Abstract

We evaluated the optical performance of an IR echelle grating produced on a silicon wafer with anisotropic etching techniques. We measured the diffraction efficiency of a sample with a 55° blaze angle and 25-μm groove spacing. We also calculated the efficiency for typical triangular and trapezoidal groove profiles of etched gratings. The diffraction efficiency for unpolarized light can be approximately as high as the efficiency of right-angle groove gratings. The great potential of the etched silicon grating lies in its ease of fabrication, its excellent surface quality, and the high reproducibility of the production process. Compact high-resolution diffraction gratings can be produced by etching the grating pattern into the rear side of a transparent prism. When used in internal reflection, this increases the resolving power of the grating by a factor equal to the refractive index of the prism over a front surface grating of the same length.

© 1994 Optical Society of America

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References

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  1. L. Comerford, P. Zory, “Selectively etched diffraction gratings in GaAs,” Appl. Phys. Lett. 25, 208–210 (1974).
    [CrossRef]
  2. W. T. Tsang, S. Wang, “Preferentially etched diffraction gratings in silicon,” J. Appl. Phys. 46, 2163–2166 (1975).
    [CrossRef]
  3. S. Sriram, E. P. Supertzi, “Novel V-groove structures on silicon,” Appl. Opt. 24, 1784–1787 (1985).
    [CrossRef] [PubMed]
  4. P. Philippe, S. Valette, O. Mata Mendez, D. Maystre, “Wavelength demultiplexer: using echelette gratings on silicon substrate,” Appl. Opt. 24, 1006–1011 (1985).
    [CrossRef] [PubMed]
  5. M. Josse, D. L. Kendall, “Rectangular-profile diffraction grating from single-crystal silicon,” Appl. Opt. 19, 72–76 (1980).
    [CrossRef] [PubMed]
  6. L. Sica, “High resolution diffraction grating,” U.S. patent4,475,792 (9October1984).
  7. H. Dekker, “An immersion grating for an astronomical spectrograph,” in Instrumentation for Ground-Based Optical Astronomy, L. B. Robinson, ed. (Springer-Verlag, New York, 1987), pp. 183–188.
  8. K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982).
    [CrossRef]
  9. E. G. Loewen, “What’s new in gratings?,” in Instrumentation for Ground-Based Optical Astronomy, L. B. Robinson, ed. (Springer-Verlag, New York, 1987), pp. 118–123.
  10. G. W. Stroke, “Diffraction gratings,” in Handbuch der Physik, (Springer-Verlag, Berlin, 1967), Vol. 29, pp. 426–754.
    [CrossRef]
  11. M. C. Hutley, Diffraction Gratings (Academic, London, 1982).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  13. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  14. D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. 21, pp. 1–67.
    [CrossRef]
  15. D. Maystre, M. Neviere, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 159–225.
    [CrossRef]
  16. R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
  17. J. Moore, H. Ling, U. U. Graf, D. T. Jaffe, “A boundary integral approach to the scattering from periodic gratings,” Microwave Opt. Technol. Lett. 5 (10), 480–483 (1992).
    [CrossRef]
  18. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. Ser. 6 4, 396–402 (1902).
    [CrossRef]
  19. S. Engman, P. Lindblom, E. Leibhardt, “Improving echelle grating efficiencies,” Phys. Scr. 28, 86–88 (1983).
    [CrossRef]

1992 (1)

J. Moore, H. Ling, U. U. Graf, D. T. Jaffe, “A boundary integral approach to the scattering from periodic gratings,” Microwave Opt. Technol. Lett. 5 (10), 480–483 (1992).
[CrossRef]

1985 (2)

1983 (1)

S. Engman, P. Lindblom, E. Leibhardt, “Improving echelle grating efficiencies,” Phys. Scr. 28, 86–88 (1983).
[CrossRef]

1982 (1)

K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982).
[CrossRef]

1980 (1)

1975 (1)

W. T. Tsang, S. Wang, “Preferentially etched diffraction gratings in silicon,” J. Appl. Phys. 46, 2163–2166 (1975).
[CrossRef]

1974 (1)

L. Comerford, P. Zory, “Selectively etched diffraction gratings in GaAs,” Appl. Phys. Lett. 25, 208–210 (1974).
[CrossRef]

1902 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. Ser. 6 4, 396–402 (1902).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Comerford, L.

