Abstract

The Wood anomalies are dark or bright bands in the spectrum produced by a diffraction grating. They occur at observed wavelengths for which light of the same wavelength is diffracted in another order so as to graze the surface of the grating. The equations describing the position of the anomalies are discussed for a variety of grating arrangements. Some experimental observations of Wood anomalies are described, including a new finding concerning the reluctance of two anomalies to coincide. Finally, a discussion is given of spectrophotometric errors introduced by Wood anomalies.

© 1962 Optical Society of America

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References

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  1. R. W. Wood, Phil. Mag. 4, 396 (1902).
  2. R. W. Wood, Phil. Mag. 23, 310 (1912).
  3. R. W. Wood, Phys. Rev. 48, 928 (1935).
    [CrossRef]
  4. C. H. Palmer, J. Opt. Soc. Am. 42, 269 (1952).
    [CrossRef]
  5. C. H. Palmer, J. Opt. Soc. Am. 46, 50 (1956); ibid. 51, 1438 (1961).
    [CrossRef]
  6. Rayleigh, Proc. Roy Soc. (London) A79, 399 (1907); Phil. Mag. 14, 60 (1907).
  7. W. Voigt, Nachr. Ges. Wiss. Göttingen K1, 545 (1910);Nachr. Ges. Wiss. Göttingen71 (1911).
  8. U. Fano, Ann. Physik. 32, 393 (1938); Phys. Rev. 50, 573 (1936); ibid. 51, 288 (1937); J. Opt. Soc. Am. 31, 213 (1941).
    [CrossRef]
  9. K. Artmann, Z. Physik 119, 529 (1942).
    [CrossRef]
  10. V. Twersky, J. Appl. Phys. 23, 407, 1099 (1952); J. Opt. Soc. Am. 42, 855 (1952); ibid. 50, 1134 (1960); ibid. 52, 145 (1962); J. Acoust. Soc. Am. 22, 539 (1950); ibid. 24, 42 (1962); IRE Trans. on Antennas and Propagation AP-4, 330 (1956); ibid. AP-7, S307 (1959); J. Research. Natl. Bur. Standards 64D, 715 (1960); Sylvania Electronic Defense Labs, “Notes on Scattering by Gratings,” Report EDL-M105 (1957); “On Scattering of Waves by the Infinite Grating of Circular Cylinders,” Report EDL-E28 (1958); “Multiple Scattering of Waves and Optical Phenomena,” Report EDL-L20 (1961).
    [CrossRef]
  11. J. R. Wait, Appl. Sci. Research B4, 393 (1955).
    [CrossRef]
  12. S. N. Karp, J. Radlow, IRE Trans. on Antennas and Propagation AP-4, 654 (1956); S. N. Karp, New York University, Inst. of Mathematical Sciences, Division of Electromagnetic Research, “Diffraction by an Infinite Grating of Arbitrary Cylinders,” Research Report No. EM-85 (1955).
    [CrossRef]
  13. B. A. Lippmann, J. Opt. Soc. Am. 43, 408 (1953); B. A. Lippmann, A. Oppenheim, “Towards a Theory of Wood’s Anomalies,” Contract No. OSR-TR-54-25 (June30, 1954).
    [CrossRef]
  14. W. C. Meecham, J. Appl. Phys. 27, 361 (1956). Wood anomalies have been observed with 3.2-cm microwaves by W. C. Meecham, C. W. Peters, J. Appl. Phys. 28, 216 (1957).
    [CrossRef]
  15. R. F. Millar, Can. J. Phys. 38, 272 (1960); ibid. 39, 81, 104 (1961).
    [CrossRef]
  16. A. S. Makas, W. S. Shurclift, J. Opt. Soc. Am. 45, 998 (1955).
    [CrossRef]
  17. J. Strong, Phys. Rev. 46, 326 (1943); ibid. 48, 480 (1935); ibid. 49, 291 (1936).
  18. R. J. Meltzer, J. D. Keller, Symposium on Molecular Structure and Spectroscopy,Ohio State University, June12–16, 1961.
  19. S. Broderson, J. Opt. Soc. Am. 43, 1216 (1953).
    [CrossRef]

1960 (1)

R. F. Millar, Can. J. Phys. 38, 272 (1960); ibid. 39, 81, 104 (1961).
[CrossRef]

1956 (3)

W. C. Meecham, J. Appl. Phys. 27, 361 (1956). Wood anomalies have been observed with 3.2-cm microwaves by W. C. Meecham, C. W. Peters, J. Appl. Phys. 28, 216 (1957).
[CrossRef]

