Abstract

A trilayer pellicle that consists of a high-index center layer that is symmetrically coated on both sides by a low-index film can be designed to produce differential reflection and transmission phase shifts of ±90° at oblique incidence and equal throughput for the p and the s polarizations. Such a device splits a beam of incident linearly polarized light into two orthogonal circularly polarized components that travel in well-separated angular directions. Examples of infrared dual quarter-wave retarders that use a symmetrically coated Ge pellicle at 77° angle of incidence are presented. A 50–50% splitter requires a symmetric pellicle with at least five layers. Error analysis shows that the thicknesses of the high-index layers must be tightly controlled. These circular polarization beam splitters are intended for operation with a well-collimated light source and can be used as the basis of a novel circular polarization Michelson interferometer.

© 2002 Optical Society of America

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References

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  1. See, for example, W. A. Schucliff, Polarized Light (Harvard University, Cambridge, Mass., 1962).
  2. D. A. Holmes, “Wave optics theory of rotatory compensators,” J. Opt. Soc. Am. 54, 1340–1347 (1964).
    [CrossRef]
  3. R. M. A. Azzam, F. A. Mahmoud, “Tilted bilayer membranes as simple transmission quarter-wave plates,” J. Opt. Soc. Am. A 18, 421–425 (2001).
    [CrossRef]
  4. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  5. S. D. Jacobs, K. A. Cerqua, K. L. Marshall, A. Schmid, M. J. Guardalben, K. J. Skerrett, “Liquid-crystal laser optics: design, fabrication, and performance,” J. Opt. Soc. Am. B 5, 1962–1975 (1988).
    [CrossRef]
  6. J. A. Davis, J. Adachi, C. R. Fernandez-Pousa, I. Moreno, “Polarization beam splitters using diffraction gratings,” Opt. Lett. 26, 587–589 (2001).
    [CrossRef]
  7. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chap. 4.
  8. E. Ritter, “Optical film materials and their applications,” Appl. Opt. 15, 2318–2327 (1976).
    [CrossRef] [PubMed]
  9. J. A. Dobrowolski, “Optical properties of films and coatings,” Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 1, Chap. 42.
  10. R. M. A. Azzam, F. A. Mahmoud, “Circular polarization Michelson interferometer,” presented at the 1999 Annual Meeting of the Optical Society of America, Santa Clara, Calif., 26–30 Sept. 1999, paper TuXX66.

2001 (2)

1989 (1)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

1988 (1)

1976 (1)

1964 (1)

Adachi, J.

Azzam, R. M. A.

R. M. A. Azzam, F. A. Mahmoud, “Tilted bilayer membranes as simple transmission quarter-wave plates,” J. Opt. Soc. Am. A 18, 421–425 (2001).
[CrossRef]

R. M. A. Azzam, F. A. Mahmoud, “Circular polarization Michelson interferometer,” presented at the 1999 Annual Meeting of the Optical Society of America, Santa Clara, Calif., 26–30 Sept. 1999, paper TuXX66.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chap. 4.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chap. 4.

Cerqua, K. A.

Chipman, R. A.

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Davis, J. A.

Dobrowolski, J. A.

J. A. Dobrowolski, “Optical properties of films and coatings,” Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 1, Chap. 42.

Fernandez-Pousa, C. R.

Guardalben, M. J.

Holmes, D. A.

Jacobs, S. D.

Mahmoud, F. A.

R. M. A. Azzam, F. A. Mahmoud, “Tilted bilayer membranes as simple transmission quarter-wave plates,” J. Opt. Soc. Am. A 18, 421–425 (2001).
[CrossRef]

R. M. A. Azzam, F. A. Mahmoud, “Circular polarization Michelson interferometer,” presented at the 1999 Annual Meeting of the Optical Society of America, Santa Clara, Calif., 26–30 Sept. 1999, paper TuXX66.

Marshall, K. L.

Moreno, I.

Ritter, E.

Schmid, A.

Schucliff, W. A.

See, for example, W. A. Schucliff, Polarized Light (Harvard University, Cambridge, Mass., 1962).

Skerrett, K. J.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Eng. (1)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Opt. Lett. (1)

Other (4)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chap. 4.

J. A. Dobrowolski, “Optical properties of films and coatings,” Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 1, Chap. 42.

R. M. A. Azzam, F. A. Mahmoud, “Circular polarization Michelson interferometer,” presented at the 1999 Annual Meeting of the Optical Society of America, Santa Clara, Calif., 26–30 Sept. 1999, paper TuXX66.

See, for example, W. A. Schucliff, Polarized Light (Harvard University, Cambridge, Mass., 1962).

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Figures (4)

Fig. 1
Fig. 1

Reflection and transmission of light by a tilted pellicle that consists of three optically isotropic layers (1, 2, and 3) with uniform thicknesses d 1, d 2, and d 3. The pellicle is immersed in a transparent ambient medium (0). The linear polarizations p and s are parallel and perpendicular to the plane of incidence, respectively, and φ is the angle of incidence.

Fig. 2
Fig. 2

Loci of multiple solutions (ζ1, ζ2) of Eq. (8) for symmetric trilayer transmission quarter-wave retarders for both Δ t = +90° and Δ t = -90° are presented by the closed contours. Superimposed are the corresponding solution loci for Eq. (7), |τ| = 1, for a coated Ge trilayer (with indices 1.35, 4, 1.35) at φ = 75° angle of incidence. Note that the two solution loci do not intersect.

Fig. 3
Fig. 3

Loci of multiple solutions (ζ1, ζ2) of Eq. (8) for symmetric trilayer transmission quarter-wave retarders for both Δ t = +90° and Δ t = -90° are presented by the closed contours. Superimposed are the corresponding solution loci for Eq. (7), |τ| = 1, for a coated Ge trilayer (with indices 1.35, 4, 1.35) at φ = 77° angle of incidence. The intersection points x, y, u, and v represent trilayer pellicles that function as dual QWR in transmission and reflection without diattenuation.

Fig. 4
Fig. 4

Loci of multiple solutions (ζ1, ζ2) of Eq. (10) for symmetric trilayer reflection quarter-wave retarders for both Δ r = +90° and Δ r = -90°. There are four solution branches; the two branches represented by the closed contours coincide with the closed contours for transmission QWR in Fig. 3. Superimposed are the corresponding solution loci for Eq. (9), |ρ| = 1, for the same coated Ge trilayer (with indices 1.35, 4, 1.35) at φ = 77° angle of incidence. The intersection points x, y, u, and v represent trilayer pellicles that function as dual QWR in transmission and reflection without diattenuation.

Equations (10)

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τ=Tp/Ts=tan Ψt expjΔt,
ρ=Rp/Rs=tan Ψr expjΔr.
τ=fφ, n1, n2, ζ1, ζ2,
ρ=gφ, n1, n2, ζ1, ζ2.
ζi=di/Di, i=1, 2, 3,
Di=λ/2ni2-sin2 φ-1/2,  i=1, 2, 3
|τ|=|Tp|/|Ts|=1,
argτ=Δt=±90°.
|ρ|=|Rp|/|Rs|=1
argρ=Δr=±90°.

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