Abstract

A hexagonal array not only is a nature-preferred pattern but also is widely used in optoelectronical materials and devices. We report a simple method of hexagonal array illumination based on the Talbot effect that has a theoretical efficiency of 100%. An experimental efficiency of 90.6% with a binary phase 0,π hexagonal grating is given. This method should be highly interesting for applications of hexagonal array illumination in optical devices as well as in other hexagonal cells.

© 2002 Optical Society of America

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References

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2000 (1)

1999 (1)

1997 (1)

1995 (1)

1993 (1)

1991 (3)

1990 (1)

1965 (1)

Arkwright, J. W.

Arrizón, V.

Cui, B.

Das, K. K.

Honda, T.

Iftekharuddin, K. M.

Karim, M. A.

Kida, J.

Liu, L.

Liu, X.

Lohmann, A. W.

López-Olazagasti, E.

Madamopoulos, N.

Madou, M.

M. Madou, Fundamentals of Microfabrication (CRC Press, New York, 1997), pp. 71–86.

Mortimore, D. B.

Nemoto, S.

Riza, N. A.

Stankovic, S.

Thomas, J. A.

Tschudi, T.

Winthrop, J. T.

Worthington, C. R.

Zhou, C.

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Figures (3)

Fig. 1
Fig. 1

Illustration of the optical setup for HA illumination.

Fig. 2
Fig. 2

Experimental result of near-field HA illumination at the half-Talbot distance of z=zT/2=3tx2/4λ, where tx and ty denote periods in the x and y dimensions, respectively, and ty=3tx. For the binary phase gratings in Fig. 1 as the hexagonal grating, a white hexagon corresponds to phase π and a black hexagon corresponds to phase 0.

Fig. 3
Fig. 3

Experimental spectra of the HA binary phase grating in Fig. 2. The circles were added to show the HA spots of Eq. (8). Note that the intensities inside the circles are zero.

Tables (1)

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Table 1 Parity Relations of k, m, and k2-km+m2 in Eq. (6)

Equations (9)

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replx,y= combx/txcomby/3tx+combx/tx-1/2comby/3tx-1/2/3tx2,
Ufx,fy=Tfx,fyRfx,fy,
Rfx,fy= combtxfxcomb3txfy×1+expiπfx+3fytx.
ux,y=m=-+n=-+cmn expi2πmxtx+ny3tx=c00+Δu,
uzx,y=expi2πλzmncmn expi2πmxtx+ny3tx×expiπλz3m2+n23tx2.
uzx,y= mncmn expi2πmxtx+ny3tx×expi2πz3tx2/2λk2-km+m2.
uzx,y= c00+mncmnB×expi2πmxtx+ny3tx,
Sm,n= combm/4combn/4+combm/4-1/2combn/4-1/2.
uzx,y=c00-Δu1=0c00-Δu2=2.

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