Abstract

The field-stitching method introduced previously [Opt. Lett. 21, 1508 (1996)] allows large-period gratings containing small-scale local structure to be analyzed without requiring excessive computing power. Multiple scattering and the polarization of the electromagnetic field are taken into account by standard rigorous analysis. A variety of calculations demonstrating the accuracy and the speed of the method are made. Also, we report on the optimization by simulated annealing of fan-out gratings with periods of up to 240λ and of diffractive cylindrical lenses with a period of 1200λ, which has been made possible by field-stitching analysis.

© 1997 Optical Society of America

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References

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  1. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [Crossref]
  2. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
    [Crossref]
  3. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  4. B. Layet, M. R. Taghizadeh, “Analysis of gratings with large periods and small feature sizes by stitching of the electromagnetic field,” Opt. Lett. 21, 1508–1510 (1996).
    [Crossref] [PubMed]
  5. C. P. Barrett, P. Blair, G. S. Buller, D. T. Neilson, B. Robertson, E. C. Smith, M. R. Taghizadeh, A. C. Walker, “Components for implementation of free-space optical crossbars,” Appl. Opt. 35, 6934–6944 (1996).
    [Crossref] [PubMed]
  6. A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991).
    [Crossref]
  7. J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
    [Crossref]
  8. E. Sidick, A. Knoesen, J. Mait, “Design and rigorous analysis of high-efficiency array generators,” Appl. Opt. 32, 2599–2605 (1993).
    [Crossref] [PubMed]
  9. E. Noponen, J. Turunen, F. Wyrowski, “Synthesis of paraxial-domain diffractive elements by rigorous electromagnetic theory,” J. Opt. Soc. Am. A 12, 1128–1133 (1995).
    [Crossref]
  10. R. Brauer, O. Bryngdahl, “Design strategy of diffractive elements with prescribed diffraction angles in nonparaxial region,” Opt. Commun. 115, 411–416 (1995).
    [Crossref]
  11. E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
    [Crossref]
  12. J. T. Sheridan, C. J. R. Sheppard, “Coherent imaging of periodic thick fine isolated structures,” J. Opt. Soc. Am. A 4, 614–632 (1993).
    [Crossref]
  13. F. Montiel, M. Nevière, “Electromagnetic theory of Bragg–Fresnel linear zone plates,” J. Opt. Soc. Am. A 12, 2672–2678 (1995).
    [Crossref]
  14. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
    [Crossref]
  15. A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
    [Crossref] [PubMed]
  16. H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–40.

1996 (2)

1995 (3)

1993 (4)

1992 (1)

1991 (1)

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991).
[Crossref]

1981 (2)

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[Crossref]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[Crossref]

1978 (1)

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[Crossref]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[Crossref]

Barrett, C. P.

Blair, P.

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[Crossref]

Brauer, R.

R. Brauer, O. Bryngdahl, “Design strategy of diffractive elements with prescribed diffraction angles in nonparaxial region,” Opt. Commun. 115, 411–416 (1995).
[Crossref]

Bryngdahl, O.

R. Brauer, O. Bryngdahl, “Design strategy of diffractive elements with prescribed diffraction angles in nonparaxial region,” Opt. Commun. 115, 411–416 (1995).
[Crossref]

Buller, G. S.

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[Crossref]

Gaylord, T. K.

Ichikawa, H.

Jaakkola, T.

Knoesen, A.

Knop, K.

Kuisma, S.

Layet, B.

Mait, J.

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[Crossref]

Miller, J. M.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[Crossref]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[Crossref] [PubMed]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991).
[Crossref]

Moharam, M. G.

Montiel, F.

Neilson, D. T.

Nevière, M.

Nishihara, H.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–40.

Noponen, E.

Robertson, B.

Ross, N.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[Crossref]

Sheppard, C. J. R.

Sheridan, J. T.

Sidick, E.

Smith, E. C.

Suhara, T.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–40.

Taghizadeh, M. R.

Turunen, J.

Vasara, A.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[Crossref]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[Crossref]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[Crossref] [PubMed]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991).
[Crossref]

Walker, A. C.

Westerholm, J.

Wyrowski, F.

Appl. Opt. (3)

J. Mod. Opt. (1)

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

Opt. Acta (1)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[Crossref]

Opt. Commun. (2)

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Rigorous diffraction analysis of Dammann gratings,” Opt. Commun. 81, 337–342 (1991).
[Crossref]

R. Brauer, O. Bryngdahl, “Design strategy of diffractive elements with prescribed diffraction angles in nonparaxial region,” Opt. Commun. 115, 411–416 (1995).
[Crossref]

Opt. Lett. (1)

Other (2)

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–40.

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of a grating and associated parameters.

Fig. 2
Fig. 2

Efficiency, uniformity, and TOE of a 200λ period 1×13 fan-out grating as a function of the local period of the FS calculation.

Fig. 3
Fig. 3

Focal spot intensity measure α, shape measure β, and the TOE of a 300λ period f/2 cylindrical diffractive lens array as a function of the local period of the FS calculation.

Fig. 4
Fig. 4

TOE’s of a 1×33 fan-out grating and an f/3 lens as a function of the local period of the FS calculation.

Fig. 5
Fig. 5

Calculation time and number of matrix elements of equally accurate BKK and FS calculations as a function of the grating period.

Fig. 6
Fig. 6

Efficiency and uniformity of scalar designed (line) and FS optimized (bars) 1×7 fan-out gratings as a function of the grating period.

Fig. 7
Fig. 7

Efficiency and uniformity of scalar designed (line) and FS optimized (bars) 1×33 fan-out gratings as a function of the grating period.

Fig. 8
Fig. 8

Efficiency of standard (line) and FS optimized (bars) 1200λ period f/3 cylindrical diffractive lens arrays as a function of the f-number.

Fig. 9
Fig. 9

Focal intensity (axial component of the Poynting vector) of standard (solid curve) and FS optimized (dashed curve) 1200λ period cylindrical diffractive lens arrays of various f-numbers as a function of the position.

Tables (1)

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Table 1 (a) Minimum Feature Sizes and (b) Average Feature Sizes of Scalar and FS-Designed 1×7 and 1×33 Fan-out Gratings

Equations (9)

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

Tp=1d n=1Nm=m(-)m(+)Tm(n)δn exp{iγm[xs+(1-n)w]}×(n-1)wnw exp(iγmx)exp(-iγpx)dx,
Ctt=m=1Ntm2,
Caa=m=1Nam2,
Cta=m=1Ntmam,
α=Cta/Ctt,
β2=1-Cta2/CttCaa.
merit=wαα-wββ.
Δr=maxm1N|1-Nam/η|,
merit=m=1N(am-ηg/N)2,

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