## Entirely Electromagnetic Analysis of Microlenses Without a Beam-Shaping Aperture

Applied Optics, Vol. 40, Issue 10, pp. 1686-1691 (2001)

http://dx.doi.org/10.1364/AO.40.001686

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### Abstract

We suggest an approach for numerically studying the performance of cylindrical microlenses without a beam-shaping aperture based on the boundary-element method (BEM). We divide the infinite microlens boundary into two components: The first part is an infinite expanded flat interface excluding the curved interface, and the second part is only the originally curved microlens interface. The resulting transmitted field can be regarded as the composition of two fields: One is generated by the first boundary, and the other is contributed from the second boundary. We carry out numerical simulations for two microlens systems, with or without aperture. We find that, for the nonapertured system, an ideal focusing feature is still observed; however, the axial distribution of the transmitted field exhibits an oscillation, different from the apertured system. It is expected that the current approach may provide a useful technique for the analysis of micro-optical elements.

© 2001 Optical Society of America

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

**Citation**

Juan Liu, Bi-Zhen Dong, Ben-Yuan Gu, and Guo-Zhen Yang, "Entirely Electromagnetic Analysis of Microlenses Without a Beam-Shaping Aperture," Appl. Opt. **40**, 1686-1691 (2001)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-10-1686

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### References

- J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).
- K. Hirayama, E. N. Glytsis, T. K. Gaylord, and D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
- J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113–130 (1999).
- K. Hirayama, K. Igarashi, Y. Hayashi, E. N. Glytsis, and T. K. Gaylord, “Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods,” J. Opt. Soc. Am. A 16, 1294–1302 (1999).
- E. N. Glytsis, M. E. Harrigan, T. K. Gaylord, and K. Hirayama, “Effects of fabrication errors on the performance of cylindrical diffractive lenses: rigorous boundary-element method and scalar approximation,” Appl. Opt. 37, 6591–6602 (1998).
- E. N. Glytsis, M. E. Harrigan, K. Hirayama, and T. K. Gaylord, “Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation,” Appl. Opt. 37, 34–43 (1998).
- V. P. Koronkevich and I. G. Pal’chikova, “Modern zone plates,” Avtometriya 1, 85–100 (1992).
- V. Moreno, J. F. Roman, and J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
- A. Wang and A. Prata, Jr., “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161–1169 (1995).
- P. Blattner and H. P. Herzig, “Rigorous diffraction theory applied to microlenses,” J. Mod. Opt. 45, 1395–1403 (1998).
- D. W. Prather, S. Shi, and J. S. Bergey, “Field stitching algorithm for the analysis of electrically large diffractive optical elements,” Opt. Lett. 24, 273–275 (1999).
- D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).
- D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
- M. S. Mirotznik, D. W. Prather, and J. N. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1321 (1996).
- B. Lichtenberg and N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
- E. Noponen, J. Turunen, and A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
- Y. Nakata and M. Koshiba, “Boundary-element analysis of plane-wave diffraction from groove-type dielectric and metallic gratings,” J. Opt. Soc. Am. A 7, 1494–1502 (1990).
- J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995).
- D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1837 (1994).
- S. Kagami and I. Fukai, “Application of boundary-element method to electro-magnetic field problems,” IEEE Trans. Microwave Theory Tech. MTT-32, 455–461 (1984).
- K. Yashiro and S. Ohkawa, “Boundary element method for electromagnetic field problems,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chaps. 3, 4, and 6.
- R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), Chap. 6.
- M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43–47.

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