Abstract

A new, to our knowledge, analytical method is presented to characterize the performance of modified-Wollaston-prism-based compact, static Fourier-transform spectrometers. With the aid of an exact ray-tracing method for birefringent media, the interference of the two wave fronts produced by the beam splitter is computed at an arbitrarily positioned detector array. It is shown that a compact, static Fourier-transform spectrometer employing a single modified Wollaston prism can be designed such that the fringes are perpendicular to the incident beam. The effects of aperture size, coherence of the source, and incidence angle on the resulting interferogram are quantified.

© 2000 Optical Society of America

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References

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  1. J. Courtial, B. A. Patterson, W. Hirst, A. R. Harvey, A. J. Duncan, W. Sibbett, M. J. Padgett, “Static Fourier-transform ultraviolet spectrometer for gas detection,” Appl. Opt. 36, 2813–2817 (1997).
    [CrossRef] [PubMed]
  2. D. Steers, W. Sibbett, M. J. Padgett, “Dual-purpose, compact spectrometer and fiber-coupled laser wavemeter based on a Wollaston prism,” Appl. Opt. 37, 5777–5781 (1998).
    [CrossRef]
  3. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, London, 1972).
  4. J. Courtial, B. A. Patterson, A. R. Harvey, W. Sibbett, M. J. Padgett, “Design of a static Fourier-transform spectrometer with increased field of view,” Appl. Opt. 35, 6698–6702 (1996).
    [CrossRef] [PubMed]
  5. M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
    [CrossRef]
  6. M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse, Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
    [CrossRef] [PubMed]
  7. B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
    [CrossRef]
  8. C. C. Montarou, T. K. Gaylord, “Analysis and design of modified Wollaston prisms,” Appl. Opt. 38, 6604–6616 (1999).
    [CrossRef]
  9. S. Prunet, B. Journet, G. Fortunato, “Exact calculation of the optical path difference and description of a new birefringent interferometer,” Appl. Opt. 38, 983–990 (1999).

1999

C. C. Montarou, T. K. Gaylord, “Analysis and design of modified Wollaston prisms,” Appl. Opt. 38, 6604–6616 (1999).
[CrossRef]

S. Prunet, B. Journet, G. Fortunato, “Exact calculation of the optical path difference and description of a new birefringent interferometer,” Appl. Opt. 38, 983–990 (1999).

1998

1997

1996

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

J. Courtial, B. A. Patterson, A. R. Harvey, W. Sibbett, M. J. Padgett, “Design of a static Fourier-transform spectrometer with increased field of view,” Appl. Opt. 35, 6698–6702 (1996).
[CrossRef] [PubMed]

1995

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

1994

Antoni, M.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, London, 1972).

Courtial, J.

Duncan, A. J.

Fortunato, G.

S. Prunet, B. Journet, G. Fortunato, “Exact calculation of the optical path difference and description of a new birefringent interferometer,” Appl. Opt. 38, 983–990 (1999).

Gaylord, T. K.

Harvey, A. R.

Hirst, W.

Journet, B.

S. Prunet, B. Journet, G. Fortunato, “Exact calculation of the optical path difference and description of a new birefringent interferometer,” Appl. Opt. 38, 983–990 (1999).

Montarou, C. C.

Padgett, M. J.

Patterson, B. A.

Prunet, S.

S. Prunet, B. Journet, G. Fortunato, “Exact calculation of the optical path difference and description of a new birefringent interferometer,” Appl. Opt. 38, 983–990 (1999).

Sibbett, W.

Steers, D.

Appl. Opt.

Opt. Commun.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Rev. Sci. Instrum.

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

Other

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, London, 1972).

