An optimization algorithm that combines a rigorous electromagnetic computation model with an effective iterative method is utilized to design diffractive micro-optical elements that exhibit fast convergence and better design quality. The design example is a two-dimensional 1-to-2 beam splitter that can symmetrically generate two focal lines separated by 80 μm at the observation plane with a small angle separation of ±16°. Experimental results are presented for an element with continuous profiles fabricated into a monocrystalline silicon substrate that has a width of 160 μm and a focal length of 140 μm at a free-space wavelength of 10.6 μm.

© 2004 Optical Society of America

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Bendickson, J. M.

Di, F.

Gayload, T. K.

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Grann, E. B.

Guofan, J.

Jiang, J.

Liu, H.

Mackie, D.

Mait, J. N.

Moharam, M. G.

Nordin, G. P.

Pommet, D. A.

Prather, D. W.

Qiaofeng, T.

Shi, S. Y.

Yingbai, Y.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.


J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the solution of a 2-D diffraction problem by the FDTD method.

Fig. 2
Fig. 2

Normalized electrical field intensity at the observation plane for the 1-to-2 beam splitter: (a) target intensity distribution and real intensity distribution by our DMOE at the observation plane, (b) the beam splitter’s profile, and (c) the behavior of the polarization-dependent DMOE for the TE, for the TM, and the scalar approximations.

Fig. 3
Fig. 3

Schematic diagram of the mask-moving technique.

Fig. 4
Fig. 4

The real beam splitter: (a) photograph of the beam splitter etched into a monocrystalline silicon substrate and (b) depth distribution in the width direction.

Fig. 5
Fig. 5

Schematic diagram of the experimental system.

Fig. 6
Fig. 6

Two focused lines formed experimentally by the 1-to-2 beam splitter designed by our method.

Fig. 7
Fig. 7

Experimental results: (a) trace of the gray-level cross section of Fig. 6 and (b) traces showing the designed and tested results.

Equations (2)

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Hfx=expj2πy1-cos2 α1/2/λ,
RMS=1total-1i=1total|utargetixi, y0|2-|uixi, y0|221/2,