Abstract

We present a method for designing a one-dimensional, deterministic, perfectly conducting rough surface that scatters light at a fixed scattering angle with an intensity whose dependence on the frequency of a plane wave incident normally upon it reproduces the infrared spectrum of a known substance within a specified region of frequencies. Such a surface can therefore be used in a correlation spectrometer for the identification of unknown substances.

© 2005 Optical Society of America

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References

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  8. See http://vpl.ipac.caltech.edu/spectra/.
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2003 (1)

1997 (2)

1995 (1)

1993 (1)

H. O. Edwards and J. P. Daikin, Sens. Actuators B 11, 9 (1993).
[CrossRef]

1972 (1)

1968 (1)

Butler, M. A.

Chau, F. S.

Daikin, J. P.

H. O. Edwards and J. P. Daikin, Sens. Actuators B 11, 9 (1993).
[CrossRef]

Edwards, H. O.

H. O. Edwards and J. P. Daikin, Sens. Actuators B 11, 9 (1993).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), p. 57.

Goody, R.

Houghton, J. T.

Kravitz, S. H.

Leskova, T. A.

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, 2003), p. 117.
[CrossRef]

Maradudin, A. A.

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, 2003), p. 117.
[CrossRef]

Méndez, E. R.

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, 2003), p. 117.
[CrossRef]

Muñoz-Lopez, J.

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, 2003), p. 117.
[CrossRef]

O’Donnell, K. A.

Peskett, G. D.

Ricco, A. J.

Rogers, C. D.

Senturia, S. D.

Sinclair, M. B.

Tay, F. E. H.

Taylor, F. W.

West, C. S.

Williamson, E. J.

Zabrzyski, W. J.

Zhou, G.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Lett. (1)

Sens. Actuators B (1)

H. O. Edwards and J. P. Daikin, Sens. Actuators B 11, 9 (1993).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), p. 57.

See http://vpl.ipac.caltech.edu/spectra/.

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, 2003), p. 117.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Segment of a numerically generated one-dimensional, perfectly conducting rough surface that has been designed to synthesize the infrared absorption spectrum of HF.

Fig. 2
Fig. 2

(a) Infrared absorption spectrum of HF from ω 1 c = 2 π × 3646 cm 1 to ω 15 c = 2 π × 4232 cm 1 synthesized by the approach presented in this paper. (b) Experimental absorption spectrum of HF in the same spectral range.

Equations (9)

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E 2 > ( x 1 , x 3 ω ) = exp [ i k x 1 i α 0 ( k ) x 3 ] + d q 2 π R ( q k ) exp [ i q x 1 + i α 0 ( q ) x 3 ] ,
E 2 > ( x 1 , x 3 ω ) sc = ( ω 2 π c r ) 1 2 cos θ s exp { i [ ( ω c ) r π 4 ] } R ( q 0 k ) ,
R ( q k ) = 2 π δ ( q k ) + 2 i α 0 ( k ) d x 1 ζ ( x 1 ) exp [ i ( q k ) x 1 ] + 0 ( ζ 2 ) .
E 2 > ( x 1 , x 3 ω ) sc 2 = 2 π r ( ω c ) 3 cos 2 θ s d x 1 ζ ( x 1 ) exp [ i ( ω c ) sin θ s x 1 ] 2 .
ζ ( x 1 ) = j = 1 N A j exp ( x 1 2 L j 2 ) cos ( 2 π x 1 a j ) ,
d x 1 ζ ( x 1 ) exp [ i ( ω c ) sin θ s x 1 ] = π 2 j = 1 N A j L j { exp [ ( ω c sin θ s 2 π a j ) 2 L j 2 4 ] + exp [ ( ω c sin θ s + 2 π a j ) 2 L j 2 4 ] } .
π 2 j = 1 N A j L j exp [ ( ω c sin θ s 2 π a j ) 2 L j 2 4 ] 2 π 4 j = 1 N ( A j L j ) 2 exp [ ( ω c sin θ s 2 π a j ) 2 L j 2 2 ] .
E 2 > ( x 1 , x 3 ω ) sc 2 = 1 2 r ( ω c ) 3 cos 2 θ s j = 1 N ( A j L j ) 2 exp [ ( ω ω j Δ j ) 2 ] .
I ( ω ) = 1 2 ( ω c ) 3 cos 2 θ s j = 1 N ( A j L j ) 2 exp [ ( ω ω j Δ j ) 2 ] .

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