Abstract

We have developed a new design of optical spectrometer based on the use of a chirped holographic grating inscribed on a flat substrate. This type of grating has a surface modulation with a spatially varying period. The ability of the chirped grating to focus a beam is exploited to reduce significantly the physical dimensions of the instrument. Wavelength selection is achieved by a pure translation of the chirped grating. The properties of the chirped grating spectrometer have been characterized with different lasers and arc lamps and compared with those of two commercial spectrometers. A performance parameter has been defined, enabling the various instruments to be compared.

© 2005 Optical Society of America

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Errata

Gilles Fortin and Nathalie McCarthy, "Chirped holographic grating used as the dispersive element in an optical spectrometer—erratum," Appl. Opt. 45, 2409-2409 (2006)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-45-11-2409

References

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    [CrossRef] [PubMed]
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    [CrossRef]
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2002

1997

1996

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

1994

C. Palmer, W. R. McKinney, “Imaging theory of plane-symmetric varied line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

1990

1987

1986

1983

1974

Agui, A.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Anctil, G.

Bartolini, R. A.

R. A. Bartolini, “Characteristics of relief phase holograms recorded in photoresists,” Appl. Opt. 13, 129–139 (1974).
[CrossRef] [PubMed]

R. A. Bartolini, “Photoresists,” in Holographic Recording Materials,H. M. Smith, ed. (Springer-Verlag, 1977), pp. 209–227.
[CrossRef]

Bowyer, S.

Budzinski, C.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics,R. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Fujisawa, M.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Gaylord, T. K.

Gilbert, S.

Grunwald, R.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics,R. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Harada, T.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

M. Itou, T. Harada, T. Kita, K. Hasumi, I. Koyano, K. Tanaka, “Normal incidence monochromator with an aberration-corrected concave grating for synchrotron radiation,” Appl. Opt. 25, 2240–2242 (1986).
[CrossRef] [PubMed]

Harasawa, A.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Hasumi, K.

Hecht, E.

E. Hecht, A. Zajac, Optics (Addison-Wesley, 1974).

Hettrick, M. C.

Ishii, T.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Itou, M.

Kakizaki, A.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Kita, T.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

M. Itou, T. Harada, T. Kita, K. Hasumi, I. Koyano, K. Tanaka, “Normal incidence monochromator with an aberration-corrected concave grating for synchrotron radiation,” Appl. Opt. 25, 2240–2242 (1986).
[CrossRef] [PubMed]

Koike, M.

Koyano, I.

Lepage, J.-F.

Massudi, R.

McCarthy, N.

McKinney, W. R.

C. Palmer, W. R. McKinney, “Imaging theory of plane-symmetric varied line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

W. R. McKinney, C. Palmer, “Numerical design method for aberration-reduced concave grating spectrometers,” Appl. Opt. 26, 3108–3118 (1987).
[CrossRef] [PubMed]

Moharam, M. G.

Namioka, T.

Noda, H.

Palmer, C.

C. Palmer, W. R. McKinney, “Imaging theory of plane-symmetric varied line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

W. R. McKinney, C. Palmer, “Numerical design method for aberration-reduced concave grating spectrometers,” Appl. Opt. 26, 3108–3118 (1987).
[CrossRef] [PubMed]

C. Palmer, Diffraction Grating Handbook, 4th ed. (Richardson Grating Laboratory, Rochester, N.Y., 2000).

Piché, M.

Pinz, I.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics,R. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Saitoh, Y.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Schäfer, D.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics,R. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Schönnagel, H.

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics,R. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Seya, M.

Shin, S.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Suga, S.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Tanaka, K.

Watanabe, M.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Zajac, A.

E. Hecht, A. Zajac, Optics (Addison-Wesley, 1974).

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

C. Palmer, W. R. McKinney, “Imaging theory of plane-symmetric varied line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

Rev. Sci. Instrum.

M. Fujisawa, A. Harasawa, A. Agui, M. Watanabe, A. Kakizaki, S. Shin, T. Ishii, T. Kita, T. Harada, Y. Saitoh, S. Suga, “Varied line-spacing plane grating monochromator for undulator beamline,” Rev. Sci. Instrum. 67, 345–349 (1996).
[CrossRef]

Other

R. A. Bartolini, “Photoresists,” in Holographic Recording Materials,H. M. Smith, ed. (Springer-Verlag, 1977), pp. 209–227.
[CrossRef]

C. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics,R. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

A. E. Siegman, Lasers (University Science, 1986).

E. Hecht, A. Zajac, Optics (Addison-Wesley, 1974).

C. Palmer, Diffraction Grating Handbook, 4th ed. (Richardson Grating Laboratory, Rochester, N.Y., 2000).

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Figures (13)

Fig. 1
Fig. 1

Geometry of the interfering beams used to record a chirped grating.

Fig. 2
Fig. 2

Intensity of the interference pattern calculated in the plane of the photoresist (z = 0) for (a) Rx1 = Rx2 and Ry1 = Ry2, (b) Rx1 < Rx2 and Ry1 = Ry2, (c) Rx1 = Rx2 and Ry1 < Ry2, (d) Rx1 < Rx2 and Ry1 < Ry2.

