Abstract

The design of diffractive phase elements (DPE's) for generating color pseudo-nondiffracting beams (PNDB's) in a multiple-wave illuminating system by the conjugate-gradient method is described. The axial-intensity distributions for dual-color PNDB's generated by the DPE's are shown. The color PNDB's behave as segmented axial-intensity distributions; in each of segments only one color persists. The sequence of wavelength components in the color PNDB's can be arbitrarily preset. Three-dimensional plots of a dual-color PNDB indicate the characteristics of a beam with high transverse resolution.

© 1998 Optical Society of America

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References

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1998 (1)

1996 (2)

1995 (3)

1994 (3)

1992 (1)

1991 (1)

Avriel, M.

M. Avriel, Nonlinear Programming:?Analysis and Methods, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1976), Chap.??10, p. 299.

Bará, S.

Davidson, N.

Dong, B. Z.

Ersoy, O. K.

Friberg, A. T.

Friesem, A. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, San Francisco, Calif., 1968), Chap.??4, p. 60.

Gu, B. Y.

Hasman, E.

Jaroszewicz, Z.

Kolodziejczyk, A.

Liu, H. K.

Liu, R.

Piestun, R.

Rosen, J.

Salik, B.

Shamir, J.

Sochacki, J.

Yang, G. Z.

Yariv, A.

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Figures (3)

Fig. 1
Fig. 1

Axial-intensity distribution of the dual-color PNDB's with two segments: (a) λ1=0.5145 µm is desig-nated for the first segment and λ2=0.6328 µm for the second segment. Dotted curve, 0.5145 µm; solid curve, 0.6328 µm. (b) Interchange of these two wavelengths for the two segments.

Fig. 2
Fig. 2

Three-dimensional plots of the dual-color PNDB with two segments, corresponding to Fig.  1(a): (a) λ1=0.5145µm segment, (b) λ2=0.6328µm segment.

Fig. 3
Fig. 3

Axial-intensity distribution for the color PNDB with four segments. The colors of the four segments are alternately changed as each segment takes the value λ2=0.6328 µm and then λ1=0.5145 µm. Dashed curve, λ1=0.5145µm segment; solid curve, λ2=0.6328µm segment.

Equations (10)

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U2λα, zβ=2πiλαzβexpi2πzβ/λα×0R1mρ1r1, λαexpi2πλαnλα-1hr1×expiπr12/λαzβr1dr1, 
E=α=1Nλβ=1NzWλα, zβρ˜2λα, zβ-U2λα, zβ2, 
hr1=hc sinyr1,
yk+1r1=ykr1+τkdk,  k=0, 1, 2, 3, , 
dk=-Eykr1+βk-1dk-1,  k=1, 2, 3, , 
βk-1=Eykr12Eyk-1r12,  k=1, 2, 3, , 
Eyξyξ=-2 Imα=1Nλβ=1NzWλα, zβ×2πλαnλα-1hc cosyξρ1ξ, λα×expi2πλαnλα-1hc sinyξ×1-ρ˜2λα, zβU2λα, zβGλα, zβ, ξU2*λα, zβ,
Gλα, zβ, ξ=2πiλαzβexpi2πzβ/λαexpiπξ2/λαzβξ.
Wλα, zβ=0.9Npin the signal region0.1Nz-Npin other regions,
nonuniformity=I2-I21/2I,

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