Abstract

It has long been observed that the efficiency behavior of concave gratings differs from that of the well-studied plane gratings. In particular, peak values are less, and anomalies are usually absent or at least greatly attenuated. A detailed study of a typical holographic grating shows how variations in behavior over its surface combine in producing these results.

© 1990 Optical Society of America

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References

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  1. M. C. Hutley, Diffraction Gratings (Academic, New York, 1982), Chap. 7, pp. 215–262.
  2. E. G. Loewen, “Diffraction gratings, ruled and holographic,” in Applied Optics and Optical Engineering, G. A. Vanasse, ed. (Academic, New York, 1983), Vol. IX, Chap. 2, pp. 33–71.
    [CrossRef]
  3. T. Namioka, M. Seya, H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
    [CrossRef]
  4. W. R. Hunter, “Diffraction gratings for the vacuum ultraviolet spectral region,” Nucl. Instrum. Methods 172, 259–268 (1980).
    [CrossRef]
  5. M. Nevière, W. R. Hunter, “Analysis of the changes in efficiency across the ruled area of a concave diffraction grating,” Appl. Opt. 19, 2059–2065 (1980).
    [CrossRef] [PubMed]
  6. W. R. Hunter, in Spectrometric Techniques, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1985), Vol. IV, Chap. 2, pp. 63–180.
  7. R. Petit, ed., Electromagnetic Theory of Gratings—Topics in Current Physics (Springer-Verlag, Heidelberg, 1980), Vol. 22.
    [CrossRef]
  8. E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
    [CrossRef]
  9. E. G. Loewen, M. Nevière, “Simple selection rules for VUV and XUV diffraction gratings,” Appl. Opt. 17, 1087–1092 (1978).
    [CrossRef] [PubMed]
  10. A. V. Savushkin, E. A. Sokelava, G. P. Startsev, “Optimization of the spectral and energy characteristics of concave diffraction gratings,” Sov. J. Opt. Technol. 54, 376–378 (1987).

1987 (1)

A. V. Savushkin, E. A. Sokelava, G. P. Startsev, “Optimization of the spectral and energy characteristics of concave diffraction gratings,” Sov. J. Opt. Technol. 54, 376–378 (1987).

1986 (1)

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

1980 (2)

M. Nevière, W. R. Hunter, “Analysis of the changes in efficiency across the ruled area of a concave diffraction grating,” Appl. Opt. 19, 2059–2065 (1980).
[CrossRef] [PubMed]

W. R. Hunter, “Diffraction gratings for the vacuum ultraviolet spectral region,” Nucl. Instrum. Methods 172, 259–268 (1980).
[CrossRef]

1978 (1)

1976 (1)

T. Namioka, M. Seya, H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

Hunter, W. R.

M. Nevière, W. R. Hunter, “Analysis of the changes in efficiency across the ruled area of a concave diffraction grating,” Appl. Opt. 19, 2059–2065 (1980).
[CrossRef] [PubMed]

W. R. Hunter, “Diffraction gratings for the vacuum ultraviolet spectral region,” Nucl. Instrum. Methods 172, 259–268 (1980).
[CrossRef]

W. R. Hunter, in Spectrometric Techniques, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1985), Vol. IV, Chap. 2, pp. 63–180.

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982), Chap. 7, pp. 215–262.

Loewen, E. G.

E. G. Loewen, M. Nevière, “Simple selection rules for VUV and XUV diffraction gratings,” Appl. Opt. 17, 1087–1092 (1978).
[CrossRef] [PubMed]

E. G. Loewen, “Diffraction gratings, ruled and holographic,” in Applied Optics and Optical Engineering, G. A. Vanasse, ed. (Academic, New York, 1983), Vol. IX, Chap. 2, pp. 33–71.
[CrossRef]

Mashev, L.

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

Namioka, T.

T. Namioka, M. Seya, H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

Nevière, M.

Noda, H.

