Abstract

The arrangement of binary subwavelength structures is a promising alternative to the conventional multiheight level technique to generate computer generated holograms (CGHs). However, the current heuristic design approach leads to a slight mismatch between the target signal and experimental data. To evaluate this deviation, a diffractive beam splitter design is investigated rigorously using a finite-difference time-domain (FDTD) method. Since the use of a rigorous Maxwell-equation solver like FDTD requires a massive computational effort, an alternative scalar approach, a fast Fourier transform beam propagation method (FFT-BPM), is investigated with a substantial higher computing speed, showing still a good agreement with the FDTD simulation and experimental data. Therefore, an implementation of this scalar approach into the CGH design process offers the possibility to significantly increase the accuracy.

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References

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  1. B. Goebel, L. L. Wang, and T. Tschudi, “Multilayer technology for diffractive optical elements,” Appl. Opt.35(22), 4490–4493 (1996).
    [CrossRef] [PubMed]
  2. J. M. Miller, M. R. Taghizadeh, J. Turunen, and N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt.32(14), 2519–2525 (1993).
    [CrossRef] [PubMed]
  3. M. Banasch, L.-C. Wittig, and E.-B. Kley, “Fabrication tolerances of binary and multilevel Computer Generated Holograms (CGHs) with submicron Pixel Size,” MOC´04–10th Microoptics Conference, Germany (2004).
  4. E. Noponen and J. Turunen, “Binary high-frequency-carrier diffractive optical elements: electromagnetic theory,” J. Opt. Soc. Am. A11(3), 1097–1109 (1994).
    [CrossRef]
  5. J. Mait, D. Prather, and M. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A16(5), 1157–1167 (1999).
    [CrossRef]
  6. P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff,” J. Opt. Soc. Am. A16(5), 1143–1156 (1999).
    [CrossRef]
  7. C. Ribot, P. Lalanne, M. S. Lee, B. Loiseaux, and J. P. Huignard, “Analysis of blazed diffractive optical elements formed with artificial dielectrics,” J. Opt. Soc. Am. A24(12), 3819–3826 (2007).
    [CrossRef] [PubMed]
  8. H. J. Hyvärinen, P. Karvinen, and J. Turunen, “Polarization insensitive resonance-domain blazed binary gratings,” Opt. Express18(13), 13444–13450 (2010).
    [CrossRef] [PubMed]
  9. W. Yu, K. Takahara, T. Konishi, T. Yotsuya, and Y. Ichioka, “Fabrication of multilevel phase computer-generated hologram elements based on effective medium theory,” Appl. Opt.39(20), 3531–3536 (2000).
    [CrossRef] [PubMed]
  10. W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design of binary subwavelength multi-phase level computer generated holograms,” Opt. Lett.35(5), 676–678 (2010).
    [CrossRef] [PubMed]
  11. W. Freese, T. Kämpfe, W. Rockstroh, E.-B. Kley, and A. Tünnermann, “Optimized electron beam writing strategy for fabricating computer-generated holograms based on an effective medium approach,” Opt. Express19(9), 8684–8692 (2011).
    [CrossRef] [PubMed]
  12. W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Multi-phase-level diffractive elements realized by binary effective medium patterns,” Proc. SPIE7591(75910Z), 75910Z-1–75910Z-7 (2010).
    [CrossRef]
  13. W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design and fabrication of a highly off-axis binary multi-phase level computer-generated hologram based on an effective medium approach,” Proc. SPIE7927(792710), 792710, 792710-7 (2011).
    [CrossRef]
  14. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 227–246 (1972).
  15. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).
  16. U. Levy, E. Marom, and D. Mendlovic, “Thin element approximation for the analysis of blazed gratings: simplified model and validity limits,” Opt. Commun.229(1-6), 11–21 (2004).
    [CrossRef]
  17. A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, and S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt.31(17), 3320–3336 (1992).
    [CrossRef] [PubMed]
  18. D. Pommet, M. Moharam, and E. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A11(6), 1827–1834 (1994).
    [CrossRef]
  19. S. Mellin and G. Nordin, “Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design,” Opt. Express8(13), 705–722 (2001).
    [CrossRef] [PubMed]
  20. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Boston: Artech House, 2000).
  21. M. D. Feit and J. A. Fleck., “Light propagation in graded-index optical fibers,” Appl. Opt.17(24), 3990–3998 (1978).
    [CrossRef] [PubMed]
  22. S. Kumar, T. Srinivas, and A. Selvarjan, “Beam propagation method and its application to integrated optic structures and optical fibers,” J. Phys.34, 347–358 (1989).
  23. M. D. Feit and J. A. Fleck., “Calculation of dispersion in graded-index multimode fibers by a propagating-beam method,” Appl. Opt.18(16), 2843–2851 (1979).
    [CrossRef] [PubMed]
  24. B. Hermansson, D. Yevick, and J. Saijonmaa, “Propagating-beam-method analysis of two-dimensional microlenses and three-dimensional taper structures,” J. Opt. Soc. Am. A1(6), 663–671 (1984).
    [CrossRef]
  25. M. Fertig and K.-H. Brenner, “Vector wave propagation method,” J. Opt. Soc. Am. A27(4), 709–717 (2010).
    [CrossRef] [PubMed]

