Abstract

A new rigorous vector-based design and analysis approach of diffractive lenses is presented. It combines the use of two methods: the Finite-Difference Time-Domain for the study in the near field, and the Radiation Spectrum Method for the propagation in the far field. This approach is proposed to design and optimize effective medium cylindrical diffractive lenses for high efficiency structured light illumination systems. These lenses are realised with binary subwavelength features that cannot be designed using the standard scalar theory. Furthermore, because of their finite and high frequencies characteristics, such devices prevent the use of coupled wave theory. The proposed approach is presented to determine the angular tolerance in the cases of binary subwavelength cylindrical lenses by calculating the diffraction efficiency as a function of the incidence angle.

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References

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  1. M. W. Farn, “Binary Grating with increased efficiency,” Appl. Opt. 31(22), 4453–4458 (1992).
    [CrossRef] [PubMed]
  2. B. Kress, and P. Meyrueis, Digital Diffractive Optics: An introduction to planar diffractive optics and related technologies (John Wiley and Sons, 2000).
  3. S. Sinzinger, and J. Jahns, “Diffractive Optics,” in Microoptics, (Wiley-VCH, 2nd edition, 2005), pp. 138–141.
  4. 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. A 16(5), 1143–1156 (1999).
    [CrossRef]
  5. A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
    [CrossRef]
  6. 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]
  7. J. M. Miller, N. de Beaucoudrey, P. Chavel, E. Cambril, and H. Launois, “Synthesis of a subwavelength-pulse-width spatially modulated array illuminator for 0.633 µm,” Opt. Lett. 21(17), 1399–1402 (1996).
    [CrossRef] [PubMed]
  8. F. T. Chen and H. G. Craighead, “Diffractive lens fabricated with mostly zeroth-order gratings,” Opt. Lett. 23, 1081–1083 (1996).
  9. D. W. Prather, “Design and application of subwavelength diffractive lenses for integration with infrared photodetectors,” Opt. Eng. 38(5), 870–878 (1999).
    [CrossRef]
  10. J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary Subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A 16(5), 1157–1167 (1999).
    [CrossRef]
  11. P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
    [CrossRef]
  12. P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings,” Opt. Lett. 23(14), 1081–1083 (1998).
    [CrossRef]
  13. A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech, 3rd Edition, 2005).
  14. P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
    [CrossRef]
  15. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
    [CrossRef] [PubMed]
  16. D. Khalil, “Extension of the radiation spectrum method for the reflection calculation at the end of a strongly guiding optical waveguide,” Opt. Quantum Electron. 35(8), 801–809 (2003).
    [CrossRef]
  17. M. Born, and E. Wolf, “Optics of crystals,” in Principles of Optics, (Cambridge University Press, Cambridge, 7th ed., 2005), 837–840.

2006 (1)

2003 (1)

D. Khalil, “Extension of the radiation spectrum method for the reflection calculation at the end of a strongly guiding optical waveguide,” Opt. Quantum Electron. 35(8), 801–809 (2003).
[CrossRef]

2000 (1)

1999 (4)

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. A 16(5), 1143–1156 (1999).
[CrossRef]

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary Subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A 16(5), 1157–1167 (1999).
[CrossRef]

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

D. W. Prather, “Design and application of subwavelength diffractive lenses for integration with infrared photodetectors,” Opt. Eng. 38(5), 870–878 (1999).
[CrossRef]

1998 (1)

1997 (1)

P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
[CrossRef]

1996 (3)

1992 (1)

Astilean, S.

Benech, P.

P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
[CrossRef]

Bermel, P.

Blasi, B.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Burr, G.

Cambril, E.

Chavel, P.

Chen, F. T.

Craighead, H. G.

de Beaucoudrey, N.

Doll, W.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Dreibholz, J.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Farjadpour, A.

Farn, M. W.

Gerard, P.

P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
[CrossRef]

Glaubitt, W.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Gombert, A.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Heinzel, A.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Ibanescu, M.

Ichioka, Y.

Joannopoulos, J. D.

Johnson, S. G.

Khalil, D.

D. Khalil, “Extension of the radiation spectrum method for the reflection calculation at the end of a strongly guiding optical waveguide,” Opt. Quantum Electron. 35(8), 801–809 (2003).
[CrossRef]

P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
[CrossRef]

Konishi, T.

