Abstract

We have designed and constructed a linear polarizer for use with visible and infrared radiation. The broadband polarizer consists of four germanium plates arranged in a chevron geometry. Input radiation is incident near Brewster’s angle for the first plate such that the reflected beam is preferentially s-wave polarized. This reflected beam is steered subsequently to the successive plates, always intersecting near Brewster’s angle. The beam polarization at the output of the device is almost completely s-wave polarized. The ratio of the paraxial flux of the nearly extinguished p-wave polarized light to the s-wave polarized light transmitted through the device is found to be less than 10-5 for laser illumination at wavelengths of 0.633, 1.32, 3.39, and 10.6 μm. Calculations predict that extinction ratios less than 10-5 are achievable over the wavelength range from 0.4 μm to beyond 500 μm. Alternative design geometries involving fewer plates are also described along with their advantages and disadvantages.

© 1998 Optical Society of America

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References

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  1. L. Mattsson, “A focussing VUV-polarizer for valence electron spectroscopy. Design considerations,” Uppsala University Institute of Physics Report UUIP-984 (Uppsala University, Uppsala, Sweden, 1978).
  2. L. Mattsson, B. Wannberg, H. P. Veenhuizen, I. Reineck, K. Siegbahn, “A focussing VUV-polarizer system for valence electron spectroscopy. Performance and test results,” Uppsala University Institute of Physics Report UUIP-1009 (Uppsala University, Uppsala, Sweden, 1979).
  3. L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
    [CrossRef]
  4. G. Rosenbaum, B. Feuerbacher, R. P. Godwin, M. Skibowski, “Measurement of the polarization of extreme ultraviolet synchrotron radiation with a reflecting polarimeter,” Appl. Opt. 7, 1917–1920 (1968).
    [CrossRef] [PubMed]
  5. Polarization: Definitions and Nomenclature, Instrument Polarization, CIE Publication 59 (Commission Internationale de l’Eclairage, Paris, 1984). This standards committee document received special weight in our preference of notation.
  6. J. Shumaker, “Self-study manual on optical radiation measurements. Part I - Concepts,” Natl. Bur. Stand. (U.S.) Tech. Note 910-3 (U.S. GPO, Washington, D.C., 1977), Chap. 6.
  7. Sensitivity to beam convergence and input angle are almost always asymmetric because of the necessary asymmetry of the polarizing mechanism. Typically, we refer to the most restrictive angle when quantifying this.
  8. Corning Incorporated, Corning New York, 14831. One version of this type of polarizer is manufactured under the trade name Polarcor.
  9. T. J. Bridges, J. W. Kluver, “Dichroic calcite polarizers for the infrared,” Appl. Opt. 4, 1121–1125 (1965).
    [CrossRef]
  10. II-VI Incorporated, Saxonburg, Pa. 16056. The PAZ and PAG polarizers consist of six plates of ZnSe and germanium, respectively.
  11. L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
    [CrossRef]
  12. K. Rabinovitch, R. Canfield, R. P. Madden, “A method for measuring polarization in the vacuum ultraviolet,” Appl. Opt. 4, 1005–1010 (1965).
    [CrossRef]
  13. Janos Technology, Incorporated, Townsend, New York 05353-7702. The germanium plates were specified to parallelism within 3 arc min.
  14. G. Eppeldauer, J. E. Hardis, “Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room temperature,” Appl. Opt. 30, 3091–3099 (1991).
    [CrossRef] [PubMed]
  15. Stycast 2850 FT epoxy, Gray Specialty Polymers, E. Z. Roberts and Associates, Culver City, Calif. 90232.
  16. These are type B uncertainties. We determined the expanded uncertainty by multiplying the combined standard uncertainty by 2. B. N. Taylor, C. E. Kuyatt , “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” Natl. Inst. Stand. Technol. Tech. Note 1297 (1994).
  17. T. Germer, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Md. 02889 (personal communication, 1997).
  18. J. M. Bennett, “Polarization,” in Handbook of Optics 1, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 5.
  19. Optics and Filters Oriel Corporation Catalog 3 (Oriel Corporation, Stratford, Conn., 1990).
  20. E. Collett, Polarized Light (Marcel Dekker, New York, 1993).
  21. Optics Guide 5: The Melles-Griot Catalog (Melles-Griot, Irvine, Calif., 1990).
  22. D. Kliger, J. Lewis, C. Randall, Polarized Lights in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).
  23. The Newport Catalog (Newport Corporation, Irvine, Calif., 1994); D. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985).
  24. R. Chipman, “Polarimetry,” in Handbook of Optics 2, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 22.

1991

1990

L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
[CrossRef]

1976

L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
[CrossRef]

1968

1965

Bennett, J. M.

J. M. Bennett, “Polarization,” in Handbook of Optics 1, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 5.

Bridges, T. J.

Canfield, R.

Chipman, R.

R. Chipman, “Polarimetry,” in Handbook of Optics 2, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 22.

Collett, E.

E. Collett, Polarized Light (Marcel Dekker, New York, 1993).

Eppeldauer, G.

Feuerbacher, B.

Germer, T.

