## Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods

JOSA A, Vol. 16, Issue 6, pp. 1294-1302 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001294

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### Abstract

A novel approach based on the boundary-element method (BEM) with exact and approximate Green’s functions is presented for the analysis of the performance of finite-substrate-thickness cylindrical diffractive lenses. This approach can be applied to the analysis of lenses with thicknesses of thousands of wavelengths for both TE and TM polarization. Multiple interference resonance effects between the upper and the lower boundaries of the lens are included. Also, for the cases when multiple interference resonance effects can be neglected, another approach based on the BEM with a modified approximate Green’s function is developed. It is shown that the latter approach corresponds to the cascaded application of the BEM as previously published [Appl. Opt. **37**, 34, 6591 (1998)]. To illustrate the advantages of the approaches presented, a cylindrical diffractive lens with a substrate thickness of 2 mm is analyzed. It is not possible to analyze this large-substrate-thickness lens with the previously published cascaded application of the BEM.

© 1999 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1970) Diffraction and gratings : Diffractive optics

**Citation**

Koichi Hirayama, Ken Igarashi, Yoshio Hayashi, Elias N. Glytsis, and Thomas K. Gaylord, "Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods," J. Opt. Soc. Am. A **16**, 1294-1302 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-6-1294

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### References

- H. Nishihara and T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. XXIV, pp. 1–40.
- J. R. Leger, M. G. Moharam, and T. K. Gaylord, eds., feature diffractive optics applications, Appl. Opt. 34, 2399–2559 (1995).
- H. M. Ozaktas, H. Urey, and A. W. Lohmann, “Scaling of diffractive and refractive lenses for optical computing and interconnections,” Appl. Opt. 33, 3782–3789 (1994).
- K. S. Urquhart, P. Marchand, Y. Fainman, and S. H. Lee, “Diffractive optics applied to free-space optical interconnects,” Appl. Opt. 33, 3670–3682 (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).
- F. Montiel and M. Nevière, “Electromagnetic theory of Bragg–Fresnel linear zone plates,” J. Opt. Soc. Am. A 12, 2672–2678 (1995).
- A. Wang and A. Prata, Jr., “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161–1169 (1995).
- J. Popelek and F. Urban, “The vector analysis of the real diffractive optical elements,” in Nonconventional Optical Imaging Elements, J. Nowak and M. Zajac, eds., Proc. SPIE 2169, 89–99 (1994).
- B. Lichtenberg and N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. (Bellingham) 33, 3518–3526 (1994).
- 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).
- 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).
- 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).
- 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).
- 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).
- L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), pp. 506–538.
- G. S. Smith, “Directive properties of antennas for transmission into a material half-space,” IEEE Trans. Antennas Propag. AP-32, 232–246 (1984).
- C. M. Butler, “Current induced on a conducting strip which resides on the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. AP-32, 226–231 (1984).
- C. M. Butler, X. Xu, and A. W. Glisson, “Current induced on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. AP-33, 616–624 (1985).
- P. G. Cottis and J. D. Kanellopoulos, “Scattering from dielectric cylinders embedded in a two-layer lossy medium,” Int. J. Electron. 61, 477–486 (1986).
- X. Xu and A. W. Glisson, “Scattering of TM excitation by coupled and partially buried cylinders at the interface between two media,” IEEE Trans. Antennas Propag. AP-35, 529–538 (1987).
- N. P. Zhuck and A. G. Yarovoy, “Two-dimensional scattering from an inhomogeneous dielectric cylinder embedded in a stratified medium: case of TM polarization,” IEEE Trans. Antennas Propag. 42, 16–21 (1994).
- E. Nishimura, N. Morita, and N. Kumagi, “Scattering of guided modes caused by an arbitrarily shaped broken end in a dielectric slab waveguide,” IEEE Trans. Microwave Theory Tech. MTT-31, 923–930 (1983).
- T. Kojima and J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
- M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK, Publishers, Tokyo, 1992), pp. 43–47.
- K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
- D. A. Buralli, G. M. Morris, and J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
- M. Rossi, R. E. Kunz, and H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. 34, 5996–6007 (1995).
- R. Kingslake, Optical System Design (Academic, Orlando, Fla., 1983), p. 124.

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