L. Comerford, P. Zory, “Selectively etched diffraction gratings in GaAs,” Appl. Phys. Lett. 25, 208–210 (1974).
[CrossRef]

Dekker, H.

H. Dekker, “An immersion grating for an astronomical spectrograph,” in Instrumentation for Ground-Based Optical Astronomy, L. B. Robinson, ed. (Springer-Verlag, New York, 1987), pp. 183–188.

Engman, S.

S. Engman, P. Lindblom, E. Leibhardt, “Improving echelle grating efficiencies,” Phys. Scr. 28, 86–88 (1983).
[CrossRef]

Graf, U. U.

J. Moore, H. Ling, U. U. Graf, D. T. Jaffe, “A boundary integral approach to the scattering from periodic gratings,” Microwave Opt. Technol. Lett. 5 (10), 480–483 (1992).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Hutley, M. C.

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

Jaffe, D. T.

J. Moore, H. Ling, U. U. Graf, D. T. Jaffe, “A boundary integral approach to the scattering from periodic gratings,” Microwave Opt. Technol. Lett. 5 (10), 480–483 (1992).
[CrossRef]

Josse, M.

Kendall, D. L.

Leibhardt, E.

S. Engman, P. Lindblom, E. Leibhardt, “Improving echelle grating efficiencies,” Phys. Scr. 28, 86–88 (1983).
[CrossRef]

Lindblom, P.

S. Engman, P. Lindblom, E. Leibhardt, “Improving echelle grating efficiencies,” Phys. Scr. 28, 86–88 (1983).
[CrossRef]

Ling, H.

J. Moore, H. Ling, U. U. Graf, D. T. Jaffe, “A boundary integral approach to the scattering from periodic gratings,” Microwave Opt. Technol. Lett. 5 (10), 480–483 (1992).
[CrossRef]

Loewen, E. G.

E. G. Loewen, “What’s new in gratings?,” in Instrumentation for Ground-Based Optical Astronomy, L. B. Robinson, ed. (Springer-Verlag, New York, 1987), pp. 118–123.

Mata Mendez, O.

Maystre, D.

P. Philippe, S. Valette, O. Mata Mendez, D. Maystre, “Wavelength demultiplexer: using echelette gratings on silicon substrate,” Appl. Opt. 24, 1006–1011 (1985).
[CrossRef] [PubMed]

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. 21, pp. 1–67.
[CrossRef]

D. Maystre, M. Neviere, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 159–225.
[CrossRef]

Moore, J.

J. Moore, H. Ling, U. U. Graf, D. T. Jaffe, “A boundary integral approach to the scattering from periodic gratings,” Microwave Opt. Technol. Lett. 5 (10), 480–483 (1992).
[CrossRef]

Neviere, M.

D. Maystre, M. Neviere, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 159–225.
[CrossRef]

Petersen, K. E.

K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982).
[CrossRef]

Petit, R.

D. Maystre, M. Neviere, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 159–225.
[CrossRef]

Philippe, P.

Sica, L.

L. Sica, “High resolution diffraction grating,” U.S. patent4,475,792 (9October1984).

Sriram, S.

Stroke, G. W.

G. W. Stroke, “Diffraction gratings,” in Handbuch der Physik, (Springer-Verlag, Berlin, 1967), Vol. 29, pp. 426–754.
[CrossRef]

Supertzi, E. P.

Tsang, W. T.

W. T. Tsang, S. Wang, “Preferentially etched diffraction gratings in silicon,” J. Appl. Phys. 46, 2163–2166 (1975).
[CrossRef]

Valette, S.

Wang, S.

W. T. Tsang, S. Wang, “Preferentially etched diffraction gratings in silicon,” J. Appl. Phys. 46, 2163–2166 (1975).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. Ser. 6 4, 396–402 (1902).
[CrossRef]

Zory, P.