T. Germer, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Md. 02889 (personal communication, 1997).

Godwin, R. P.

Hardis, J. E.

Himpsel, F. J.

L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
[CrossRef]

Jadrny, R.

L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
[CrossRef]

Karlsson, L.

L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
[CrossRef]

Kliger, D.

D. Kliger, J. Lewis, C. Randall, Polarized Lights in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

Kluver, J. W.

Kuyatt, C. E.

These are type B uncertainties. We determined the expanded uncertainty by multiplying the combined standard uncertainty by 2. B. N. Taylor, C. E. Kuyatt , “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” Natl. Inst. Stand. Technol. Tech. Note 1297 (1994).

Lewis, J.

D. Kliger, J. Lewis, C. Randall, Polarized Lights in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

Madden, R. P.

Mattson, L.

L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
[CrossRef]

Mattsson, L.

L. Mattsson, “A focussing VUV-polarizer for valence electron spectroscopy. Design considerations,” Uppsala University Institute of Physics Report UUIP-984 (Uppsala University, Uppsala, Sweden, 1978).

L. Mattsson, B. Wannberg, H. P. Veenhuizen, I. Reineck, K. Siegbahn, “A focussing VUV-polarizer system for valence electron spectroscopy. Performance and test results,” Uppsala University Institute of Physics Report UUIP-1009 (Uppsala University, Uppsala, Sweden, 1979).

McLean, A. B.

L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
[CrossRef]

Rabinovitch, K.

Randall, C.

D. Kliger, J. Lewis, C. Randall, Polarized Lights in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

Reineck, I.

L. Mattsson, B. Wannberg, H. P. Veenhuizen, I. Reineck, K. Siegbahn, “A focussing VUV-polarizer system for valence electron spectroscopy. Performance and test results,” Uppsala University Institute of Physics Report UUIP-1009 (Uppsala University, Uppsala, Sweden, 1979).

Rosenbaum, G.

Santoni, A.

L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
[CrossRef]

Shumaker, J.

J. Shumaker, “Self-study manual on optical radiation measurements. Part I - Concepts,” Natl. Bur. Stand. (U.S.) Tech. Note 910-3 (U.S. GPO, Washington, D.C., 1977), Chap. 6.

Siegbahn, K.

L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
[CrossRef]

L. Mattsson, B. Wannberg, H. P. Veenhuizen, I. Reineck, K. Siegbahn, “A focussing VUV-polarizer system for valence electron spectroscopy. Performance and test results,” Uppsala University Institute of Physics Report UUIP-1009 (Uppsala University, Uppsala, Sweden, 1979).

Skibowski, M.

Spiller, E.

L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
[CrossRef]

Taylor, B. N.

These are type B uncertainties. We determined the expanded uncertainty by multiplying the combined standard uncertainty by 2. B. N. Taylor, C. E. Kuyatt , “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” Natl. Inst. Stand. Technol. Tech. Note 1297 (1994).

Terminello, L. J.

L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
[CrossRef]

Thimm, K.

L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
[CrossRef]

Veenhuizen, H. P.

L. Mattsson, B. Wannberg, H. P. Veenhuizen, I. Reineck, K. Siegbahn, “A focussing VUV-polarizer system for valence electron spectroscopy. Performance and test results,” Uppsala University Institute of Physics Report UUIP-1009 (Uppsala University, Uppsala, Sweden, 1979).

Wannberg, B.

L. Mattsson, B. Wannberg, H. P. Veenhuizen, I. Reineck, K. Siegbahn, “A focussing VUV-polarizer system for valence electron spectroscopy. Performance and test results,” Uppsala University Institute of Physics Report UUIP-1009 (Uppsala University, Uppsala, Sweden, 1979).

Appl. Opt.

Phys. Lett. A

L. Karlsson, L. Mattson, R. Jadrny, K. Siegbahn, K. Thimm, “Valence electron spectroscopy using polarized He I radiation,” Phys. Lett. A 58, 381–384 (1976).
[CrossRef]

Rev. Sci. Instrum.

L. J. Terminello, A. B. McLean, A. Santoni, E. Spiller, F. J. Himpsel, “Low-pass filter for soft x-ray monochromators,” Rev. Sci. Instrum. 61, 1626–1628 (1990).
[CrossRef]

Other

Janos Technology, Incorporated, Townsend, New York 05353-7702. The germanium plates were specified to parallelism within 3 arc min.

Stycast 2850 FT epoxy, Gray Specialty Polymers, E. Z. Roberts and Associates, Culver City, Calif. 90232.

These are type B uncertainties. We determined the expanded uncertainty by multiplying the combined standard uncertainty by 2. B. N. Taylor, C. E. Kuyatt , “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” Natl. Inst. Stand. Technol. Tech. Note 1297 (1994).

T. Germer, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Md. 02889 (personal communication, 1997).

J. M. Bennett, “Polarization,” in Handbook of Optics 1, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 5.

Optics and Filters Oriel Corporation Catalog 3 (Oriel Corporation, Stratford, Conn., 1990).

E. Collett, Polarized Light (Marcel Dekker, New York, 1993).

Optics Guide 5: The Melles-Griot Catalog (Melles-Griot, Irvine, Calif., 1990).