T. Namioka, M. Seya, H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

Popov, E.

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

Savushkin, A. V.

A. V. Savushkin, E. A. Sokelava, G. P. Startsev, “Optimization of the spectral and energy characteristics of concave diffraction gratings,” Sov. J. Opt. Technol. 54, 376–378 (1987).

Seya, M.

T. Namioka, M. Seya, H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

Sokelava, E. A.

A. V. Savushkin, E. A. Sokelava, G. P. Startsev, “Optimization of the spectral and energy characteristics of concave diffraction gratings,” Sov. J. Opt. Technol. 54, 376–378 (1987).

Startsev, G. P.

A. V. Savushkin, E. A. Sokelava, G. P. Startsev, “Optimization of the spectral and energy characteristics of concave diffraction gratings,” Sov. J. Opt. Technol. 54, 376–378 (1987).

Appl. Opt. (2)

J. Opt. (Paris) (1)

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Namioka, M. Seya, H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

Nucl. Instrum. Methods (1)

W. R. Hunter, “Diffraction gratings for the vacuum ultraviolet spectral region,” Nucl. Instrum. Methods 172, 259–268 (1980).
[CrossRef]

Sov. J. Opt. Technol. (1)

A. V. Savushkin, E. A. Sokelava, G. P. Startsev, “Optimization of the spectral and energy characteristics of concave diffraction gratings,” Sov. J. Opt. Technol. 54, 376–378 (1987).

Other (4)

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982), Chap. 7, pp. 215–262.

E. G. Loewen, “Diffraction gratings, ruled and holographic,” in Applied Optics and Optical Engineering, G. A. Vanasse, ed. (Academic, New York, 1983), Vol. IX, Chap. 2, pp. 33–71.
[CrossRef]

W. R. Hunter, in Spectrometric Techniques, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1985), Vol. IV, Chap. 2, pp. 63–180.

R. Petit, ed., Electromagnetic Theory of Gratings—Topics in Current Physics (Springer-Verlag, Heidelberg, 1980), Vol. 22.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Three-dimensional map of groove-depth distribution.

Fig. 2
Fig. 2

Experimental setup for local efficiency measurement.

Fig. 3
Fig. 3

Local absolute efficiency maps measured at three wavelengths: solid curve, P (or TE); dotted curve, S (or TM) polarization.

Fig. 4
Fig. 4

Comparison between experimental data (dotted curve) and theoretical calculations (solid curve) of local absolute efficiency along the meridional diameter (y = 0) for P (TE) and S (TM) polarizations.

Fig. 5
Fig. 5

Efficiency curves for various F/#’s of the same grating show the measured total relative efficiency versus wavelength through different grating apertures for TE and TM polarizations.

Fig. 6
Fig. 6

Measured relative spectral dependence for unpolarized light with F/2.1 (solid curve) compared with integrated data calculated for uniform illumination (dotted curve) and for Gaussian illumination with ϕB/ϕG = 1 (dashed curve).

Fig. 7
Fig. 7

Beam geometry: S, source; D, detector; α and β angles of incidence and of diffraction; ϕB, effective angular width of the incident Gaussian beam at 1/e intensity level.

Fig. 8
Fig. 8

Total absolute efficiency obtained by weighted summation of local values, depending on the angular width ϕB of the incident Gaussian beam at (a) 676.4 nm, (b) 600.4 nm, and (c) 441.6 nm: ϕG, angular aperture of the grating in regard to the source point; dashed curve, P (TE) polarization; solid curve, S (TM) polarization; dotted curve, unpolarized light.

Fig. 9
Fig. 9

(a) Radial groove-depth distribution: actual (solid curve) and optimized (dotted curve) (from Fig. 1). (b) Total absolute efficiency versus incident beam angular width ϕB in unpolarized light at 441.6 nm for the actual groove-depth distribution (solid curve) and for the optimized distribution (dotted curve).

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