Abstract

Until recently, the construction of polarizers for operation below ∼260 nm were limited to materials such as magnesium fluoride and crystalline quartz. These materials have a much smaller birefringence than calcite, but unlike calcite they have good transmission below 200 nm. These materials are, however, not well suited for Glan-Taylor-type polarizer designs, as they do not produce a large angular separation of the polarized components. A new material, α-barium borate, has recently become available, which transmits to just below 200 nm and has a birefringence that approaches that of calcite. We analyze the performance of various polarizer designs that use this material. Results are presented that compare theory with experimental investigation of a manufactured device.

© 2002 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).
  2. M. Bass, ed., Handbook of Optics (McGraw-Hill, New York, 1995), Vols. 1 and 2.
  3. Fujian JDSU CASIX, Inc., P.O. Box 1103, Fuzhou, Fujian 350014, China, http://www.casix.com .
  4. Halbo Optics, Chelmsford CM3 5ZA, UK, http://www.halbo.com .
  5. V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed., A. E. Siegman, ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1997).
    [CrossRef]
  6. mathematica, Wolfram Research Inc., Champaign Ill., http://www.wolfram.com .
  7. R. K. Appel, C. D. Dyer, A. W. Jones, J. N. Lockwood, “Enhanced Raman spectroscopy using collection optics designed for continuously tunable excitation,” Meas. Sci. Technol. 13, 411–420 (2002).
    [CrossRef]
  8. R. K. Appel, C. D. Dyer, J. N . Lockwood, A. J. Bell, “Ultra-broadband collection and illumination optics for Raman and photoluminescence spectroscopy in the 200–700nm waveband,” Rev. Sci. Instrum. (to be published).
  9. T. Tamir, Integrated Optics, Vol. 7 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1975).
  10. E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).
  11. D. Eimerl, L. Davis, S. Velsko, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
    [CrossRef]

2002

R. K. Appel, C. D. Dyer, A. W. Jones, J. N. Lockwood, “Enhanced Raman spectroscopy using collection optics designed for continuously tunable excitation,” Meas. Sci. Technol. 13, 411–420 (2002).
[CrossRef]

1987

D. Eimerl, L. Davis, S. Velsko, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Appel, R. K.

R. K. Appel, C. D. Dyer, A. W. Jones, J. N. Lockwood, “Enhanced Raman spectroscopy using collection optics designed for continuously tunable excitation,” Meas. Sci. Technol. 13, 411–420 (2002).
[CrossRef]

R. K. Appel, C. D. Dyer, J. N . Lockwood, A. J. Bell, “Ultra-broadband collection and illumination optics for Raman and photoluminescence spectroscopy in the 200–700nm waveband,” Rev. Sci. Instrum. (to be published).

Bell, A. J.

R. K. Appel, C. D. Dyer, J. N . Lockwood, A. J. Bell, “Ultra-broadband collection and illumination optics for Raman and photoluminescence spectroscopy in the 200–700nm waveband,” Rev. Sci. Instrum. (to be published).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

Davis, L.

D. Eimerl, L. Davis, S. Velsko, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed., A. E. Siegman, ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1997).
[CrossRef]

Dyer, C. D.

R. K. Appel, C. D. Dyer, A. W. Jones, J. N. Lockwood, “Enhanced Raman spectroscopy using collection optics designed for continuously tunable excitation,” Meas. Sci. Technol. 13, 411–420 (2002).
[CrossRef]

R. K. Appel, C. D. Dyer, J. N . Lockwood, A. J. Bell, “Ultra-broadband collection and illumination optics for Raman and photoluminescence spectroscopy in the 200–700nm waveband,” Rev. Sci. Instrum. (to be published).

Eimerl, D.

D. Eimerl, L. Davis, S. Velsko, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed., A. E. Siegman, ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1997).
[CrossRef]

Hecht, E.

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

Jones, A. W.

R. K. Appel, C. D. Dyer, A. W. Jones, J. N. Lockwood, “Enhanced Raman spectroscopy using collection optics designed for continuously tunable excitation,” Meas. Sci. Technol. 13, 411–420 (2002).
[CrossRef]

Lockwood, J. N .

R. K. Appel, C. D. Dyer, J. N . Lockwood, A. J. Bell, “Ultra-broadband collection and illumination optics for Raman and photoluminescence spectroscopy in the 200–700nm waveband,” Rev. Sci. Instrum. (to be published).

Lockwood, J. N.

R. K. Appel, C. D. Dyer, A. W. Jones, J. N. Lockwood, “Enhanced Raman spectroscopy using collection optics designed for continuously tunable excitation,” Meas. Sci. Technol. 13, 411–420 (2002).
[CrossRef]

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed., A. E. Siegman, ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1997).
[CrossRef]

Tamir, T.

T. Tamir, Integrated Optics, Vol. 7 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1975).

Velsko, S.

D. Eimerl, L. Davis, S. Velsko, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

Zajac, A.

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

J. Appl. Phys.

D. Eimerl, L. Davis, S. Velsko, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Meas. Sci. Technol.

R. K. Appel, C. D. Dyer, A. W. Jones, J. N. Lockwood, “Enhanced Raman spectroscopy using collection optics designed for continuously tunable excitation,” Meas. Sci. Technol. 13, 411–420 (2002).
[CrossRef]

Other

R. K. Appel, C. D. Dyer, J. N . Lockwood, A. J. Bell, “Ultra-broadband collection and illumination optics for Raman and photoluminescence spectroscopy in the 200–700nm waveband,” Rev. Sci. Instrum. (to be published).

