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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 5 — May. 1, 2003
  • pp: 955–958

Optimal beam splitters for the division-of-amplitude photopolarimeter

R. M. A. Azzam and A. De  »View Author Affiliations

JOSA A, Vol. 20, Issue 5, pp. 955-958 (2003)

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Optimal optical parameters of the beam splitter that is used in the division-of-amplitude photopolarimeter are determined. These are (1) 50%–50% split ratio of the all-dielectric beam splitter, (2) differential phase shifts in reflection and transmission Δr and Δt that differ by ±π/2, and (3) ellipsometric parameters (ψr, ψt)= (27.368°, 62.632°) or (62.632°, 27.368°). It is also shown that for any nonabsorbing beam splitter that splits incident unpolarized light equally, the relationship ψrt=π/2 is always satisfied.

© 2003 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(230.1360) Optical devices : Beam splitters
(260.5430) Physical optics : Polarization

R. M. A. Azzam and A. De, "Optimal beam splitters for the division-of-amplitude photopolarimeter," J. Opt. Soc. Am. A 20, 955-958 (2003)

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  1. R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27.
  2. R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 22.
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  11. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  12. For a thick uncoated dielectric slab BS, Δr and Δt assume the trivial values of 0 or ±π, and condition (6c) is violated; hence det A =0. Therefore thin-film coatings are required for the BS of DOAP.
  13. According to Eq. (4), a given error δI in the measured signal vector I results in a corresponding error δS of the derived Stokes vector S, which is given by δS =A −1 δI. Because A −1 is proportional to 1/det A, maximization of |det A | is consistent with reduction of the error δS.
  14. Equation (13a) has an infinite number of solutions, and it is by convention11 that the ellipsometric angle ψ is confined to the first quadrant, 0≤ψ≤π/2.
  15. R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
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  18. A second optimum value of ψ0 =62.63° was inadvertently missed in Eq. (26a) of Ref. 16.
  19. D. S. Sabatke, M. R. Descour, E. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
  20. J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
  21. Since the determinant of the instrument matrix appears in the denominator of various condition numbers, it is not surprising that the criterion of the maximum determinant approximately corresponds to the minimum condition number.
  22. A. De and R. M. A. Azzam, “Optimal coated silicon membrane beam splitters for the division-of-amplitude photopolarimeter (DOAP),” presented at the Annual Meeting of the Optical Society of America, Orlando, Florida, September 29–October 3, 2002, paper WZ3.

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