Abstract

We present a rigorous electromagnetic design and analysis of two-dimensional diffractive lenses (DLs) with different axial resolution and high lateral resolution. Without paraxial approximation, focusing characteristics of two kinds of DL, one with a long focal depth and a high lateral resolution, the other with high axial resolution and high lateral resolution, for f-numbers of 0.6, 1.0, 1.5, and 2.0 have been determined including the actual focal depth, the ratio between the focal depth of the designed DL and the focal depth of the conventional quadratic lens, and the spot size of the central lobe at the actual focal plane. Numerical and graphic results show that the designed DLs indeed have a long focal depth and a high lateral resolution, or high axial resolution and high lateral resolution by use of different preset focal depths.

© 2003 Optical Society of America

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References

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Appl. Opt. (2)

J. Comput. Phys. (1)

J. P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

P. Torok and T. Wilson, �??Rigorous theory for axial resolution in confocal microscopes,�?? Opt. Commun. 137, 127�??135 (1997).
[CrossRef]

Opt. Eng. (2)

D. W. Prather, S. Y. Shi, and J. Sonsrtoem, �??Electromagnetic analysis of finite-thickness diffractive elements,�?? Opt. Eng. 41, 1792�??1796 (2002).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (3)

Proc. SPIE (1)

D. W. Prather, M. S. Mirotznik, and J. N. Mait, �??Boundary element method for vector modeling diffractive optical elements, �?? in Diffractive and Holographic Optics Technology II, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2404, 28�??39 (1995).
[CrossRef]

Other (1)

A. Taflove, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).

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Figures (8)

Fig. 1.
Fig. 1.

Diffractive field axial intensity distribution of DLs (f/1.0) with different preset focal depths df.

Fig. 2.
Fig. 2.

Diffractive field lateral intensity distribution of DLs (f/1.0) with different preset focal depths df at the actual focal plane.

Fig. 3.
Fig. 3.

Diffractive field lateral intensity distribution of a DL (f/1.0) with a preset focal depth: (a) df=-3.6 µm at three planes of different distances from the surface of the DL and (b) df=+3.6 µm at three planes of different distances from the suface of the DL.

Fig. 4.
Fig. 4.

Propagation plots of the intensity of the electric field of DLs (f/1.0) with different preset focal depths: (a) df=-3.6µm, (b) df=0µm, (c) df=+3.6µm.

Fig. 5.
Fig. 5.

Diffractive field axial intensity distribution of DLs (f/2.0) with different preset focal depths df.

Fig. 6.
Fig. 6.

Diffractive field lateral intensity distribution of DLs (f/2.0) with different preset focal depths df at the actual focal plane.

Fig. 7.
Fig. 7.

Diffractive field lateral intensity distribution of a DL (f/2.0) with a preset focal depth at three different planes of distances from the surface of the DL: (a) df=-14.4 µm and (b) df=+14.4 µm.

Fig. 8.
Fig. 8.

Propagation plot of the intensity of the electric field of DLs (f/2.0) with different preset focal depths: (a) df=-14.4 µm, (b) df=0 µm, (c) df=+14.4 µm.

Tables (1)

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Table 1. Focusing characteristics of DLs with different preset focal depths for several f-numbers*

Equations (7)

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E z t = 1 ε ( H y x H x y σ E z )
H x t = 1 μ ( E z y + σ * H x )
H y t = 1 μ ( E z x σ * H y )
H ( f x ) = exp ( j 2 π y 0 1 cos 2 α λ )
y ( x ) = n 2 n 1 n 2 ( f 2 + x 2 f m λ ) x m x min ( x m + 1 , D 2 )
f ( x ) = f 0 + d f x 2 ( D 2 ) 2
y ( x ) = n 2 n 1 n 2 ( ( f 0 + d f x 2 ( D 2 ) 2 ) 2 + x 2 ( f 0 + d f x 2 ( D 2 ) 2 ) m λ )

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