L. Comerford, P. Zory, “Selectively etched diffraction gratings in GaAs,” Appl. Phys. Lett. 25, 208–210 (1974).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

L. Comerford, P. Zory, “Selectively etched diffraction gratings in GaAs,” Appl. Phys. Lett. 25, 208–210 (1974).
[CrossRef]

J. Appl. Phys. (1)

W. T. Tsang, S. Wang, “Preferentially etched diffraction gratings in silicon,” J. Appl. Phys. 46, 2163–2166 (1975).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

J. Moore, H. Ling, U. U. Graf, D. T. Jaffe, “A boundary integral approach to the scattering from periodic gratings,” Microwave Opt. Technol. Lett. 5 (10), 480–483 (1992).
[CrossRef]

Philos. Mag. Ser. 6 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. Ser. 6 4, 396–402 (1902).
[CrossRef]

Phys. Scr. (1)

S. Engman, P. Lindblom, E. Leibhardt, “Improving echelle grating efficiencies,” Phys. Scr. 28, 86–88 (1983).
[CrossRef]

Proc. IEEE (1)

K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982).
[CrossRef]

Other (10)

E. G. Loewen, “What’s new in gratings?,” in Instrumentation for Ground-Based Optical Astronomy, L. B. Robinson, ed. (Springer-Verlag, New York, 1987), pp. 118–123.

G. W. Stroke, “Diffraction gratings,” in Handbuch der Physik, (Springer-Verlag, Berlin, 1967), Vol. 29, pp. 426–754.
[CrossRef]

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

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

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

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. 21, pp. 1–67.
[CrossRef]

D. Maystre, M. Neviere, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 159–225.
[CrossRef]

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

L. Sica, “High resolution diffraction grating,” U.S. patent4,475,792 (9October1984).

H. Dekker, “An immersion grating for an astronomical spectrograph,” in Instrumentation for Ground-Based Optical Astronomy, L. B. Robinson, ed. (Springer-Verlag, New York, 1987), pp. 183–188.

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Figures (7)

Fig. 1
Fig. 1

Groove profile of an etched grating. The angles between the crystal lattice planes (indicated by the dotted lines) determine the blaze angle (55°) and the groove apex angle (70°). Our sample grating has a groove spacing d of 25 μm. The width a of the flat groove tops (2.4 μ in our case) depends on the details of the fabrication process.

Fig. 2
Fig. 2

SEM of a sample grating etched into silicon. The micrograph shows the bottom end of two grooves at a magnification of 1600×. The three wide, dark, vertical stripes are the residual flats between grooves. The groove bottoms are very sharp straight lines showing the excellent surface quality of the etched groove walls. The horizontal lines are artifacts produced by a scanning instability of the SEM.

Fig. 3
Fig. 3

Simplified schematics of the measurement setup. The CO2 laser beam is focused by a lens (L) through an aperture (A) and collimated by an off-axis parabolic mirror (OAP). The radiation reflected by the grating (G) is focused by the same off-axis mirror through a second aperture (A′) onto the detector (D). The two apertures are offset with respect to each other in the direction perpendicular to the paper plane. The grating can be rotated out of the beam path to expose a flat reference mirror (RM).

Fig. 4
Fig. 4

Comparison between the measured (polygonal markers) and calculated (solid curves) near-Littrow diffraction efficiency of an etched grating (groove spacing, 25 μm; 2.4-μm-wide flat-topped grooves). Both polarizations are shown: (a) P polarization (E field parallel to grooves); (b) S polarization (E field perpendicular to grooves) for wavelengths near 10 μm in −3rd, −4th, and −5th diffraction order.

Fig. 5
Fig. 5

Comparison between the calculated near-Littrow diffraction efficiency of (a) an etched grating (70° apex angle) and (b) a ruled grating (90° apex angle). Both gratings have a blaze angle of 54.7° and a groove spacing of 25 μm. The flat bottoms of the etched grating grooves are 3 μm wide. Note that the peak efficiency of unpolarized light (heavy solid curve) is almost the same for both gratings. As in Fig. 4 we show data calculated for λ = 10 μm in −3rd to −5th order.

Fig. 6
Fig. 6

Concept for a compact, high-resolution diffraction grating based on the described anisotropic etching techniques. The combination of the transparent prism with the back surface grating increases the resolution by a factor of n over a front surface grating of the same length. The orientation of the crystal lattice planes is indicated by the dotted lines.

Fig. 7
Fig. 7

Measured intensity distribution in the diffraction pattern produced by the etched grating sample illuminated with a He–Ne laser. The width of the envelope function (sin x/x)2 is a direct measure of the width of the flat groove tops.

Tables (1)

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Table 1 Effect of Flat Groove Tops or Bottoms in Etched Gratings (Apex Angle 70°) on the Calculated Diffraction Efficiencya

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