2011 (2)

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design and fabrication of a highly off-axis binary multi-phase level computer-generated hologram based on an effective medium approach,” Proc. SPIE7927(792710), 792710, 792710-7 (2011).
[CrossRef]

W. Freese, T. Kämpfe, W. Rockstroh, E.-B. Kley, and A. Tünnermann, “Optimized electron beam writing strategy for fabricating computer-generated holograms based on an effective medium approach,” Opt. Express19(9), 8684–8692 (2011).
[CrossRef] [PubMed]

2010 (4)

2007 (1)

2004 (1)

U. Levy, E. Marom, and D. Mendlovic, “Thin element approximation for the analysis of blazed gratings: simplified model and validity limits,” Opt. Commun.229(1-6), 11–21 (2004).
[CrossRef]

2001 (1)

2000 (1)

1999 (2)

1996 (1)

1994 (2)

1993 (1)

1992 (1)

1989 (1)

S. Kumar, T. Srinivas, and A. Selvarjan, “Beam propagation method and its application to integrated optic structures and optical fibers,” J. Phys.34, 347–358 (1989).

1984 (1)

1979 (1)

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 227–246 (1972).

Astilean, S.

Brenner, K.-H.

Cambril, E.

Chavel, P.

Feit, M. D.

Fertig, M.

Fleck, J. A.

Freese, W.

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design and fabrication of a highly off-axis binary multi-phase level computer-generated hologram based on an effective medium approach,” Proc. SPIE7927(792710), 792710, 792710-7 (2011).
[CrossRef]

W. Freese, T. Kämpfe, W. Rockstroh, E.-B. Kley, and A. Tünnermann, “Optimized electron beam writing strategy for fabricating computer-generated holograms based on an effective medium approach,” Opt. Express19(9), 8684–8692 (2011).
[CrossRef] [PubMed]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Multi-phase-level diffractive elements realized by binary effective medium patterns,” Proc. SPIE7591(75910Z), 75910Z-1–75910Z-7 (2010).
[CrossRef]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design of binary subwavelength multi-phase level computer generated holograms,” Opt. Lett.35(5), 676–678 (2010).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 227–246 (1972).

Goebel, B.

Grann, E.

Hermansson, B.

Huignard, J. P.

Hyvärinen, H. J.

Ichikawa, H.

Ichioka, Y.

Jaakkola, T.

Kämpfe, T.

