Abstract

We report on the wavelength-multiplexing diffractive phase element (WMDPE) capable of generating independent spot patterns for different wavelengths. The iterative method proposed by Bengtsson [Appl. Opt. 37, 1998] for designing a kinoform that produces different patterns for two wavelengths is extended to the WMDPE for multiple wavelengths (more than two wavelengths). Effectiveness of the design algorithm is verified by design and computer simulations on the WMDPE’s for four and nine wavelengths. The WMDPE for three wavelengths (441.6, 543.5, and 633 nm) is designed with five phase levels and is fabricated by electron-beam lithography. We observed that the individual spot patterns are reconstructed for the design wavelengths correctly. Performance of the WMDPE is evaluated by computer simulations on the uniformity error, the light efficiency, and the contrast. On the basis of the results, the characteristics of the WMDPE’s are discussed in terms of various conditions of fabrication and usage.

© 2001 Optical Society of America

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References

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  1. W. Däschner, P. Long, R. Stein, C. Wu, S. H. Lee, “Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single optical exposure with a gray-scale mask on high-energy beam-sensitive glass,” Appl. Opt. 36, 4675–4680 (1997).
    [CrossRef] [PubMed]
  2. D. Prongué, H. P. Herzig, R. Dändliker, M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. 31, 5706–5711 (1992).
    [CrossRef] [PubMed]
  3. T. Dresel, M. Beyerlein, J. Schwider, “Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption,” Appl. Opt. 35, 6865–6874 (1996).
    [CrossRef] [PubMed]
  4. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef] [PubMed]
  5. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  6. M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990).
    [CrossRef] [PubMed]
  7. V. V. Kotlyar, I. V. Nikolski, V. A. Soifer, “Adaptive iterative algorithm for focusators synthesis,” Optik 88, 17–19 (1991).
  8. M. W. Farn, M. B. Stern, W. B. Veldkamp, S. S. Medeiros, “Color separation by use of binary optics,” Opt. Lett. 18, 1214–1216 (1993).
    [CrossRef] [PubMed]
  9. A. P. Wood, “Design of infrared hybrid refractive-diffractive lens,” Appl. Opt. 31, 2253–2258 (1992).
    [CrossRef] [PubMed]
  10. B. Dong, G. Zhang, G. Yang, B. Gu, S. Zheng, D. Li, Y. Chen, X. Cui, M. Chen, H. Liu, “Design and fabrication of a diffractive phase element for wavelength demultiplexing and spatial focusing simultaneously,” Appl. Opt. 35, 6859–6864 (1996).
    [CrossRef] [PubMed]
  11. M. Kato, K. Sakuda, “Computer-generated holograms: application to intensity variable and wavelength demultiplexing holograms,” Appl. Opt. 31, 630–635 (1992).
    [CrossRef] [PubMed]
  12. G. Yang, B. Gu, X. Tan, M. P. Chang, B. Dong, O. K. Ersoy, “Iterative optimization approach for the design of diffractive phase elements simultaneously implementing several optical functions,” J. Opt. Soc. Am. A 11, 1632–1640 (1994).
    [CrossRef]
  13. B. Gu, G. Yang, B. Dong, M. P. Chang, O. K. Ersoy, “Diffractive-phase-element design that implements several optical functions,” Appl. Opt. 34, 2564–2570 (1995).
    [CrossRef] [PubMed]
  14. G. Yang, B. Dong, B. Gu, J. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithm for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994).
    [CrossRef] [PubMed]
  15. J. Bengtsson, “Kinoforms designed to produce different fan-out patterns for two wavelengths,” Appl. Opt. 37, 2011–2020 (1998).
    [CrossRef]
  16. J. Bengtsson, “Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method,” Appl. Opt. 36, 8435–8444 (1997).
    [CrossRef]

1998 (1)

1997 (2)

1996 (2)

1995 (1)

1994 (2)

1993 (1)

1992 (3)

1991 (1)

V. V. Kotlyar, I. V. Nikolski, V. A. Soifer, “Adaptive iterative algorithm for focusators synthesis,” Optik 88, 17–19 (1991).

1990 (1)

1989 (1)

1972 (1)

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

Bengtsson, J.

Beyerlein, M.

Chang, M. P.

Chen, M.

Chen, Y.

Cui, X.

Dändliker, R.

Däschner, W.

Dong, B.

Dresel, T.

Ersoy, O. K.

Farn, M. W.

Friberg, A. T.

Gale, M. T.

Gerchberg, R. W.

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

Gu, B.

Guest, C. C.

Herzig, H. P.

Kato, M.

Kim, M. S.

Kotlyar, V. V.

V. V. Kotlyar, I. V. Nikolski, V. A. Soifer, “Adaptive iterative algorithm for focusators synthesis,” Optik 88, 17–19 (1991).

Lee, S. H.

Li, D.

Liu, H.

Long, P.

Medeiros, S. S.

Nikolski, I. V.

V. V. Kotlyar, I. V. Nikolski, V. A. Soifer, “Adaptive iterative algorithm for focusators synthesis,” Optik 88, 17–19 (1991).

Prongué, D.

Sakuda, K.

Saxton, W. O.

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

Schwider, J.

Soifer, V. A.

V. V. Kotlyar, I. V. Nikolski, V. A. Soifer, “Adaptive iterative algorithm for focusators synthesis,” Optik 88, 17–19 (1991).

Stein, R.

Stern, M. B.

Tan, X.

Turunen, J.

Vasara, A.

Veldkamp, W. B.

Wood, A. P.

Wu, C.

Yang, G.

Zhang, G.

Zheng, S.

