Abstract

We present an extension of the direct-binary-search algorithm for designing high-efficiency multi-wavelength diffractive optics that reconstruct in the Fresnel domain. A fast computation method for solving the optimization problem is proposed. Examples of three-wavelength diffractive optics with over 90% diffraction efficiency are presented. These diffractive optical elements reconstruct three distinct image patterns when probed using the design wavelengths. Detailed parametric and sensitivity studies are conducted, which provide insight into the diffractive optic’s performance when subject to different design conditions as well as common systematic and fabrication errors.

© 2012 OSA

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References

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  1. B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (John Wiley, 2000).
  2. C. Dankwart, C. Falldorf, R. Gläbe, A. Meier, C. V. Kopylow, and R. B. Bergmann, “Design of diamond-turned holograms incorporating properties of the fabrication process,” Appl. Opt. 49(20), 3949–3955 (2010).
    [CrossRef] [PubMed]
  3. D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34(14), 2462–2468 (1995).
    [CrossRef] [PubMed]
  4. D. Faklis and G. M. Morris, “Polychromatic diffractive lenses,” U.S. patent 5,589,982 (31 December 1996).
  5. D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. 31(26), 5706–5711 (1992).
    [CrossRef] [PubMed]
  6. J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing 6(1/2/3/4), 207 (2010).
    [CrossRef]
  7. R. Menon, P. Rogge, and H.-Y. Tsai, “Design of diffractive lenses that generate optical nulls without phase singularities,” J. Opt. Soc. Am. A 26(2), 297–304 (2009).
    [CrossRef] [PubMed]
  8. H.-Y. Tsai, H. I. Smith, and R. Menon, “Reduction of focal-spot size using dichromats in absorbance modulation,” Opt. Lett. 33(24), 2916–2918 (2008).
    [CrossRef] [PubMed]
  9. T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27(14), 2960–2971 (1988).
    [CrossRef] [PubMed]
  10. Y. Arieli, S. Noach, S. Ozeri, and N. Eisenberg, “Design of diffractive optical elements for multiple wavelengths,” Appl. Opt. 37(26), 6174–6177 (1998).
    [CrossRef] [PubMed]
  11. D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. 34(14), 2469–2475 (1995).
    [CrossRef] [PubMed]
  12. S. Noach, A. Lewis, Y. Arieli, and N. Eisenberg, “Integrated diffractive andrefractive elements for spectrum shaping,” Appl. Opt. 35(19), 3635–3639 (1996).
    [CrossRef] [PubMed]
  13. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26(14), 2788–2798 (1987).
    [CrossRef] [PubMed]
  14. T. R. M. Sales and D. H. Raguin, “Multiwavelength operation with thin diffractive elements,” Appl. Opt. 38(14), 3012–3018 (1999).
    [CrossRef] [PubMed]

2010

J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing 6(1/2/3/4), 207 (2010).
[CrossRef]

C. Dankwart, C. Falldorf, R. Gläbe, A. Meier, C. V. Kopylow, and R. B. Bergmann, “Design of diamond-turned holograms incorporating properties of the fabrication process,” Appl. Opt. 49(20), 3949–3955 (2010).
[CrossRef] [PubMed]

2009

2008

1999

1998

1996

1995

1992

1988

1987

Allebach, J. P.

Arieli, Y.

Barbastathis, G.

J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing 6(1/2/3/4), 207 (2010).
[CrossRef]

Bergmann, R. B.

Dändliker, R.

Dankwart, C.

Domínguez-Caballero, J. A.

J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing 6(1/2/3/4), 207 (2010).
[CrossRef]

Eisenberg, N.

Faklis, D.

Falldorf, C.

Gale, M. T.

George, N.

Gläbe, R.

Herzig, H. P.

Kopylow, C. V.

Lee, S. J.

J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing 6(1/2/3/4), 207 (2010).
[CrossRef]

Lewis, A.

Meier, A.

Menon, R.

Morris, G. M.

Noach, S.

Ozeri, S.

Prongué, D.

Raguin, D. H.

Rogge, P.

Sales, T. R. M.

Seldowitz, M. A.

Smith, H. I.

Sommargren, G. E.

Stone, T.

Sweeney, D. W.

Takahashi, S.

J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing 6(1/2/3/4), 207 (2010).
[CrossRef]

Tsai, H.-Y.

Appl. Opt.

M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26(14), 2788–2798 (1987).
[CrossRef] [PubMed]

T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27(14), 2960–2971 (1988).
[CrossRef] [PubMed]

Y. Arieli, S. Noach, S. Ozeri, and N. Eisenberg, “Design of diffractive optical elements for multiple wavelengths,” Appl. Opt. 37(26), 6174–6177 (1998).
[CrossRef] [PubMed]

T. R. M. Sales and D. H. Raguin, “Multiwavelength operation with thin diffractive elements,” Appl. Opt. 38(14), 3012–3018 (1999).
[CrossRef] [PubMed]

D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34(14), 2462–2468 (1995).
[CrossRef] [PubMed]

D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. 34(14), 2469–2475 (1995).
[CrossRef] [PubMed]

S. Noach, A. Lewis, Y. Arieli, and N. Eisenberg, “Integrated diffractive andrefractive elements for spectrum shaping,” Appl. Opt. 35(19), 3635–3639 (1996).
[CrossRef] [PubMed]

D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. 31(26), 5706–5711 (1992).
[CrossRef] [PubMed]

C. Dankwart, C. Falldorf, R. Gläbe, A. Meier, C. V. Kopylow, and R. B. Bergmann, “Design of diamond-turned holograms incorporating properties of the fabrication process,” Appl. Opt. 49(20), 3949–3955 (2010).
[CrossRef] [PubMed]

Int. J. Nanomanufacturing

J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing 6(1/2/3/4), 207 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (John Wiley, 2000).