C. H. Palmer, J. Opt. Soc. Am. 46, 50 (1956); ibid. 51, 1438 (1961).
[CrossRef]

S. N. Karp, J. Radlow, IRE Trans. on Antennas and Propagation AP-4, 654 (1956); S. N. Karp, New York University, Inst. of Mathematical Sciences, Division of Electromagnetic Research, “Diffraction by an Infinite Grating of Arbitrary Cylinders,” Research Report No. EM-85 (1955).
[CrossRef]

1955 (2)

1953 (2)

1952 (2)

C. H. Palmer, J. Opt. Soc. Am. 42, 269 (1952).
[CrossRef]

V. Twersky, J. Appl. Phys. 23, 407, 1099 (1952); J. Opt. Soc. Am. 42, 855 (1952); ibid. 50, 1134 (1960); ibid. 52, 145 (1962); J. Acoust. Soc. Am. 22, 539 (1950); ibid. 24, 42 (1962); IRE Trans. on Antennas and Propagation AP-4, 330 (1956); ibid. AP-7, S307 (1959); J. Research. Natl. Bur. Standards 64D, 715 (1960); Sylvania Electronic Defense Labs, “Notes on Scattering by Gratings,” Report EDL-M105 (1957); “On Scattering of Waves by the Infinite Grating of Circular Cylinders,” Report EDL-E28 (1958); “Multiple Scattering of Waves and Optical Phenomena,” Report EDL-L20 (1961).
[CrossRef]

1943 (1)

J. Strong, Phys. Rev. 46, 326 (1943); ibid. 48, 480 (1935); ibid. 49, 291 (1936).

1942 (1)

K. Artmann, Z. Physik 119, 529 (1942).
[CrossRef]

1938 (1)

U. Fano, Ann. Physik. 32, 393 (1938); Phys. Rev. 50, 573 (1936); ibid. 51, 288 (1937); J. Opt. Soc. Am. 31, 213 (1941).
[CrossRef]

1935 (1)

R. W. Wood, Phys. Rev. 48, 928 (1935).
[CrossRef]

1912 (1)

R. W. Wood, Phil. Mag. 23, 310 (1912).

1910 (1)

W. Voigt, Nachr. Ges. Wiss. Göttingen K1, 545 (1910);Nachr. Ges. Wiss. Göttingen71 (1911).

1907 (1)

Rayleigh, Proc. Roy Soc. (London) A79, 399 (1907); Phil. Mag. 14, 60 (1907).

1902 (1)

R. W. Wood, Phil. Mag. 4, 396 (1902).

Artmann, K.

K. Artmann, Z. Physik 119, 529 (1942).
[CrossRef]

Broderson, S.

Fano, U.

U. Fano, Ann. Physik. 32, 393 (1938); Phys. Rev. 50, 573 (1936); ibid. 51, 288 (1937); J. Opt. Soc. Am. 31, 213 (1941).
[CrossRef]

Karp, S. N.

S. N. Karp, J. Radlow, IRE Trans. on Antennas and Propagation AP-4, 654 (1956); S. N. Karp, New York University, Inst. of Mathematical Sciences, Division of Electromagnetic Research, “Diffraction by an Infinite Grating of Arbitrary Cylinders,” Research Report No. EM-85 (1955).
[CrossRef]

Keller, J. D.

R. J. Meltzer, J. D. Keller, Symposium on Molecular Structure and Spectroscopy,Ohio State University, June12–16, 1961.

Lippmann, B. A.

Makas, A. S.

Meecham, W. C.

W. C. Meecham, J. Appl. Phys. 27, 361 (1956). Wood anomalies have been observed with 3.2-cm microwaves by W. C. Meecham, C. W. Peters, J. Appl. Phys. 28, 216 (1957).
[CrossRef]

Meltzer, R. J.

R. J. Meltzer, J. D. Keller, Symposium on Molecular Structure and Spectroscopy,Ohio State University, June12–16, 1961.

Millar, R. F.

R. F. Millar, Can. J. Phys. 38, 272 (1960); ibid. 39, 81, 104 (1961).
[CrossRef]

Palmer, C. H.

Radlow, J.

S. N. Karp, J. Radlow, IRE Trans. on Antennas and Propagation AP-4, 654 (1956); S. N. Karp, New York University, Inst. of Mathematical Sciences, Division of Electromagnetic Research, “Diffraction by an Infinite Grating of Arbitrary Cylinders,” Research Report No. EM-85 (1955).
[CrossRef]

Rayleigh,

Rayleigh, Proc. Roy Soc. (London) A79, 399 (1907); Phil. Mag. 14, 60 (1907).

