Abstract

The design of a diffractive phase element (DPE) that simultaneously implements wavelength demultiplexing and focusing is carried out on the basis of the general theory of amplitude-phase retrieval. The designed DPE is fabricated with optical contact lithography. Three masks are needed to produce the surface-relief structure of the DPE with eight quantized levels in depths. Experiments demonstrate that the designed DPE can successfully implement both the functions of demultiplexing three different-wavelength beams and focusing each component at a predesignated position simultaneously. Experimental measurements are in good agreement with the results of numerical simulations.

© 1996 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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1995 (2)

1994 (2)

1993 (4)

1992 (1)

Amitai, Y.

Y. Amitai, “Design of wavelength-division multiplexing/demultiplexing using substrate-mode holographic elements,” Opt. Commun. 98, 24–28 (1993).
[CrossRef]

Chang, M.-P.

Dong, B.

Dong, B.-Z.

Ersoy, O. K.

Farn, M. W.

Goodman, J. W.

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

Gu, B.

Gu, B.-Y.

Ishii, Y.

Kato, M.

Kewitsch, A.

Kubota, T.

Medeiros, S. S.

Sakuda, K.

Segev, M.

Stern, M. B.

Tan, X.

Weldkamp, W. B.

Yang, G.

Yang, G.-Z.

Yariv, A.

Zhang, G.-Q.

B. Dong, G. Yang, B. Gu, G.-Q. Zhang, “Diffractive phase elements that implement wavelength demultiplexing and spatial annular focusing simultaneously,” J. Opt. Soc. Am. A (to be published).

Zhuang, J.-Y.

Appl. Opt. (5)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

Y. Amitai, “Design of wavelength-division multiplexing/demultiplexing using substrate-mode holographic elements,” Opt. Commun. 98, 24–28 (1993).
[CrossRef]

Opt. Lett. (2)

Other (2)

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

B. Dong, G. Yang, B. Gu, G.-Q. Zhang, “Diffractive phase elements that implement wavelength demultiplexing and spatial annular focusing simultaneously,” J. Opt. Soc. Am. A (to be published).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of a polychromatic optical system.

Fig. 2
Fig. 2

(a) Modulation-depth distribution of the designed surface-relief-type DPE with eight quantized levels. The needed etch depth is 0.155 μm, the size of each pixel is 30 μm, and the total number of pixels is 256. (b) Output intensity distribution generated by the designed DPE. Three intensity peaks appear at the predesignated positions x 2 λ 1 0 = 0.87 mm for λ1 = 0.5145 μm, x 2 λ 2 0 = 3.43 mm for λ2 = 0.5900 μm, and x 2 λ 3 0 = 4.741 mm for λ3 = 0.6328 μm.

Fig. 3
Fig. 3

Photographic masks for an eight-level DPE: (a) mask 1, (b) mask 2, and (c) mask 3.

Fig. 4
Fig. 4

Section of a surface-relief trace of the eight-level DPE obtained by scanning with a Sloan Dektak profilometer.

Fig. 5
Fig. 5

Experimental setup of the polychromatic system for evaluating the performance of the designed DPE. HM1–HM3 represent the beam splitter. M1–M3 are mirrors.

Fig. 6
Fig. 6

Measurements of the incident light consisting of three laser beams for achieving wavelength demultiplexing and spatial focusing: (a) The output intensity distribution as measured with a CCD camera. Three strong intensity peaks are located at the predesignated positions, x 2 λ 1 0 = 0.95 mm for λ1 = 0.5145 μm, x 2 λ 2 0 = 3.48 mm for λ2 = 0.5900 μm, and x 2 λ 3 0 = 4.73 mm for λ3 = 0.6328 μm, respectively. (b) A magnified photograph of the three focused lines generated by the fabricated DPE.

Equations (12)

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U 1 α = U 1 ( X 1 , λ α ) = ρ 1 ( X 1 , λ α ) exp [ i ϕ 1 ( X 1 , λ α ) ] .
U 2 α = U 2 ( X 2 , λ α ) = ρ 2 ( X 2 , λ α ) exp [ i ϕ 2 ( X 2 , λ α ) ] .
U 2 ( X 2 , λ α ) = G ( X 2 , X 1 ; l , λ α ) U 1 ( X 1 , λ α ) d X 1 .
U 2 ( X 2 , λ α ) = G ^ ( λ α ) U 1 ( X 1 , λ α ) ,
U 1 k ( λ α ) = ρ 1 k α exp [ i 2 π h 1 k ( n s - 1 ) / λ α ] , k = 1 , 2 , 3 , , N 1 ,             α = 1 , 2 , 3 , , N λ ,
U 2 m α = ρ 2 m α exp ( i ϕ 2 m α ) , m = 1 , 2 , 3 , , N 2 s ,             α = 1 , 2 , 3 , , N λ .
U 2 m α = k = 1 N 1 G m k ( λ α ) U 1 k ( λ α ) .
D 2 = α = 1 N λ [ U 2 α - G ^ ( λ α ) U 1 α ] 2 = 1 N 2 s N λ α ( k ρ 2 k α 2 + k j ρ 1 k α ρ 1 j α A k j ( λ α , λ α ) × exp [ - i 2 π ( h 1 k - h 1 j ) ( n s - 1 ) / λ ] - k j ρ 2 k α ρ 1 j α G k j ( λ α ) × exp { - i [ ϕ 2 k α - 2 π h 1 j ( n s - 1 ) / λ α ] + c . c . } ) ,
exp [ i 2 π h 1 k ( n s - 1 ) / λ 0 ] = Q ˜ k * Q ˜ k ,             k = 1 , 2 , 3 , , N 1 ,
Q ˜ k = α [ 2 π ( n s - 1 ) / λ α ] × { j k ' ρ 1 j α exp [ - i 2 π h 1 j ( n s - 1 ) / λ α ] A j k ( λ α ) - j ρ 2 j α exp ( - i ϕ 2 j α ) G j k ( λ α ) } × ρ 1 k α exp [ i ( 2 π h 1 k ( n s - 1 ) / λ 0 ) ( λ 0 / λ α - 1 ) ] , exp ( i ϕ 2 k γ ) = j G k j ( λ γ ) ρ 1 j γ exp [ i 2 π h 1 j ( n s - 1 ) / λ γ ] | j G k j ( λ γ ) ρ 1 j γ exp [ i 2 π h 1 j ( n s - 1 ) / λ γ ] | , k = 1 , 2 , 3 , , N 2 s ,             γ = 1 , 2 , 3 , , N λ .
G ( x 2 , x 1 ; l , λ α ) = ( 1 i λ α l ) 1 / 2 exp ( i 2 π l / λ α ) × exp [ i π ( x 2 - x 1 ) 2 / λ α l ] ,
I ( x 2 , λ α ) = | k = 1 N 1 G ( x 2 , x 1 k ; l , λ α ) exp [ i 2 π h 1 ( n s - 1 ) / λ α ] | 2 .

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