D. Kliger, J. Lewis, C. Randall, Polarized Lights in Optics and Spectroscopy (Academic, San Diego, Calif., 1990).

The Newport Catalog (Newport Corporation, Irvine, Calif., 1994); D. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985).

R. Chipman, “Polarimetry,” in Handbook of Optics 2, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 22.

II-VI Incorporated, Saxonburg, Pa. 16056. The PAZ and PAG polarizers consist of six plates of ZnSe and germanium, respectively.

L. Mattsson, “A focussing VUV-polarizer for valence electron spectroscopy. Design considerations,” Uppsala University Institute of Physics Report UUIP-984 (Uppsala University, Uppsala, Sweden, 1978).

L. Mattsson, B. Wannberg, H. P. Veenhuizen, I. Reineck, K. Siegbahn, “A focussing VUV-polarizer system for valence electron spectroscopy. Performance and test results,” Uppsala University Institute of Physics Report UUIP-1009 (Uppsala University, Uppsala, Sweden, 1979).

Polarization: Definitions and Nomenclature, Instrument Polarization, CIE Publication 59 (Commission Internationale de l’Eclairage, Paris, 1984). This standards committee document received special weight in our preference of notation.

J. Shumaker, “Self-study manual on optical radiation measurements. Part I - Concepts,” Natl. Bur. Stand. (U.S.) Tech. Note 910-3 (U.S. GPO, Washington, D.C., 1977), Chap. 6.

Sensitivity to beam convergence and input angle are almost always asymmetric because of the necessary asymmetry of the polarizing mechanism. Typically, we refer to the most restrictive angle when quantifying this.

Corning Incorporated, Corning New York, 14831. One version of this type of polarizer is manufactured under the trade name Polarcor.

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Figures (9)

Fig. 1
Fig. 1

Extinction ratio versus wavelength of an infrared wire grid polarizer as measured with a Fourier-transform spectrometer. The wire grid polarizer consists of gold lines patterned with a 0.25-μm period on a barium fluoride substrate.

Fig. 2
Fig. 2

Idealized detail of the radiation impinging on a dielectric plate. The primary, first-surface reflected beam and the primary refracted beam are represented by the darker dashed lines. The lighter dashed lines show the first few secondary beams resulting from second-surface reflections. These secondary beams become continually lighter. When the angle of incidence is near Brewster’s angle, the reflected radiation is almost entirely s-wave polarized.

Fig. 3
Fig. 3

Reflectances α and β for s and p wave, respectively, for the first surface of a vacuum germanium interface as a function of incident angle. These are shown for wavelengths of 10.6 μm (solid curve) and 0.633 μm (dashed curve). The 0.633-μm p wave does not quite reach zero (β ≈ 0.0038 at 80°) at the minimum because of absorption. At 0.633 μm the complex index of refraction is given by n ≈ 5.5 and k ≈ 0.7.

Fig. 4
Fig. 4

P-wave transmittance of a single germanium plate at Brewster’s angle (solid curve) and that raised to the fourth power to approximate the major principal transmittance k 1 of a four-plate transmissive Brewster’s angle polarizer (dashed curve).

Fig. 5
Fig. 5

Extinction ratio (solid curve) and major principal transmittance k 1 (dashed curve) calculated with Fresnel theory for four germanium plates reflecting at 76.5 deg. Only first-surface reflections are considered. The 0.22 sr (f/14) beam divergence used in the calculation limits the extinction ratio from achieving complete null. Though not shown, the curves extend nearly featurelessly to beyond 500 μm.

Fig. 6
Fig. 6

(a) Sketch of the chevron geometry considered for the four germanium plates. There is no image inversion. (b) Basic K-geometry polarizer shown with two Brewster plates and one plane mirror. Because three reflections are involved there is image inversion. An off-center displaced input beam is displaced at the exit to be parallel but not collinear with the input. An angularly off-axis input beam is deviated angularly at the exit to be nonparallel with the input beam.

Fig. 7
Fig. 7

Germanium chevron polarizer construction.

Fig. 8
Fig. 8

Detector signal (open circles) measured at 1.32 μm and the ideal cos2 ϕ (solid curve) as a function of the rotation angle ϕ. The inset shows the minimum of the data.

Fig. 9
Fig. 9

Detector signal measured at 3.39 μm as a function of the rotation angle ∅. We obtained the dotted curve data using the uncoated germanium plates in the polarizer. The dashed curve data were obtained when we used the germanium plates with the back surface painted black. The solid curve data were obtained with use of the wedged germanium plates and are nearly indistinguishable from the ideal cos2 ∅ (not shown).

Tables (2)

Tables Icon

Table 1 Extinction Ratio ρ and the Major Principal Transmittance k1 of the Germanium Chevron Polarizers at the Four Laser Wavelengths

Tables Icon

Table 2 Summary of the Major Performance Parameters of the Germanium Chevron Polarizers and Other Polarizer Types

Equations (3)

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

ρ=[1-α1+β]m[1+α1-β]m.
ρ=H0+H90-H0-H90H0+H90+H0-H90H902H0.
δλλ<λnt.

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