Abstract

A sapphire disk is used as a variable birefringent beam splitter for the linearly polarized pump beam in an oscillator–amplifier dye laser system. Rotation of the disk varies the extent of retardation. The induced elliptical polarization results in a variable back surface reflectance between ≈0.02–0.15 for the green spectral region. Reflectances are measured on two disks with different thicknesses and compared with an approximate model describing the reflectance as a function of angle of rotation of the disk.

© 1981 Optical Society of America

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References

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  1. See, for example, R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
    [CrossRef]
  2. E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).
  3. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 322–358.
  4. M. Elshazly-Zaghloul, R. M. A. Azzam, J. Opt. Soc. Am. 70, 880 (1980).
    [CrossRef]
  5. L. P. Mosteller, F. Wooten, J. Opt. Soc. Am. 58, 511 (1968).
    [CrossRef]
  6. H. Schopper, Z. Phys. 132, 146 (1952).
    [CrossRef]
  7. D. den Engelsen, J. Opt. Soc. Am. 61, 1460 (1971).
    [CrossRef]
  8. T. P. Sosnowski, Opt. Commun. 4, 408 (1972).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 699.

1980 (1)

1975 (1)

See, for example, R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

1972 (1)

T. P. Sosnowski, Opt. Commun. 4, 408 (1972).
[CrossRef]

1971 (1)

1968 (1)

1952 (1)

H. Schopper, Z. Phys. 132, 146 (1952).
[CrossRef]

Azzam, R. M. A.

M. Elshazly-Zaghloul, R. M. A. Azzam, J. Opt. Soc. Am. 70, 880 (1980).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 322–358.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 322–358.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 699.

den Engelsen, D.

Elshazly-Zaghloul, M.

Hänsch, T. W.

See, for example, R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

Hecht, E.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).

Mosteller, L. P.

Schopper, H.

H. Schopper, Z. Phys. 132, 146 (1952).
[CrossRef]

Sosnowski, T. P.

T. P. Sosnowski, Opt. Commun. 4, 408 (1972).
[CrossRef]

Wallenstein, R.

See, for example, R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 699.

Wooten, F.

Zajac, A.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).

J. Opt. Soc. Am. (3)

Opt. Commun. (2)

T. P. Sosnowski, Opt. Commun. 4, 408 (1972).
[CrossRef]

See, for example, R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

Z. Phys. (1)

H. Schopper, Z. Phys. 132, 146 (1952).
[CrossRef]

Other (3)

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 322–358.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 699.

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Figures (6)

Fig. 1
Fig. 1

Top view of the beam splitter in an oscillator–amplifier dye laser system. The pump beam is horizontally polarized (D in the plane of incidence) and incident at θ1 = 45° with the beam splitter. Typically 10–20% of the incident beam is split off to the oscillator.

Fig. 2
Fig. 2

(a) Coordinate systems (xyz) and (ijz) used at the front surface of the beam splitter disk (top view). The x ˆ axis is in the plane of the disk and in the plane of incidence. The z ˆ axis is perpendicular to the plane of the figure. The incident beam makes an angle θ1 with the normal to the interface (the ŷ axis). The ordinary and extraordinary rays both make an angle approximately θ2 with the ŷ axis and propagate along the j ˆ axis in the plane of incidence. (b) Front view of the disk: the (xyz) and (ijz) coordinate systems with the beam splitter rotated by an angle ϕ about the ŷ axis. Vector ĉ is in the direction of the optical axis (c axis) and in the ( x ˆ , z ˆ ) plane.

Fig. 3
Fig. 3

Decomposition of the Dt vector into an ordinary Do (perpendicular to the principal plane) and an extraordinary De (in the principal plane). The principal plane is spanned by j ˆ and ĉ.

Fig. 4
Fig. 4

Experimental setup for measurement of the reflectance off the beam splitter (top view). A horizontally polarized beam from an Ar laser is used for the measurements. The beam is incident at an angle θ1 = 45° with the disk. Intensities are measured with a photodiode.

Fig. 5
Fig. 5

Total reflectance RTOTAL vs angle of rotation ϕ of the 3.20-mm thick beam splitter about the normal to the front surface. RTOTAL refers to reflection off the back surface only and does not include the (constant) front surface reflectance. The solid line is the measured curve, and the dotted line is the calculated reflectance.

Fig. 6
Fig. 6

Reflectance curve for the 1.04-mm beam splitter. The solid line is the measured reflectance, and the dashed line is the calculated one. RTOTAL is the reflectance off the back surface and does not include the (constant) front surface reflectance.

Equations (11)

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D t = D t i ˆ = D t i ˆ ,
c ˆ = ( cos ϕ x ˆ + sin ϕ z ˆ ) .
D o = D t cos γ ( j ˆ × c ˆ ) | j ˆ × c ˆ | ,
D o = D t sin ϕ ( sin ϕ i ˆ cos ϕ cos θ 2 z ˆ ) ( cos 2 ϕ cos 2 θ 2 + sin 2 ϕ ) ,
D e = D t D o ,
D e = D t cos ϕ cos θ 2 ( cos ϕ cos θ 2 i ˆ + sin ϕ z ˆ ) ( cos 2 ϕ cos 2 θ 2 + sin 2 ϕ ) .
Δ Φ 2 π d λ cos θ 2 ( n e n o ) sin 2 θ ,
Δ Φ 2 π d λ cos θ 2 ( n e n o ) [ 1 1 2 ( n ¯ ) 2 cos 2 ϕ ] ,
I | ( D o ) i exp ( i Δ Φ ) + ( D e ) i | 2 = D t 2 ( r ) 2 ( cos 2 ϕ cos 2 θ 2 + sin 2 ϕ ) 2 × ( sin 4 ϕ + cos 4 ϕ cos 4 θ 2 + 2 sin 2 ϕ cos 2 ϕ cos 2 θ 2 cos Δ Φ ) ,
I | ( D o ) z exp ( i Δ Φ ) + ( D e ) z | 2 = D t 2 4 ( r ) 2 ( cos 2 ϕ cos 2 θ 2 + sin 2 ϕ ) 2 cos 2 ϕ sin 2 ϕ cos 2 θ 2 sin 2 ( Δ Φ / 2 ) .
R TOTAL = I + I D t 2 .

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