Abstract

We suggest and numerically demonstrate a specific design method of broadband mid-IR echelette grating. The method, which applies the compensating of the efficiency blaze in TM-plane polarization to Rayleigh anomalies, is called compensating effect method. This idea allows the grating designer to realize fully the considerable advantages of this type of echelette grating with an apex angle 90° and a blaze angle 19.47°, especially, it can be fabricated easily with conventional (holographic and ruled) techniques. Its diffraction efficiency in unpolarized light has a minimum value of 40%. The cases of Littrow mount and off-Littrow mount are both discussed.

© 2008 Optical Society of America

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References

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  1. W. Brügel, An introduction to infrared spectroscopy, (London: Methuen & Co. LTD., New York, John Wiley & Sons Inc., 1962).
  2. M. Ishikawa, M. Inoue, T. Kita, and T. Iwasaki, "Infrared Spectrophotometers using a double blazed grating," J. Spectrosc. Soc. Jpn 27, 304-310 (1978).
    [CrossRef]
  3. P. D. Maker, R. E. Muller, D. W. Wilson, and P. Mouroulis, "New convex grating types manufactured by electron beam lithography," in Diffractive Optics and Micro-Optics 10, OSA Technical Digest Series, 234-236 (1998).
  4. D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
    [CrossRef]
  5. E. Popov, J. Hoose, B. Frankel, C. Keast, M. Fritze, T. Fan, D. Yost, and S. Rabe, "Low polarization dependent diffraction grating for wavelength demultimlexing," Opt. Express 12, 269-275 (2004).
    [CrossRef] [PubMed]
  6. D. Maystre, "Integral Method," in Electromagnetic Theory of Gratings, R. Petit, (Springer-Verlag, 1980).
  7. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos Mag. 4, 396-402 (1902).
  8. A. Hessel and A. A. Oliner, "A new theory of Wood�??s anomalies on optical gratings," Appl. Opt. 4, 1275-1297 (1965).
    [CrossRef]
  9. C. H. Palmer, Jr., "Parallel diffraction grating anomalies," J. Opt. Soc. Am. 42, 269 (1952).
    [CrossRef]
  10. A. Marechal and G. W. Stroke, "Sur l�??origine des effets de polarisation et de diffraction dans les réseaux optiques,�??�?? C. R. Acad. Sci. 249, 2042-2044 (1959).
  11. P. Vincent and M. Nevière, "The Reciprocity Theorem for Corrugated Surfaces used in Conical Diffraction Mountings," Opt. Acta 26, 889-898 (1979).
    [CrossRef]
  12. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997), Chap. 4.

2004 (1)

2003 (1)

D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
[CrossRef]

1979 (1)

P. Vincent and M. Nevière, "The Reciprocity Theorem for Corrugated Surfaces used in Conical Diffraction Mountings," Opt. Acta 26, 889-898 (1979).
[CrossRef]

1978 (1)

M. Ishikawa, M. Inoue, T. Kita, and T. Iwasaki, "Infrared Spectrophotometers using a double blazed grating," J. Spectrosc. Soc. Jpn 27, 304-310 (1978).
[CrossRef]

1965 (1)

1959 (1)

A. Marechal and G. W. Stroke, "Sur l�??origine des effets de polarisation et de diffraction dans les réseaux optiques,�??�?? C. R. Acad. Sci. 249, 2042-2044 (1959).

1952 (1)

1902 (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos Mag. 4, 396-402 (1902).

Backlund, J.

D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
[CrossRef]

Fan, T.

Frankel, B.

Fritze, M.

Hessel, A.

Hoose, J.

Inoue, M.

M. Ishikawa, M. Inoue, T. Kita, and T. Iwasaki, "Infrared Spectrophotometers using a double blazed grating," J. Spectrosc. Soc. Jpn 27, 304-310 (1978).
[CrossRef]

Ishikawa, M.

M. Ishikawa, M. Inoue, T. Kita, and T. Iwasaki, "Infrared Spectrophotometers using a double blazed grating," J. Spectrosc. Soc. Jpn 27, 304-310 (1978).
[CrossRef]

Iwasaki, T.

M. Ishikawa, M. Inoue, T. Kita, and T. Iwasaki, "Infrared Spectrophotometers using a double blazed grating," J. Spectrosc. Soc. Jpn 27, 304-310 (1978).
[CrossRef]

Keast, C.

Kita, T.

M. Ishikawa, M. Inoue, T. Kita, and T. Iwasaki, "Infrared Spectrophotometers using a double blazed grating," J. Spectrosc. Soc. Jpn 27, 304-310 (1978).
[CrossRef]

Maker, P. D.

D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
[CrossRef]

Marechal, A.