Shurclift, W. S.

Strong, J.

J. Strong, Phys. Rev. 46, 326 (1943); ibid. 48, 480 (1935); ibid. 49, 291 (1936).

Twersky, V.

V. Twersky, J. Appl. Phys. 23, 407, 1099 (1952); J. Opt. Soc. Am. 42, 855 (1952); ibid. 50, 1134 (1960); ibid. 52, 145 (1962); J. Acoust. Soc. Am. 22, 539 (1950); ibid. 24, 42 (1962); IRE Trans. on Antennas and Propagation AP-4, 330 (1956); ibid. AP-7, S307 (1959); J. Research. Natl. Bur. Standards 64D, 715 (1960); Sylvania Electronic Defense Labs, “Notes on Scattering by Gratings,” Report EDL-M105 (1957); “On Scattering of Waves by the Infinite Grating of Circular Cylinders,” Report EDL-E28 (1958); “Multiple Scattering of Waves and Optical Phenomena,” Report EDL-L20 (1961).
[CrossRef]

Voigt, W.

W. Voigt, Nachr. Ges. Wiss. Göttingen K1, 545 (1910);Nachr. Ges. Wiss. Göttingen71 (1911).

Wait, J. R.

J. R. Wait, Appl. Sci. Research B4, 393 (1955).
[CrossRef]

Wood, R. W.

R. W. Wood, Phys. Rev. 48, 928 (1935).
[CrossRef]

R. W. Wood, Phil. Mag. 23, 310 (1912).

R. W. Wood, Phil. Mag. 4, 396 (1902).

Ann. Physik. (1)

U. Fano, Ann. Physik. 32, 393 (1938); Phys. Rev. 50, 573 (1936); ibid. 51, 288 (1937); J. Opt. Soc. Am. 31, 213 (1941).
[CrossRef]

Appl. Sci. Research (1)

J. R. Wait, Appl. Sci. Research B4, 393 (1955).
[CrossRef]

Can. J. Phys. (1)

R. F. Millar, Can. J. Phys. 38, 272 (1960); ibid. 39, 81, 104 (1961).
[CrossRef]

IRE Trans. on Antennas and Propagation (1)

S. N. Karp, J. Radlow, IRE Trans. on Antennas and Propagation AP-4, 654 (1956); S. N. Karp, New York University, Inst. of Mathematical Sciences, Division of Electromagnetic Research, “Diffraction by an Infinite Grating of Arbitrary Cylinders,” Research Report No. EM-85 (1955).
[CrossRef]

J. Appl. Phys. (2)

V. Twersky, J. Appl. Phys. 23, 407, 1099 (1952); J. Opt. Soc. Am. 42, 855 (1952); ibid. 50, 1134 (1960); ibid. 52, 145 (1962); J. Acoust. Soc. Am. 22, 539 (1950); ibid. 24, 42 (1962); IRE Trans. on Antennas and Propagation AP-4, 330 (1956); ibid. AP-7, S307 (1959); J. Research. Natl. Bur. Standards 64D, 715 (1960); Sylvania Electronic Defense Labs, “Notes on Scattering by Gratings,” Report EDL-M105 (1957); “On Scattering of Waves by the Infinite Grating of Circular Cylinders,” Report EDL-E28 (1958); “Multiple Scattering of Waves and Optical Phenomena,” Report EDL-L20 (1961).
[CrossRef]

W. C. Meecham, J. Appl. Phys. 27, 361 (1956). Wood anomalies have been observed with 3.2-cm microwaves by W. C. Meecham, C. W. Peters, J. Appl. Phys. 28, 216 (1957).
[CrossRef]

J. Opt. Soc. Am. (5)

Nachr. Ges. Wiss. Göttingen (1)

W. Voigt, Nachr. Ges. Wiss. Göttingen K1, 545 (1910);Nachr. Ges. Wiss. Göttingen71 (1911).

Phil. Mag. (2)

R. W. Wood, Phil. Mag. 4, 396 (1902).

R. W. Wood, Phil. Mag. 23, 310 (1912).

Phys. Rev. (2)

R. W. Wood, Phys. Rev. 48, 928 (1935).
[CrossRef]

J. Strong, Phys. Rev. 46, 326 (1943); ibid. 48, 480 (1935); ibid. 49, 291 (1936).

Proc. Roy Soc. (London) (1)

Rayleigh, Proc. Roy Soc. (London) A79, 399 (1907); Phil. Mag. 14, 60 (1907).

