Abstract

Practical collimating diffractive cylindrical lenses of 2, 4, 8, and 16 discrete levels are analyzed with a sequential application of the two-region formulation of the rigorous electromagnetic boundary-element method (BEM). A Gaussian beam of TE or TM polarization is incident upon the finite-thickness lens. F/4, F/2, and F/1.4 lenses are analyzed and near-field electric-field patterns are presented. The near-field wave-front quality is quantified by its mean-square deviation from a planar wave front. This deviation is found to be less than 0.05 free-space wavelengths. The far-field intensity patterns are determined and compared with the ones predicted by the approximate Fraunhofer scalar diffraction analysis. The diffraction efficiencies determined with the rigorous BEM are found to be generally lower than those obtained with the scalar approximation. For comparison, the performance characteristics of the corresponding continuous Fresnel (continuous profile within a zone but discontinuous at zone boundaries) and continuous refractive lenses are determined by the use of both the BEM and the scalar approximation. The diffraction efficiency of the continuous Fresnel lens is found to be similar to that of the 16-level diffractive lens but less than that of the continuous refractive lens. It is shown that the validity of the scalar approximation deteriorates as the lens f-number decreases.

© 1998 Optical Society of America

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1997 (3)

1996 (2)

K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1321 (1996).
[CrossRef]

1995 (4)

1994 (4)

1993 (1)

1991 (1)

T. Kojima, 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. Pt. 2 74, 11–20 (1991).
[CrossRef]

1989 (1)

Bryngdahl, O.

Buralli, D. A.

Crosignani, B.

S. Solimeno, B. Crosignani, A. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

Di Porto, A.

S. Solimeno, B. Crosignani, A. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

Fainman, Y.

Gallagher, N. C.

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Grann, E. B.

Herzig, H. P.

Hirayama, K.

Ido, J.

T. Kojima, 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. Pt. 2 74, 11–20 (1991).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), Chap. 6.

Kingslake, R.

R. Kingslake, Optical System Design (Academic, Orlando, Fla., 1983), p. 124.

Kojima, T.

T. Kojima, 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. Pt. 2 74, 11–20 (1991).
[CrossRef]

Koshiba, M.

M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43–47.

Kunz, R. E.

Lee, S. H.

Lichtenberg, B.

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
[CrossRef]

Lohmann, A. W.

Mait, J. N.

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 12, 34–43 (1997).
[CrossRef]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1321 (1996).
[CrossRef]

J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995).
[CrossRef]

Marchand, P.

Mirotznik, M. S.

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 12, 34–43 (1997).
[CrossRef]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1321 (1996).
[CrossRef]

Moharam, M. G.

Montiel, F.

Morris, G. M.

Nevière, M.

Nishihara, H.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 1–40.

Noponen, E.

Ozaktas, H. M.

Pommet, D. A.

Popelek, J.

J. Popelek, F. Urban, “The vector analysis of the real diffractive optical elements,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 89–99 (1994).

Prata, A.

Prather, D. W.

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 12, 34–43 (1997).
[CrossRef]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1321 (1996).
[CrossRef]

Rogers, J. R.

Rossi, M.

Schmitz, M.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 20.

Solimeno, S.

S. Solimeno, B. Crosignani, A. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

Suhara, T.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 1–40.

Turunen, J.

Urban, F.

J. Popelek, F. Urban, “The vector analysis of the real diffractive optical elements,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 89–99 (1994).

Urey, H.

Urquhart, K. S.

Vasara, A.

Wang, A.

Wilson, D. W.

Appl. Opt. (4)

Electron. Commun. Jpn. Pt. 2 (1)

T. Kojima, 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. Pt. 2 74, 11–20 (1991).
[CrossRef]

J. Mod. Opt. (1)

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1321 (1996).
[CrossRef]

J. Opt. Soc. Am. A (9)

Opt. Eng. (1)

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
[CrossRef]

Other (11)

P. K. Banerjee, R. Butterfield, eds., Developments in Boundary Element Methods (Applied Science, London, 1979).

M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43–47.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 1–40.

J. R. Leger, M. G. Moharam, T. K. Gaylord, eds., Feature Issue on Diffractive Optics Applications, Appl. Opt.34, 2399–2559 (1995).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

M. G. Moharam, T. K. Gaylord, J. R. Leger, eds., Feature Issue on Diffractive Optics Modeling, J. Opt. Soc. Am. A12, 1026–1169 (1995).

J. Popelek, F. Urban, “The vector analysis of the real diffractive optical elements,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 89–99 (1994).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), Chap. 6.

S. Solimeno, B. Crosignani, A. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 20.

R. Kingslake, Optical System Design (Academic, Orlando, Fla., 1983), p. 124.

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