Abstract

Asymmetric transmission gratings operating in the resonance domain are designed by modeling of the dose-controlled electron-beam lithography process with Gaussian convolution. We aim to exceed some efficiency limit ηs over a specified spectral range and to maximize ηs. The resultant continuous-profile gratings are fabricated by electron-beam lithography and proportional reactive-ion etching into SiO2. We demonstrate gratings with good signal-to-noise ratio and a diffraction efficiency greater than 40% for wavelengths from 400 to 750 nm.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  2. J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
    [CrossRef]
  3. M. C. Hutley, Diffraction Gratings (Academic, London, 1982).
  4. N. K. Sheridan, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
    [CrossRef]
  5. M. Nevière, “Electromagnetic study of transmission gratings,” Appl. Opt. 30, 4540–4547 (1991).
    [CrossRef] [PubMed]
  6. T. Hyvarinen, E. Herrala, A. Dall’Ava, “Direct sight imaging spectrograph: a unique add-on component brings spectral imaging to industrial applications,” in Digital Solid State Cameras: Designs and Applications, G. M. Williams, ed., Proc. SPIE3302, 165–175 (1998).
    [CrossRef]
  7. E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 31, 5910–5912 (1992).
    [CrossRef] [PubMed]
  8. H. J. Gerritsen, M. L. Jepsen, “Rectangular surface-relief transmission gratings with a very large first-order diffraction efficiency (∼95%) for unpolarized light,” Appl. Opt. 37, 5823–5829 (1998).
    [CrossRef]
  9. J. Turunen, “Diffraction theory of microrelief gratings,” Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed., (Taylor & Francis, London, 1997), Chap. 2.
  10. W. Däshner, M. Larsson, S. H. Lee, “Fabrication of monolithic diffractive optical elements by the use of e-beam direct write on an analog resist and single chemically assisted ion-beam-etching step,” Appl. Opt. 34, 2534–2539 (1995).
    [CrossRef]
  11. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Computer J. 7, 308–313 (1964).
    [CrossRef]
  12. P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
    [CrossRef]
  13. M. B. Stern, T. R. Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
    [CrossRef]
  14. M. Eisner, J. Schwider, “Transferring resist microlenses into silicon by reactive ion etching,” Opt. Eng. 35, 2979–2982 (1996).
    [CrossRef]
  15. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994); errata 13, 543 (1996).
  16. L. Li, J. Chandezon, “Improvement of the coordinate transformation method for surface relief gratings with sharp edges,” J. Opt. Soc. Am. A 13, 2247–2255 (1996).
    [CrossRef]
  17. L. Li, J. Chandezon, G. Granet, J.-P. Plumey, “Rigorous and efficient grating-analysis method made easy for optical engineers,” Appl. Opt. 38, 304–313 (1999).
    [CrossRef]
  18. M. T. Gale, “Replication,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), Chap. 6.

1999

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

L. Li, J. Chandezon, G. Granet, J.-P. Plumey, “Rigorous and efficient grating-analysis method made easy for optical engineers,” Appl. Opt. 38, 304–313 (1999).
[CrossRef]

1998

1996

L. Li, J. Chandezon, “Improvement of the coordinate transformation method for surface relief gratings with sharp edges,” J. Opt. Soc. Am. A 13, 2247–2255 (1996).
[CrossRef]

M. Eisner, J. Schwider, “Transferring resist microlenses into silicon by reactive ion etching,” Opt. Eng. 35, 2979–2982 (1996).
[CrossRef]

1995

1994

M. B. Stern, T. R. Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994); errata 13, 543 (1996).

1992

J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 31, 5910–5912 (1992).
[CrossRef] [PubMed]

1991

1968

N. K. Sheridan, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
[CrossRef]

1964

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Computer J. 7, 308–313 (1964).
[CrossRef]

Baraldi, L.

J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
[CrossRef]

Chandezon, J.

Dall’Ava, A.

T. Hyvarinen, E. Herrala, A. Dall’Ava, “Direct sight imaging spectrograph: a unique add-on component brings spectral imaging to industrial applications,” in Digital Solid State Cameras: Designs and Applications, G. M. Williams, ed., Proc. SPIE3302, 165–175 (1998).
[CrossRef]

Däshner, W.

Eisner, M.

M. Eisner, J. Schwider, “Transferring resist microlenses into silicon by reactive ion etching,” Opt. Eng. 35, 2979–2982 (1996).
[CrossRef]

Gale, M. T.

J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
[CrossRef]

M. T. Gale, “Replication,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), Chap. 6.

Gerritsen, H. J.