T. Tamir, Integrated Optics, Vol. 7 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1975).

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

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

M. Bass, ed., Handbook of Optics (McGraw-Hill, New York, 1995), Vols. 1 and 2.

Fujian JDSU CASIX, Inc., P.O. Box 1103, Fuzhou, Fujian 350014, China, http://www.casix.com .

Halbo Optics, Chelmsford CM3 5ZA, UK, http://www.halbo.com .

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed., A. E. Siegman, ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1997).
[CrossRef]

mathematica, Wolfram Research Inc., Champaign Ill., http://www.wolfram.com .

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Figures (14)

Fig. 1
Fig. 1

Principal refractive indices of optical materials. Solid and dashed curves are the ordinary and the extraordinary refractive indices for each material.

Fig. 2
Fig. 2

Index ellipsoid of a negative uniaxial crystal.

Fig. 3
Fig. 3

Crystal polarizers. There is a small gap between the two prisms that is not shown. The gap can be an air space or some coupling material such as cement. The polarizer types are (a) and (b) Rochon, (c) Glan–Thompson (cemented) or Glan–Foucault (air spaced), (d) Lippich (cemented) or Glan–Taylor (air spaced). The construction of each polarizer depends on the orientation of the crystal axes, which is indicated for each prism component. The schematics are for a negative uniaxial material.

Fig. 4
Fig. 4

Passage of an extraordinary wave through a Rochon polarizer.

Fig. 5
Fig. 5

Performance of a Rochon polarizer with (a) magnesium fluoride, (b) sapphire, (c) calcite, (d) α-BBO. The solid and the dashed curves refer to the prism geometries shown in Figs. 3(a) and 3(b), respectively.

Fig. 6
Fig. 6

Analysis of a Glan–Taylor polarizer.

Fig. 7
Fig. 7

Schematic operational range of a Glan–Taylor polarizer. Correct polarizer operation is in the shaded region where the ordinary wave is totally internally reflected and the extraordinary wave is transmitted.

Fig. 8
Fig. 8

Model performance of α-BBO Glan–Taylor polarizer. The three graphs are for a cut angle θ of (a) 36°, (b) 37°, and (c) 38°. The solid and dashed curves correspond to the bounds set by inequalities (9) and (10), respectively. The azimuth angle ϕex for each curve is indicated.

Fig. 9
Fig. 9

Model performance of a calcite Glan–Taylor polarizer. The cut angle θ is 38°. The solid and dashed curves correspond to the bounds set by inequalities (9) and (10), respectively. The azimuth angle ϕex for each curve is indicated.

Fig. 10
Fig. 10

Beam walk-off of the α-BBO Glan–Taylor polarizer. The cut angle θ is 36.6°. The solid and the dashed curves correspond to the bounds set by inequalities (9) and (10), respectively. The azimuth angle ϕex for each curve is indicated.

Fig. 11
Fig. 11

Polarizer rotated through an angle δ. The air gap between the two constituent prisms is exaggerated for reasons of clarity.

Fig. 12
Fig. 12

α-BBO Glan–Taylor polarizer operated at upper and lower bounds of operation for various rotations of polarizer. (a) Transmission of p-polarized T ex (extraordinary wave); (b) transmission of s-polarized T ord (ordinary wave). The rotation angle δ is as indicated on each curve.

Fig. 13
Fig. 13

Transmission of β-BBO along a 3.72-mm path length according to Ref. 11.

Fig. 14
Fig. 14

Comparison of experimental measurement and theoretical operation of a Glan–Taylor polarizer: (a) α-BBO, (b) calcite. The solid curve and shaded region are the theoretical operational region, calculated for θ = 36.6° and ϕex = 0° in the case of the α-BBO; and θ = 39.88° and ϕex = 0° in the case of the calcite. The square symbols are the measured upper and lower bounds of operation. The circle symbols are the limit of multiple reflections occurring within the polarizer air gap (multiple reflections are observed in measurements made between each respective set of square and circle symbols).

Tables (1)

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Table 1 Polarizer Cut Angles θ (deg)a

Equations (26)

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1nee2α=cos2 αno2+sin2 αne2,
ρα=±tan-1no2ne2 tan α ± α,
n1 sin90-θc=n2 sin90-θc+θ1,
sin θ2=n2 sin θ1.
k=xˆk sin α sin ϕ+yˆ k sin α cos ϕ+zˆ k cos α,
p=yˆ cos2 θ sin θ+zˆ cos θ sin2 θ.
k·p=kp cos β,
cos β=sin α cos ϕ cos θ+cos α sin θ.
neeαsin β1,
no sin β>1,
tan γin=cos αsin α cos ϕ.
tan α=1tan γin cos ϕ.
sin γex=n sin γin,
sin ϕex=n sin ϕ
no=2.7471+0.01878λ2-0.01822-0.01354λ21/2,
ne=2.3174+0.01224λ2-0.01667-0.01516λ21/2.
sin δ=n sin δ,
n sin β=sin ξ,
β=θ-δ.
exR1=tanδ-δtanδ+δ2,
exR2=tanβ-ξtanβ+ξ2.
ordR1=sinδ-δsinδ+δ2,
ordR2=sinβ-ξsinβ+ξ2.
R=n-1n+12.
Tex=1-exR121-exR22,
Tord=1-ordR121-ordR22.

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