Abstract

A conventional method to synthesize diffractive optical elements and computer-generated holograms (CGH’s) with high diffraction efficiency relies on an increase of phase levels. To fabricate such a device, one should perform electron-beam (e-beam) lithography with multiple-dose exposures or multiple-step photolithography. Here we describe a one-step method, which is based on the effective medium theory, for the fabrication of a multilevel phase CGH. The phase modulations required in cells of a CGH are constructed by means of dividing these cells into fine (subwavelength) structures. The surface features of these fine structures control their corresponding indices, and their values can be calculated according to the effective medium theory. By proper selection of the fine structures, based on the requirements of the phase modulation of the cells, a CGH with multilevel phases is synthesized when a binary structure is relieved on the dielectric material. Then the CGH can be fabricated by direct e-beam lithography or one-step photolithography through an amplitude mask followed by an ion-etching treatment. The experimental results showed that the reconstructed wave field is in good agreement with that simulated by a computer, indicating the effectiveness of the proposed method.

© 2000 Optical Society of America

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References

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1995

D. Mendlovic, I. Kiryuschev, “Two channel computer generated hologram and its application for optical correlation,” Opt. Commun. 116, 322–325 (1995).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

1992

1991

1990

1987

1972

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik 35, 237–246 (1972).

Allebach, J. P.

Astilean, S.

Bengtsson, J.

Bryngdahl-Lalanne, D.

P. Lalanne, D. Bryngdahl-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Cescato, L. H.

Chavel, P.

Chen, F. T.

Craighead, H. G.

Farn, M. W.

Gaylord, T. K.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik 35, 237–246 (1972).

Gluch, E.

Grann, E. B.

Iwata, K.

Kato, M.

Kikuta, H.

Kiryuschev, I.

D. Mendlovic, I. Kiryuschev, “Two channel computer generated hologram and its application for optical correlation,” Opt. Commun. 116, 322–325 (1995).
[CrossRef]

Kubo, H.

Lalanne, P.

P. Lalanne, S. Astilean, P. Chavel, “Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings,” Opt. Lett. 23, 1081–1083 (1998).
[CrossRef]

P. Lalanne, D. Bryngdahl-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Maharam, M. G.

Marom, E.

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, G. Shabtay, E. Marom, “High-efficiency arbitrary array generator,” Appl. Opt. 35, 6875–6880 (1996).
[CrossRef] [PubMed]

D. Mendlovic, I. Kiryuschev, “Two channel computer generated hologram and its application for optical correlation,” Opt. Commun. 116, 322–325 (1995).
[CrossRef]

Moharam, M. G.

Ohira, Y.

Pommet, D. A.

Sakuda, K.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik 35, 237–246 (1972).

Seldowitz, M. A.

Shabtay, G.

Southwell, W. H.

Streibl, N.

Sweeney, D. W.

Zalevsky, Z.

Appl. Opt.

J. Mod. Opt.

P. Lalanne, D. Bryngdahl-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

D. Mendlovic, I. Kiryuschev, “Two channel computer generated hologram and its application for optical correlation,” Opt. Commun. 116, 322–325 (1995).
[CrossRef]

Opt. Lett.

Optik

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik 35, 237–246 (1972).

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Figures (6)

Fig. 1
Fig. 1

(a) Target pattern, (b) synthesized multilevel phase CGH pattern, and (c) reconstructed image of the synthesized CGH.

Fig. 2
Fig. 2

(a) 2-D subwavelength grating relieved on the dielectric material, (b) zeroth diffraction efficiency with respect to the period of the grating (depth d = 1.5λ, filling factor f = 0.5, n = 1.467).

Fig. 3
Fig. 3

Fabrication steps with use of e-beam lithography: (a) e-beam patterning through the resist, (b) development, (c) chromium evaporation, (d) lift-off of resist, (e) result after etching process.

Fig. 4
Fig. 4

Synthesized surface profiles for obtaining the desired phase modulations based on effective medium theory in the pixels of (a) 0, (b) π/2, (c) π, (d) 3π/2 phase modulations (white, exposure; black, nonexposure).

Fig. 5
Fig. 5

Scanning electron microscope photograph of the CGH after etching process: (a) top view, (b) side view.

Fig. 6
Fig. 6

Reconstructed image captured by CCD camera when the fabricated CGH is illuminated with an 800-nm-wavelength laser.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

nTE2=fn2+1-f,
nTM-2=fn-2+1-f,
δϕ=ϕ1-ϕ2=2πdn-1/λ,

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