Granet, G.

Herrala, E.

T. Hyvarinen, E. Herrala, A. Dall’Ava, “Direct sight imaging spectrograph: a unique add-on component brings spectral imaging to industrial applications,” in Digital Solid State Cameras: Designs and Applications, G. M. Williams, ed., Proc. SPIE3302, 165–175 (1998).
[CrossRef]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

Hyvarinen, T.

T. Hyvarinen, E. Herrala, A. Dall’Ava, “Direct sight imaging spectrograph: a unique add-on component brings spectral imaging to industrial applications,” in Digital Solid State Cameras: Designs and Applications, G. M. Williams, ed., Proc. SPIE3302, 165–175 (1998).
[CrossRef]

Jay, T. R.

M. B. Stern, T. R. Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

Jepsen, M. L.

Kettunen, V.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

Laakkonen, P.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

Larsson, M.

Lautanen, J.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

Lee, S. H.

Li, L.

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Computer J. 7, 308–313 (1964).
[CrossRef]

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Computer J. 7, 308–313 (1964).
[CrossRef]

Nevière, M.

Noponen, E.

Oppliger, Y.

J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
[CrossRef]

Plumey, J.-P.

Regnault, P.

J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
[CrossRef]

Schirmer, M.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

Schwider, J.

M. Eisner, J. Schwider, “Transferring resist microlenses into silicon by reactive ion etching,” Opt. Eng. 35, 2979–2982 (1996).
[CrossRef]

Sheridan, N. K.

N. K. Sheridan, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
[CrossRef]

Stauffer, J. M.

J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
[CrossRef]

Stern, M. B.

M. B. Stern, T. R. Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

Turunen, J.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 31, 5910–5912 (1992).
[CrossRef] [PubMed]

J. Turunen, “Diffraction theory of microrelief gratings,” Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed., (Taylor & Francis, London, 1997), Chap. 2.

Vasara, A.

Appl. Opt.

Appl. Phys. Lett.

N. K. Sheridan, “Production of blazed holograms,” Appl. Phys. Lett. 12, 316–318 (1968).
[CrossRef]

Computer J.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Computer J. 7, 308–313 (1964).
[CrossRef]

J. Mod. Opt.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

J. M. Stauffer, Y. Oppliger, P. Regnault, L. Baraldi, M. T. Gale, “Electron beam writing of continuous resist profiles for optical applications,” J. Vac. Sci. Technol. B 10, 2526–2529 (1992).
[CrossRef]

Opt. Eng.

M. B. Stern, T. R. Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

M. Eisner, J. Schwider, “Transferring resist microlenses into silicon by reactive ion etching,” Opt. Eng. 35, 2979–2982 (1996).
[CrossRef]

Other

M. T. Gale, “Replication,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), Chap. 6.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

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

J. Turunen, “Diffraction theory of microrelief gratings,” Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed., (Taylor & Francis, London, 1997), Chap. 2.

T. Hyvarinen, E. Herrala, A. Dall’Ava, “Direct sight imaging spectrograph: a unique add-on component brings spectral imaging to industrial applications,” in Digital Solid State Cameras: Designs and Applications, G. M. Williams, ed., Proc. SPIE3302, 165–175 (1998).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Simulated grating profiles p(x). Dashed curve, w = 0.3; continuous curve, w = 0.5; dashed–dotted curve, w = 0.7.

Fig. 2
Fig. 2

Diffraction efficiencies of optimized grating profiles. Dashed curve, w = 0.3; continuous curve, w = 0.5, dashed–dotted curve, w = 0.7.

Fig. 3
Fig. 3

(a) SEM of a fabricated grating profile. (b) Fabricated grating profile read from a SEM (continuous curve) and corresponding theoretical model (dashed curve).

Fig. 4
Fig. 4

Calculated efficiencies for the grating profile in Fig. 3(b) and measured efficiencies (crosses, TE polarization; circles, TM polarization) for some wavelengths. Continuous curve, average of TE and TM polarizations; dashed curve, TE polarization; dashed–dotted curve, TM polarization.

Fig. 5
Fig. 5

Intensity distribution of a He–Ne laser beam the in the far field of the grating. Measurement distance, 5.5 m; detector size, 2 mm × 2 mm.

Tables (1)

Tables Icon

Table 1 Optimized Incidence Angles θin and Relief Heights h with Corresponding Minimum and Maximum Deflection Angles θmin and θmax

Equations (2)

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

gx=2/πw exp-2x2/w2,
px=pix * gx.

Metrics