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design and fabrication of a highly off-axis binary multi-phase level computer-generated hologram based on an effective medium approach,” Proc. SPIE7927(792710), 792710, 792710-7 (2011).
[CrossRef]

W. Freese, T. Kämpfe, W. Rockstroh, E.-B. Kley, and A. Tünnermann, “Optimized electron beam writing strategy for fabricating computer-generated holograms based on an effective medium approach,” Opt. Express19(9), 8684–8692 (2011).
[CrossRef] [PubMed]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Multi-phase-level diffractive elements realized by binary effective medium patterns,” Proc. SPIE7591(75910Z), 75910Z-1–75910Z-7 (2010).
[CrossRef]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design of binary subwavelength multi-phase level computer generated holograms,” Opt. Lett.35(5), 676–678 (2010).
[CrossRef] [PubMed]

Karvinen, P.

Kley, E.-B.

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design and fabrication of a highly off-axis binary multi-phase level computer-generated hologram based on an effective medium approach,” Proc. SPIE7927(792710), 792710, 792710-7 (2011).
[CrossRef]

W. Freese, T. Kämpfe, W. Rockstroh, E.-B. Kley, and A. Tünnermann, “Optimized electron beam writing strategy for fabricating computer-generated holograms based on an effective medium approach,” Opt. Express19(9), 8684–8692 (2011).
[CrossRef] [PubMed]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Multi-phase-level diffractive elements realized by binary effective medium patterns,” Proc. SPIE7591(75910Z), 75910Z-1–75910Z-7 (2010).
[CrossRef]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design of binary subwavelength multi-phase level computer generated holograms,” Opt. Lett.35(5), 676–678 (2010).
[CrossRef] [PubMed]

Konishi, T.

Kuisma, S.

Kumar, S.

S. Kumar, T. Srinivas, and A. Selvarjan, “Beam propagation method and its application to integrated optic structures and optical fibers,” J. Phys.34, 347–358 (1989).

Lalanne, P.

Launois, H.

Lee, M. S.

Levy, U.

U. Levy, E. Marom, and D. Mendlovic, “Thin element approximation for the analysis of blazed gratings: simplified model and validity limits,” Opt. Commun.229(1-6), 11–21 (2004).
[CrossRef]

Loiseaux, B.

Mait, J.

Marom, E.

U. Levy, E. Marom, and D. Mendlovic, “Thin element approximation for the analysis of blazed gratings: simplified model and validity limits,” Opt. Commun.229(1-6), 11–21 (2004).
[CrossRef]

Mellin, S.

Mendlovic, D.

U. Levy, E. Marom, and D. Mendlovic, “Thin element approximation for the analysis of blazed gratings: simplified model and validity limits,” Opt. Commun.229(1-6), 11–21 (2004).
[CrossRef]

Miller, J. M.

Mirotznik, M.

Moharam, M.

Noponen, E.

Nordin, G.

Pommet, D.

Prather, D.

Ribot, C.

Rockstroh, W.

Ross, N.

Saijonmaa, J.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 227–246 (1972).

Selvarjan, A.

S. Kumar, T. Srinivas, and A. Selvarjan, “Beam propagation method and its application to integrated optic structures and optical fibers,” J. Phys.34, 347–358 (1989).

Srinivas, T.

S. Kumar, T. Srinivas, and A. Selvarjan, “Beam propagation method and its application to integrated optic structures and optical fibers,” J. Phys.34, 347–358 (1989).

Taghizadeh, M. R.

Takahara, K.

Tschudi, T.

Tünnermann, A.

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design and fabrication of a highly off-axis binary multi-phase level computer-generated hologram based on an effective medium approach,” Proc. SPIE7927(792710), 792710, 792710-7 (2011).
[CrossRef]

W. Freese, T. Kämpfe, W. Rockstroh, E.-B. Kley, and A. Tünnermann, “Optimized electron beam writing strategy for fabricating computer-generated holograms based on an effective medium approach,” Opt. Express19(9), 8684–8692 (2011).
[CrossRef] [PubMed]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Multi-phase-level diffractive elements realized by binary effective medium patterns,” Proc. SPIE7591(75910Z), 75910Z-1–75910Z-7 (2010).
[CrossRef]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design of binary subwavelength multi-phase level computer generated holograms,” Opt. Lett.35(5), 676–678 (2010).
[CrossRef] [PubMed]

Turunen, J.