Fig. 3
Fig. 3

Reflection of parallel rays by a CG: (a) the period increases with x, (b) the period decreases with x, (c) example of the aberration experienced by the −1 order.

Fig. 4
Fig. 4

Schematic design of the spectrometer with a chirped grating.

Fig. 5
Fig. 5

Setup used to record the chirped grating: M’s, mirrors; SL, spherical lens; CL’s, cylindrical lenses; PH, pinhole. The y axis is perpendicular to the plane of the layout.

Fig. 6
Fig. 6

Local grating period as a function of position x on the chirped grating.

Fig. 7
Fig. 7

Reflectivity profiles in the 0 order and in the −1 order as a function of position x on the grating for a reading beam in (a) TM polarization (⊥ to grooves) and (b) TE polarization (|| to grooves).

Fig. 8
Fig. 8

Normalized spectral density of the Ar+ laser beam measured with CGS-1.

Fig. 9
Fig. 9

Individual lines of the Ar+ laser measured with (a) CGS-1 and (b) the OO spectrometer (λ is given in nanometers).

Fig. 10
Fig. 10

Individual lines of the five-wavelength He–Ne laser measured with (a) CGS-2 and (b) the JA spectrometer (λ is given in nanometers).

Fig. 11
Fig. 11

Doublet of the sodium lamp measured with CGS-3 and the JA and the OO spectrometers.

Fig. 12
Fig. 12

Tungsten halogen lamp spectrum measured with CGS-4 and the OO spectrometer.

Fig. 13
Fig. 13

Parameters of beam 1 in the xz plane.

Tables (2)

Tables Icon

Table 1 Four Configurations of the CGS

Tables Icon

Table 2 Comparison of the Values Measured with CGS-1 and the Theoretical Values of λ

Equations (16)

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E i ( x i , y i , z i ) = E 0 i [ q x i ( z i ) q y i ( z i ) ] 1 / 2 × exp { - j 2 π λ w [ x i 2 2 q x i ( z i ) + y i 2 2 q y i ( z i ) + z i ] } ,
1 q = 1 R - j λ w π W 2 ,
I ( x , y , 0 ) = E 1 ( x , y , 0 ) 2 + E 2 ( x , y , 0 ) 2 + 2 E 1 ( x , y , 0 ) E 2 ( x , y , 0 ) × cos [ ϕ 2 ( x , y , 0 ) - ϕ 1 ( x , y , 0 ) ] ,
Λ x ( x ) Λ x ( x , 0 ) = λ w | x cos 2 ψ 1 R x 1 ( x ) { 1 - x sin ψ 1 2 R x 1 ( x ) × [ 1 - ( z R x 1 x sin ψ 1 + z x 1 ) 2 ] } + sin ψ 1 - x cos 2 ψ 2 R x 2 ( x ) { 1 - x sin ψ 2 2 R x 2 ( x ) × [ 1 - ( z R x 2 x sin ψ 2 + z x 2 ) 2 ] } - sin ψ 2 | - 1 .
sin β m = sin β inc + m λ Λ x ( x ) ,
λ out = 2 Λ x ( x ) sin ( γ ) cos ( Ω / 2 ) ,
p = λ Δ λ N m .
Λ α ( x , y ) = | α [ ϕ 2 ( x , y , 0 ) - ϕ 1 ( x , y , 0 ) 2 π ] | = 2 π | { [ ϕ 2 ( x , y , 0 ) - ϕ 1 ( x , y , 0 ) ] α } - 1 | .
Λ y ( x , y ) = λ w | y [ 1 R y 1 ( x ) - 1 R y 2 ( x ) ] | ,
Λ x ( x , y ) = λ w F 2 ( x , y ) - F 1 ( x , y ) ,
F i ( x , y ) = x cos 2 ψ i R x i ( x ) { 1 - x sin ψ i 2 R x i ( x ) × [ 1 - ( z R x i x sin ψ i + z x i ) 2 ] } - y 2 sin ψ i 2 R y i 2 ( x ) × [ 1 - ( z R y i x sin ψ i + z yi ) 2 ] + sin ψ i .
ϕ i ( x , y , 0 ) = 1 2 [ arctan ( x sin ψ i + z x i z R x i ) + arctan ( x sin ψ i + z y i z R i ) ] - 2 π λ w [ ( ( x cos ψ i ) 2 2 R x i ( x ) ) + y 2 2 R y i ( x ) + x sin ψ i + z U V i ] ,
z R α i π W V α i 2 / λ w 1 + ( π W V α i 2 λ w R V α i ) 2 ,
z α i R V α i 1 + ( λ w R V α i π W V α i 2 ) 2 ,
R V α i = ( A α i + B α i / R U ) 2 + B α i 2 ( λ w / π W U 2 ) 2 ( A α i + B α i / R U ) ( C α i + D α i / R U ) + B α i D α i ( λ w / π W U 2 ) 2 ,
W V α i = W U [ ( A α i + B α i / R U ) 2 + B α i 2 ( λ w / π W U 2 ) 2 A α i D α i - B α i C α i ] 1 / 2 .

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