Z. Physik (1)

K. Artmann, Z. Physik 119, 529 (1942).
[CrossRef]

Other (1)

R. J. Meltzer, J. D. Keller, Symposium on Molecular Structure and Spectroscopy,Ohio State University, June12–16, 1961.

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Figures (16)

Fig. 1
Fig. 1

Diffraction grating nomenclature.

Fig. 2
Fig. 2

Wood anomalies in the zero order of a grating with its rulings perpendicular to the monochromator slit.

Fig. 3
Fig. 3

Apparatus for the study of Wood anomalies. L, source; S, slit; C1 and C2, collimating lenses; G, grating; M, Newtonian mirror. The spectrophotometer is a Beckman DK-2.

Fig. 4
Fig. 4

Typical zero-order anomalies. The order of diffraction of the grazing light is designated by m = −1 and +2. The calculated Rayleigh wavelengths are shown by vertical lines.

Fig. 5
Fig. 5

Observed and calculated zero-order anomalies of a 600 line/mm grating. The m values are the diffraction orders of grazing light.

Fig. 6
Fig. 6

Detailed study of the zero-order anomalies in the vicinity of coincident Rayleigh wavelengths.

Fig. 7
Fig. 7

Observed and calculated zero-order anomalies of an 1800 line/mm grating.

Fig. 8
Fig. 8

Zero-order Wood anomalies (m = ±1) of a 600 line/mm grating with rulings perpendicular to the slit.

Fig. 9
Fig. 9

Wood anomalies in the first-order diffracted spectrum of a 600 line/mm grating for 0°, 4°, and 9° half-angle between incident and diffracted beam. The Rayleigh wavelengths are shown by vertical lines.

Fig. 10
Fig. 10

Wood anomalies in the first-order spectrum of the Cary Model 14 Spectrophotometer. The Rayleigh wavelengths are shown by vertical lines. The abrupt changes in intensity near 1150, 880, and 400 mμ are due to changes in slit width.

Fig. 11
Fig. 11

Effect on the Wood anomalies of reversing the blaze direction and of reversing the incidence and diffraction angles for a 600 line/mm grating.

Fig. 12
Fig. 12

Wood anomalies in the first-order spectrum of a 600 line/mm grating viewed in the direction of its normal. The curve marked M was made with the zero-order beam returned to the grating. Rayleigh wavelengths are shown by vertical lines.

Fig. 13
Fig. 13

Wood anomalies in the second-order spectrum of a 600 line/mm grating viewed in the direction of its normal. The curve marked M was made with the zero-order beam returned to the grating. Rayleigh wavelengths are shown by vertical lines.

Fig. 14
Fig. 14

Wood anomalies in the spectrum of the Beckman IR-7 spectrophotometer. Rayleigh wavelengths are shown by vertical lines.

Fig. 15
Fig. 15

Comparison of reflection spectra of mica, glass, and epoxy resin made with a Beckman IR-7 prism-grating spectrophotometer and a Beckman IR-4 double-prism spectrophotomer. The Rayleigh wavelength is marked with a vertical line.

Fig. 16
Fig. 16

Comparison of absorption spectra of a Polaroid film in two orientations recorded on a double-grating spectrophotometer and a Beckman DK-2 prism spectrophotometer. Rayleigh wavelengths are shown by vertical lines.

Equations (20)

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n λ = a ( sin ϕ i + sin ϕ d )
n λ = 2 a sin ϕ cos α
ϕ = ϕ i ± α = ϕ d α .
λ R = a m ± ( sin ϕ i ± 1 ) .
λ R = 2 a / ( m + m ) .
λ R = ± a cos ϕ 0 / m ± .
n λ = 2 a sin ϕ
( n + k ) λ = a ( sin ϕ + sin π / 2 )
k λ = a ( sin ϕ sin π / 2 )
λ R = 2 a / ( n + 2 k ) .
( n + k ) λ = a ( sin ϕ i + 1 )
k λ = a ( sin ϕ i 1 ) .
λ R = 2 a n + 2 k { 1 ± [ 2 n k + k 2 / ( n + 2 k ) ] sin α 1 + [ n tan α / ( n + 2 k ) ] 2 }
1 + ( n tan α n + 2 k ) 2 1
Δ λ λ R 0 4 n k + k 2 n + 2 k sin α ,
λ R = a ( 1 sin ϕ d ) k , k = 1,2,3 ,
λ R = a ( 1 + sin ϕ d ) n + k , k = 1,2,3 , .
λ R = a k
λ R = a n + k .
n λ vacuum = a ( sin ϕ i ± μ )

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