Vasara, A.

Wang, L. L.

Westerholm, J.

Yevick, D.

Yotsuya, T.

Yu, W.

Appl. Opt. (6)

J. Opt. Soc. Am. A (7)

J. Phys. (1)

S. Kumar, T. Srinivas, and A. Selvarjan, “Beam propagation method and its application to integrated optic structures and optical fibers,” J. Phys.34, 347–358 (1989).

Opt. Commun. (1)

U. Levy, E. Marom, and D. Mendlovic, “Thin element approximation for the analysis of blazed gratings: simplified model and validity limits,” Opt. Commun.229(1-6), 11–21 (2004).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 227–246 (1972).

Proc. SPIE (2)

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Multi-phase-level diffractive elements realized by binary effective medium patterns,” Proc. SPIE7591(75910Z), 75910Z-1–75910Z-7 (2010).
[CrossRef]

W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design and fabrication of a highly off-axis binary multi-phase level computer-generated hologram based on an effective medium approach,” Proc. SPIE7927(792710), 792710, 792710-7 (2011).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Boston: Artech House, 2000).

M. Banasch, L.-C. Wittig, and E.-B. Kley, “Fabrication tolerances of binary and multilevel Computer Generated Holograms (CGHs) with submicron Pixel Size,” MOC´04–10th Microoptics Conference, Germany (2004).

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Figures (10)

Fig. 1
Fig. 1

Target signal (a), designed phase function (b) and resultant EM pattern (c) of the CGH unit cell. The intensity of each pixel is given as a fraction of the total incident intensity I 0 .

Fig. 2
Fig. 2

3D computational domain for the FDTD simulation of the EM CGH.

Fig. 3
Fig. 3

Near field distribution from an ideal TEA element (a) compared with FDTD calculations for TE and TM polarization of the corresponding EM pattern (b).

Fig. 4
Fig. 4

Far field distribution from an ideal TEA element (a) compared with FDTD calculations for TE and TM polarization of the corresponding EM pattern (b).

Fig. 5
Fig. 5

Schematic diagram for the FFT-BPM algorithm.

Fig. 6
Fig. 6

Cross Correlation C BPMFDTD as a function of the sampling distance Δz in propagation direction (a) and Δx in lateral direction (b).

Fig. 7
Fig. 7

Near field of the EM pattern calculated via FFT-BPM (a) and FDTD (b).

Fig. 8
Fig. 8

Far field of the EM pattern calculated via FFT-BPM (a) and FDTD (b).

Fig. 9
Fig. 9

Scanning-electron micrograph of the EM pattern (a) and a photograph of the corresponding measured intensity distribution (b).

Fig. 10
Fig. 10

Sketch of the numbering of the 10 main spots (a) and diagram to compare the intensity of the main spots calculated with different methods and experimental data (b).

Tables (1)

Tables Icon

Table 1 Intensity deviation to FDTD simulationa

Equations (5)

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h= N1 N λ n1 ,
I( k x , k y )=| P z |=| E ˜ x ( k x , k y ) H ˜ * y ( k x , k y ) E ˜ y ( k x , k y ) H ˜ * x ( k x , k y ) |
C 12 = I 1 ( k x , k y ) I ¯ 1 I 1 ( k x , k y ) I ¯ 1 , I 2 ( k x , k y ) I ¯ 2 I 2 ( k x , k y ) I ¯ 2
U(x,y,z+Δz)= FF T 1 [ FFT(U(x,y,z)) e iΔz n ¯ 2 k 0 2 ( k x 2 + k y 2 ) D ] ASPW(U(x,y,z)) e iΔzΔn( x,y ) k 0 L
I( k x , k y )= | U ˜ ( k x , k y ) | 2

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