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Figures (6)

Fig. 1
Fig. 1

(a) CWP made from a positive uniaxial birefringent material. Two triangular pieces of birefringent material are cemented together with their optic axes (o.a.’s) orthogonal to each other. In one piece, the optic axis is perpendicular to the plane of incidence, whereas in the other piece the optic axis lies in the plane of incidence and is parallel to the entrance and exit faces of the prism. A linearly polarized beam is incident on the entrance face and is split into two orthogonally polarized beams as shown. The wedge angle between the normal to the exterior interfaces and the middle interface is γ. (b) MWP made from positive uniaxial birefringent material. The two optic axes are again perpendicular to each other. However, the optic axis that lies in the plane of incidence is inclined with respect to the entrance and exit faces of the prism. The inclination angle between the normal to the exterior interfaces and the latter optical axis is δ.

Fig. 2
Fig. 2

Operation of a FTS based on a MWP. The MWP is tilted so that the light is incident at an angle α. The input light is divided into TE- and TM-polarized beams after passing through the prism. The TE- (dot) and TM- (double arrow) polarized beams resulting from two incident beams are shown. The prism material is a negative birefringent material such as calcite. Placed between crossed polarizers, interference fringes are formed at the PAS (dashed line). An x, y system is associated with the MWP. The optic axis (o.a.) of the first wedge of the prism is perpendicular to the plane of incidence whereas it lies in the plane of incidence in the second wedge of the prism. The AOS is shown. The plane of the detector array is assigned with a coordinate system u det, v det. Point B is the intersection point between the PAS and the AOS. The angles between the TE-polarized beam and the AOS and the TM-polarized beam and the AOS are, respectively, ξ4 TE and ξ4 TM.

Fig. 3
Fig. 3

Interferogram produced by a source of wavelength λ = 500 nm. The MWP is made of calcite and is tilted so that its PAS is perpendicular to the AOS. The wedge angle between the x axis of the prism and its middle interface is γ = 88.4 deg, and the optic axis inclination angle between the x axis of the prism and the optic axis in the second wedge of the prism is δ = 80 deg. The incident beam waist is ω0 = 5 mm.

Fig. 4
Fig. 4

Interferogram produced by a source of wavelength λ equal to 500 nm. The MWP is made of calcite and is tilted so that its PAS is perpendicular to the AOS. The wedge angle between the x axis of the prism and its middle interface is γ = 88.4 deg, and the optic axis inclination angle between the x axis of the prism and the optic axis in the second wedge of the prism is δ = 80 deg. The incident beam waist is ω0 = 10 mm.

Fig. 5
Fig. 5

Interferogram produced by a source of wavelength λ equal to 500 nm. The MWP is made of calcite and is tilted so that its PAS is perpendicular to the AOS. The wedge angle between the x axis of the prism and its middle interface is γ = 88.4 deg, and the optic axis inclination angle between the x axis of the prism and the optic axis in the second wedge of the prism is δ = 80 deg. The incident beam waist is ω0 = 15 mm.

Fig. 6
Fig. 6

Interferogram produced by a source with a Gaussian spectral distribution centered at 500 nm and a waist of 3 nm. The MWP is made of calcite and is tilted so that its PAS is perpendicular to the AOS. The wedge angle between the x axis of the prism and its middle interface is γ = 88.4 deg, and the optic axis inclination angle between the x axis of the prism and the optic axis in the second wedge of the prism is δ = 80 deg. The incident beam waist is ω0 = 15 mm. The lower dashed curves show the interferogram when the material dispersion is not taken into account. The upper dashed curves show the interferogram when a material exhibiting anomalous dispersion is used.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Λ=λ2 sinΔβ/2.
y4TE=x4TE-wtan β4TE+y3,4TE, y4TM=x4TM-wtan β4TM+y3,4TM,
ydet=mdetxdet+bdet,
xdetTE=bdet-w tan β4TE+y3,4TEmdet-tan β4TE, xdetTM=bdet-w tan β4TM+y3,4TMmdet-tan β4TM, ydetTE=xdetTE-wtan β4TE+y3,4TE, ydetTM=xdetTM-wtan β4TM+y3,4TM.
ETE=expjωt-kvdetTEvdetTE, ETM=expjωt-kvdetTMvdetTM,
kvdetTE=k0 sin ξ4TE, kvdetTM=k0 sin ξ4TM,

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