadeh, "Grating effects on sidelobe suppression in MIM plasmonic filters," Progress In Electromagnetics Research, Vol. 135, 271-280, 2013.

14. Edee, K., I. Fenniche, G. Granet, and B. Guizal, "Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings," Progress In Electromagnetics Research, Vol. 133, 17-35, 2013.

15. Sun, N.-H., J.-J. Liau, Y.-W. Kiang, S.-C. Lin, R.-Y. Ro, J.-S. Chiang, and H.-W. Chang, "Numerical analysis of apodized fiber Bragg gratings using coupled mode theory," Progress In Electromagnetics Research, Vol. 99, 289-306, 2009.

16. Frances, F., C. Neipp, A. Marquez, A. Belendez, I. Pascual, "Analysis of reflection gratings by a matrix method approach," Progress In Electromagnetics Research, Vol. 118, 167-183, 2011.

17. Born, M. and E.Wolf, Principle of Optics, 7th Ed., Cambridge University Press, Cambridge, 1999.

18. Sammar, A. and J.-M. Andre, "Diffraction of multilayer gratings and zone plates in the X-ray region using the born approximation," J. Opt. Soc. Am. A, Vol. 10, 600-613, 1993.

19. Sammar, A. and J.-M. Andre, "Dynamical theory of stratified Fresnel linear zone plates," J. Opt. Soc. Am. A, Vol. 10, 2324-2337, 1993.

20. Le, Z. and S. Pan, "Application of quantum scattering theory to 2-D focusing multilayer reflection circular zone plate," Opt. Commun., Vol. 159, 285-292, 1999.

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