Zhuang, J.

Appl. Opt. (11)

W. Däschner, P. Long, R. Stein, C. Wu, S. H. Lee, “Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single optical exposure with a gray-scale mask on high-energy beam-sensitive glass,” Appl. Opt. 36, 4675–4680 (1997).
[CrossRef] [PubMed]

D. Prongué, H. P. Herzig, R. Dändliker, M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. 31, 5706–5711 (1992).
[CrossRef] [PubMed]

T. Dresel, M. Beyerlein, J. Schwider, “Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption,” Appl. Opt. 35, 6865–6874 (1996).
[CrossRef] [PubMed]

A. P. Wood, “Design of infrared hybrid refractive-diffractive lens,” Appl. Opt. 31, 2253–2258 (1992).
[CrossRef] [PubMed]

B. Dong, G. Zhang, G. Yang, B. Gu, S. Zheng, D. Li, Y. Chen, X. Cui, M. Chen, H. Liu, “Design and fabrication of a diffractive phase element for wavelength demultiplexing and spatial focusing simultaneously,” Appl. Opt. 35, 6859–6864 (1996).
[CrossRef] [PubMed]

M. Kato, K. Sakuda, “Computer-generated holograms: application to intensity variable and wavelength demultiplexing holograms,” Appl. Opt. 31, 630–635 (1992).
[CrossRef] [PubMed]

B. Gu, G. Yang, B. Dong, M. P. Chang, O. K. Ersoy, “Diffractive-phase-element design that implements several optical functions,” Appl. Opt. 34, 2564–2570 (1995).
[CrossRef] [PubMed]

G. Yang, B. Dong, B. Gu, J. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithm for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994).
[CrossRef] [PubMed]

J. Bengtsson, “Kinoforms designed to produce different fan-out patterns for two wavelengths,” Appl. Opt. 37, 2011–2020 (1998).
[CrossRef]

J. Bengtsson, “Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method,” Appl. Opt. 36, 8435–8444 (1997).
[CrossRef]

M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Optik (2)

V. V. Kotlyar, I. V. Nikolski, V. A. Soifer, “Adaptive iterative algorithm for focusators synthesis,” Optik 88, 17–19 (1991).

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

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Figures (17)

Fig. 1
Fig. 1

Model of the WMDPE in design.

Fig. 2
Fig. 2

Flowchart of design algorithm.

Fig. 3
Fig. 3

Definition of the areas of spot and ghost.

Fig. 4
Fig. 4

Design results of the WMDPE for nine wavelengths; (a) distribution of phase modulation and (b) calculated output patterns.

Fig. 5
Fig. 5

Dependence of peak spot intensity and spot area on βX.

Fig. 6
Fig. 6

Design results of the WMDPE for four wavelengths; (a) distribution of phase modulation and (b) calculated output patterns.

Fig. 7
Fig. 7

Method of phase quantization.

Fig. 8
Fig. 8

Design results of the WMDPE for three wavelengths; (a) distribution of quantized phase modulation and (b) calculated output patterns for three wavelengths.

Fig. 9
Fig. 9

Optical microscopic picture of the fabricated WMDPE.

Fig. 10
Fig. 10

Optical setup for observing output pattern of the fabricated WMDPE.

Fig. 11
Fig. 11

Obtained output pattern in the experiment.

Fig. 12
Fig. 12

Dependence of performance measures on the number of output spots.

Fig. 13
Fig. 13

Dependence of performance measures on the number of multiplexed wavelengths.

Fig. 14
Fig. 14

Variation of performance measures versus the output distance.

Fig. 15
Fig. 15

Variation of performance measures versus the maximum phase modulation.

Fig. 16
Fig. 16

Variation of performance measures versus wavelength interval Δλ.

Fig. 17
Fig. 17

Wavelength resolution of the WMDPE for two wavelengths versus the maximum phase modulation (left), the output distance (middle), and the pixel number (right).

Tables (3)

Tables Icon

Table 1 Parameters of the Designed WMDPE’s

Tables Icon

Table 2 Performance Measures of the Designed WMDPE’s

Tables Icon

Table 3 Parameters of the WMDPE’s for Performance Evaluation

Equations (24)

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Ulm=Uol exp(jΔφl)Alm exp(jφlm),
Alm exp(jφlm)=1λL expjk2L[(um-xl)2+(vm-yl)2].
Δφl(Y)=λAλYΔφl(A).
UmAm exp(jφm)
=lUlm=lAolAlm exp(jφlm)exp{j[φol+Δφl(A)]}.
ΔUmAlm cos[ϕlm-δφl(A)]-Alm cosϕlm,
ϕlm=φm-[φlm+φol+Δφl(A)].
f[δφl(A)]=XWXSX cosλAλXδφl(A)-αl(X)+const.,
SX=sgn(S1X) (S1X2+S2X2)1/2,
S1X=mMXwmAlm cos ϕlm,
S2X=mMXwmAlm sin ϕlm,
αl(X)=arctanS2XS1X,
wm=wmoldIXaveImp,
WA=1,
WY=WYoldIAaveβYIYaveq,
βX=(λX/λA)2.
Δφl(A)=γΓ,
(Γ={γ|0γ(maximumphasemodulation)}),
wm=1,
WX=1.
Unif.Err.=maxλX(Im)-minλX(Im)maxλX(Im)+minλX(Im),
Light.Eff.=(summationofpowerwithinallspotsforonewavelength)(totalpowerofilluminatinglightforonewavelength).
Contrast=minλX(Im)-maxλX(Ighost)minλX(Im)+maxλX(Ighost),
1λA-1λB=1λB-1λC=,

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