A. Marechal and G. W. Stroke, "Sur l�??origine des effets de polarisation et de diffraction dans les réseaux optiques,�??�?? C. R. Acad. Sci. 249, 2042-2044 (1959).

Mouroulis, P.

D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
[CrossRef]

Muller, R. E.

D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
[CrossRef]

Nevière, M.

P. Vincent and M. Nevière, "The Reciprocity Theorem for Corrugated Surfaces used in Conical Diffraction Mountings," Opt. Acta 26, 889-898 (1979).
[CrossRef]

Oliner, A. A.

Palmer, C. H.

Popov, E.

Rabe, S.

Stroke, G. W.

A. Marechal and G. W. Stroke, "Sur l�??origine des effets de polarisation et de diffraction dans les réseaux optiques,�??�?? C. R. Acad. Sci. 249, 2042-2044 (1959).

Vincent, P.

P. Vincent and M. Nevière, "The Reciprocity Theorem for Corrugated Surfaces used in Conical Diffraction Mountings," Opt. Acta 26, 889-898 (1979).
[CrossRef]

Wilson, D. W.

D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
[CrossRef]

Wood, R. W.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos Mag. 4, 396-402 (1902).

Yost, D.

Appl. Opt. (1)

C. R. Acad. Sci. (1)

A. Marechal and G. W. Stroke, "Sur l�??origine des effets de polarisation et de diffraction dans les réseaux optiques,�??�?? C. R. Acad. Sci. 249, 2042-2044 (1959).

J. Opt. Soc. Am. (1)

J. Spectrosc. Soc. Jpn (1)

M. Ishikawa, M. Inoue, T. Kita, and T. Iwasaki, "Infrared Spectrophotometers using a double blazed grating," J. Spectrosc. Soc. Jpn 27, 304-310 (1978).
[CrossRef]

Opt. Acta (1)

P. Vincent and M. Nevière, "The Reciprocity Theorem for Corrugated Surfaces used in Conical Diffraction Mountings," Opt. Acta 26, 889-898 (1979).
[CrossRef]

Opt. Express (1)

Philos Mag. (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos Mag. 4, 396-402 (1902).

Proc. SPIE (1)

D. W. Wilson, P. D. Maker, R. E. Muller, P. Mouroulis, and J. Backlund, "Recent advances in blazed grating fabrication by electron-beam lithography," Proc. SPIE 5173, 115-126 (2003).
[CrossRef]

Other (4)

W. Brügel, An introduction to infrared spectroscopy, (London: Methuen & Co. LTD., New York, John Wiley & Sons Inc., 1962).

P. D. Maker, R. E. Muller, D. W. Wilson, and P. Mouroulis, "New convex grating types manufactured by electron beam lithography," in Diffractive Optics and Micro-Optics 10, OSA Technical Digest Series, 234-236 (1998).

D. Maystre, "Integral Method," in Electromagnetic Theory of Gratings, R. Petit, (Springer-Verlag, 1980).

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997), Chap. 4.

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Figures (5)

Fig. 1.
Fig. 1.

Atomic-force microscope scan of the polygonal grating

Fig. 2.
Fig. 2.

The efficiencies of perfectly metallic echelette gratings show the efficiency blaze for both polarizations in -1st order Littrow mount. Left: the case of TM for the blaze angle α=10°, Right: the case of TE when α varies from 5°to 25°.

Fig. 3.
Fig. 3.

The efficiency curves show the influence of the distances between blaze wavelengths and Rayleigh anomalies to the strength of TM Rayleigh anomalies. Left: the case of strong influence with α=5°, right: the case of weak one with α=19.47°.

Fig. 4.
Fig. 4.

The compares of efficiency curves in unpolarized light. Left: the compared curves computed by three design methods for echelette and polygonal gratings, right: The efficiency compare of the deep sinusoidal grooves (the ratio of groove depth to grating period is 0.36) and echelette grating designed by method 3.

Fig. 5.
Fig. 5.

The influence of deviation angle δ to “UN” efficiency in -1st order Littrow mount for the gratings with different apex angles but the same blaze angle (α=19.47°). Left: the apex angle is 90°, right: the apex angle is 95°.

Tables (1)

Tables Icon

Table. 1. Strength of Rayleigh anomalies for the echelette grating (α=5°, ϕ=90°).

Equations (5)

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sin θ m = sin θ i + m λ d
2 sin θ i = m ε λ d
λ R m d = ± 2 2 m m ε
sin θ R m = m ε 2 m m ε
λ d = ± 2 cos 2 ( δ 2 ) [ m δ + 2 m 2 m ( m m δ ) sin ( δ 2 ) ] 4 m ( m m σ ) cos 2 ( δ 2 ) + m δ 2

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