D. Faklis and G. M. Morris, “Polychromatic diffractive lenses,” U.S. patent 5,589,982 (31 December 1996).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of the optimization problem geometry. (b) Target binary images used for the design example containing 3 letters to be reconstructed by 3 distinct wavelengths.

Fig. 2
Fig. 2

Multi-wavelength DOE designed for 3 discrete wavelengths and target images. (a) DOE’s optimized height profile map. (b) Magnified view of a 13 X 13 pixels region outlined by the white square in (a). Reconstructed image amplitude distributions at (c) λ = 405nm, (d) 532nm and (e) 633nm. The refractive indices at these wavelengths were 1.6894 (405nm), 1.6482 (532nm) and 1.6347 (633nm). The corresponding optical efficiencies are indicated on top of each figure. The average diffraction efficiency is 79.8%.

Fig. 3
Fig. 3

Convergence plots. Evolution of (a) average efficiency and (b) number of perturbed pixels with number of iterations.

Fig. 4
Fig. 4

(a) Average efficiency as a function number of height quantization levels. Larger number of levels results in higher diffraction efficiency until an upper bound is reached. The inset images show the corresponding reconstructed amplitude distributions at the two extreme points. (b) Average efficiency as a function of reconstruction distance. The highest efficiency is achieved near the distance calculated using the grating equation. (c) Average diffraction efficiency as a function of total number of pixels. (d) Average efficiency as a function of number of design wavelengths.

Fig. 5
Fig. 5

Reconstructed amplitude distributions for various designs with varying number of wavelengths. All other parameters are kept the same. The refractive indices used for the simulation were 1.7302 (351nm), 1.6894 (405nm), 1.6482 (532nm), 1.6347 (633nm), 1.628 (720nm) and 1.622 (850nm). These values were obtained by ellipsometric measurements on a 1.5μm-thick film of S1813 photoresist.

Fig. 6
Fig. 6

DOE’s chromatic effects. (a) Reconstructed amplitude distributions when the DOE is illuminated by wavelengths other than what it is designed for; (b) Diffraction efficiency as a function of illumination wavelength.

Fig. 7
Fig. 7

Effect of defocus as a function of average diffraction efficiency for (a) λ = 405nm, (b) 532nm and (c) 633nm.

Fig. 8
Fig. 8

Effect of pixel-height error on DOE’s average diffraction efficiency. (a) Random pixel-height error; (b) Uniform pixel height error.

Equations (9)

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h( x,y )= m n Δ h p m,n rect( xm Δ x Δ x )rect( yn Δ y Δ y ) ,
T( x,y;λ )= e iϕ( x,y;λ ) =1+ m n rect( xm Δ x Δ x )rect( yn Δ y Δ y )( e ia( λ ) p m,n 1 ) ,
U(x',y';λ)= e ikd iλd g illum (x,y;λ)T(x,y;λ) e i k 2d [ ( x'x ) 2 + ( y'y ) 2 ] dxdy = e ikd [ 1+ Δ x Δ y e i k 2d ( x ' 2 +y ' 2 ) m n Κ m,n ( λ ) ( e i k d ( x'm Δ x +y'n Δ y ) sinc( x' Δ x λd )sinc( y' Δ y λd ) e i k 2d ( x ' 2 +y'2 ) ) ],
U(x',y';λ)=1+ Δ x Δ y Q( x',y' ){ T c ( x,y )Q( x,y ) },
minC( p m,n ) ; C=1 η ¯ ( p m,n ) subject to p m,n Ζ, p m,n [0, N levels ]
η ¯ ( p m,n )= λ [ m n I T ( λ ) | U( p m,n ) | 2 P in ( λ ) ]( W ( λ ) N λ ) ;
T new ( x,y;λ )=T( x,y;λ ) e ia( λ )rect( xm' Δ x Δ x )rect( yn' Δ y Δ y ) =T( x,y;λ )+[ Ψ m',n' ( λ ) rect( xm' Δ x Δ x )rect( yn' Δ y Δ y ) ],
U pert ( x',y';λ )= Ζ m',n' ( x',y';λ ) Ω( x',y';λ ),
Ω( x',y';λ )= Δ x Δ y e ikd e i k 2d ( x ' 2 +y ' 2 ) [ sinc( x' Δ x λd )sinc( y' Δ y λd ) e i k 2d ( x ' 2 +y ' 2 ) ].

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