Abstract

A design for diffractive phase elements (DPE’s) that implement wavelength demultiplexing and annular focusing simultaneously is presented based on the general theory of amplitude phase retrieval. The optical system considered is illuminated by a beam of polychromatic light consisting of several wavelengths. With the use of an iterative algorithm the pattern of a surface-relief DPE can be determined by solving the relevant equations. Computer simulations are carried out for several model examples. The calculation results show that the designed DPE’s can satisfactorily achieve the desired functions.

© 1997 Optical Society of America

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References

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1996 (1)

1995 (3)

1994 (2)

1993 (4)

1992 (1)

1986 (1)

1978 (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.

Chang, M.-P.

Dammann, H.

Dong, B.

Dong, B. Z.

Ersoy, O. K.

Fainman, Y.

Farn, M. W.

Ford, J. E.

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.

Xu, F.

Yang, G.

Yang, G. Z.

Yariv, A.

Zhang, G.

Zhuang, J. Y.

Appl. Opt. (8)

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. (3)

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

Polychromatic diffractive optical system.

Fig. 2
Fig. 2

(a) Distribution of the modulation depth of 16 quantized phase levels of the designed DPE. The aperture size of the designed DPE is 3 mm, the average size of pixel is 5.85 µm, and the required etch depth of the DPE is 0.156 µm for n0=1.459. (b) Output pattern generated by the DPE, corresponding to the case of two wavelength demultiplexing components, λ1=0.6328 µm and λ2=0.5145 µm and producing two focused annuli with radii r2f1=5.28 mm and r2f2=7.29 mm, respectively.

Fig. 3
Fig. 3

(a) Profile of the modulation depth of 16 quantized phase levels of the designed DPE. The required etch depth, the aperture size, and average pixel size are as same as in Fig. 2(b). (b) Output pattern generated by the designed DPE, corresponding to the case of two wavelength demultiplexing components, λ1=0.5145 µm and λ2=0.5900 µm and producing two focused annuli with radii r2f1=3.56 mm and r2f2=6.56 mm, respectively.

Fig. 4
Fig. 4

(a) Distribution of the modulation depth of 16 quantized phase levels of the designed DPE. The aperture size is still taken as 3 mm, the average pixel size is 3.09 µm, and the required etch depth is 0.156 µm for n0=1.459. (b) Output pattern generated by the DPE, corresponding to the case of three wavelength demultiplexing components, λ1=0.5900 µm, λ2=0.6328, µm, and λ3=0.5145 µm and producing three focused annuli with radii r2f1=1.59 mm, r2f2=3.89 mm, and r2f3=7.29 mm, respectively.

Equations (20)

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U1α=U1(X1, λα)=ρ1(X1, λα)exp[iϕ1(X1, λα)].
U2α=U2(X2, λα)=ρ2(X2, λα)exp[iϕ2(X2, λα)].
U2(X2, λα)= G(X2, X1, λα)U1(X1, λα)dX1.
U2(X2, λα)=Gˆ(λα)U1(X1, λα),
U1j(λα)=ρ1jα exp[i2πh1j(nsα-1)/λα],
j=1, 2, 3N1,α=1, 2, 3Nλ,
U2mα=ρ2mα exp(iϕ2mα),m=1, 2, 3N2s,
U2mα=j=1N1 Gmj(λα)U1j.
D2=α [U2α-Gˆ(λα)U1α]2=α Tr[U2α+U2α-U2α+Gˆ(λα)U1α-U1α+Gˆ+(λα)U2α+U1α+Gˆ+(λα)G(λα)U1α].
exp[i2πh1k(n0-1)/λ0]=Q˜k*|Q˜k|,k=1, 2, 3N1,
Q˜k=α2πnsα-1/λαjk  ρ1jα×exp-i2πh1jnsα-1/λαAjkλα-j ρ2jα×exp-iϕ2jαGjkλαρ1kα×expi2πh1kn0-1/λ0λ0nsα-1λαn0-1-1,
exp(iϕ2kγ)=jGkj(λγ)ρ1jγ exp[i2πh1j(nsα-1)/λγ]jGkj(λγ)ρ1jγ exp[i2πh1j(nsα-1)/λγ],
k=1, 2, 3N2s,γ=1, 2, 3Nλ,
GX2, X1; l, λα=expi2πl/λαiλαlexpiπλαlx2-x12+y2-y12.
U2(r2)=0R1m G(r2, r1)U1(r1)dr1,
Gr2, r1; l, λα=2πiλαlexpi2πl/λαexpiπr22+r12λαl×J02πr2r1λαlr1,
J0(x)=12π02π exp[ix cos(θ1-θ2)]dθ1.
I(r2, λα)=0R1m G(r2, r1; l, λα)exp[i2πh1(r1)×(nsα-1)/λα]dr12.
η=1NλαI(λα, r2fα)m I(λα, r2m),
T=1NλαβαI(λβ, r2fα)I(λβ, r2fα),

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