Lalanne, P.

Launois, H.

Lemercier-Lalanne, D.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Mait, J. N.

Miller, J. M.

Mirotznik, M. S.

Prather, D. W.

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary Subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A 16(5), 1157–1167 (1999).
[CrossRef]

D. W. Prather, “Design and application of subwavelength diffractive lenses for integration with infrared photodetectors,” Opt. Eng. 38(5), 870–878 (1999).
[CrossRef]

Rimet, R.

P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
[CrossRef]

Rodriguez, A.

Rose, K.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Roundy, D.

Sporn, D.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Takahara, K.

Tedjini, S.

P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
[CrossRef]

Wittwer, V.

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Yotsuya, T.

Yu, W.

Appl. Opt. (2)

J. Mod. Opt. (1)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

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

Opt. Commun. (1)

P. Gerard, P. Benech, D. Khalil, R. Rimet, and S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures: the Radiation Spectrum Method,” Opt. Commun. 140(1-3), 128–145 (1997).
[CrossRef]

Opt. Eng. (1)

D. W. Prather, “Design and application of subwavelength diffractive lenses for integration with infrared photodetectors,” Opt. Eng. 38(5), 870–878 (1999).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

D. Khalil, “Extension of the radiation spectrum method for the reflection calculation at the end of a strongly guiding optical waveguide,” Opt. Quantum Electron. 35(8), 801–809 (2003).
[CrossRef]

Thin Solid Films (1)

A. Gombert, W. Glaubitt, K. Rose, J. Dreibholz, B. Blasi, A. Heinzel, D. Sporn, W. Doll, and V. Wittwer, “Subwavelength-structured antireflective surfaces on glass,” Thin Solid Films 351(1-2), 73–78 (1999).
[CrossRef]

Other (4)

B. Kress, and P. Meyrueis, Digital Diffractive Optics: An introduction to planar diffractive optics and related technologies (John Wiley and Sons, 2000).

S. Sinzinger, and J. Jahns, “Diffractive Optics,” in Microoptics, (Wiley-VCH, 2nd edition, 2005), pp. 138–141.

M. Born, and E. Wolf, “Optics of crystals,” in Principles of Optics, (Cambridge University Press, Cambridge, 7th ed., 2005), 837–840.

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech, 3rd Edition, 2005).

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Figures (5)

Fig. 1
Fig. 1

a) Phase difference and b) Diffraction efficiency as a function of the period and the fill factor of a 1203.5 nm height grating in fused silica without substrate for TE polarization at 632.8 nm.

Fig. 2
Fig. 2

Phase Difference versus the fill factor of the 1203.5 nm high grating in fused silica for several periods for a TE polarization wave, using FDTD.

Fig. 3
Fig. 3

Subwavelength diffractive lens designed from blazed lens

Fig. 4
Fig. 4

Near electric field propagation modeling in an inhomogeneous medium by the FDTD method on the left (the subwavelength lens is located inside the dotted black line) and far field Poynting vector simulation by RSM on the right. The plane A corresponds to the incident plane for the FDTD and the plane B to the recovery plane for the FDTD and also the incident plane for RSM.

Fig. 5
Fig. 5

Angular tolerance of subwavelength diffractive lenses

Tables (1)

Tables Icon

Table 1 Fill factors and widths of the line in the gratings allowing to realize an 8 levels simulated diffractive element. The grating is 1203.5 nm high, for an incidence light having a TE polarization and a normal incidence.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

h = 1 2 π λ n 1 φ max
Δ φ = 2 π ( f n 2 + 1 f ) n 1
1 f l = ( n 1 ) 1 R
η = u = 0 N f E ( x u , y = y f , t = t f ) × H ( x u , y = y f , t = t f ) v = 0 N 0 E ( x v , y = y 0 , t = t 0 ) × H ( x v , y = y 0 , t = t 0 )
x u = 0.66 λ . f D + u . Δ x R S M , 0 u N f ,   N f = 1.22 λ . f D . Δ x R S M ,
x v = D 2 + v . Δ x F D T D , 0 v < N 0 ,   N 0 = D Δ x F D T D

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