Abstract

The theory of elliptical retardation plates that takes into account a phenomenon of multiple reflections is presented. An analytical form of a transition matrix for a normally incident plane wave is shown. Sample calculations of phase shift introduced by quartz retardation plates and of the output-beam parameters as a function of plate thickness and optical axis orientation are done.

© 1995 Optical Society of America

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References

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  1. D. A. Holmes, “Exact theory of retardation plates,”J. Opt. Soc. Am. 54, 1115–1120 (1964).
    [Crossref]
  2. P. Yeh, “Electromagnetic propagation in birefringent layered media,”J. Opt. Soc. Am. 69, 742–756 (1979).
    [Crossref]
  3. S. V. Rychlickij, “O vlijanii mnogokratnovo otrazenia narabotu fazovoj kwarcevoj plastinki,” Opt. Spektr. 63, 1092–1094 (1987).
  4. W. G. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), Sec. 10, pp. 109–112.
  5. A. I. Vaniurichin, V. P. Gerczanowskaja, Optiko-Elektronnyje Polarizacjonnyje Ustrojstva (Tiechnika, Kijev, U.S.S.R., 1984).
  6. G. N. Ramachadran, S. Ramaseshan, “The theory of propagation of light in anisotropic media,” in Handbuch der Physik, S. Flugge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, pp. 76–85.
  7. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957), Sec. XIV.
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1977), Sec. 2.10, pp. 119–122.

1987 (1)

S. V. Rychlickij, “O vlijanii mnogokratnovo otrazenia narabotu fazovoj kwarcevoj plastinki,” Opt. Spektr. 63, 1092–1094 (1987).

1979 (1)

1964 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1977), Sec. 2.10, pp. 119–122.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1977), Sec. 2.10, pp. 119–122.

Gerczanowskaja, V. P.

A. I. Vaniurichin, V. P. Gerczanowskaja, Optiko-Elektronnyje Polarizacjonnyje Ustrojstva (Tiechnika, Kijev, U.S.S.R., 1984).

Holmes, D. A.

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957), Sec. XIV.

Ramachadran, G. N.

G. N. Ramachadran, S. Ramaseshan, “The theory of propagation of light in anisotropic media,” in Handbuch der Physik, S. Flugge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, pp. 76–85.

Ramaseshan, S.

G. N. Ramachadran, S. Ramaseshan, “The theory of propagation of light in anisotropic media,” in Handbuch der Physik, S. Flugge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, pp. 76–85.

Rychlickij, S. V.

S. V. Rychlickij, “O vlijanii mnogokratnovo otrazenia narabotu fazovoj kwarcevoj plastinki,” Opt. Spektr. 63, 1092–1094 (1987).

Vaniurichin, A. I.

A. I. Vaniurichin, V. P. Gerczanowskaja, Optiko-Elektronnyje Polarizacjonnyje Ustrojstva (Tiechnika, Kijev, U.S.S.R., 1984).

Yeh, P.

J. Opt. Soc. Am. (2)

Opt. Spektr. (1)

S. V. Rychlickij, “O vlijanii mnogokratnovo otrazenia narabotu fazovoj kwarcevoj plastinki,” Opt. Spektr. 63, 1092–1094 (1987).

Other (5)

W. G. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), Sec. 10, pp. 109–112.

A. I. Vaniurichin, V. P. Gerczanowskaja, Optiko-Elektronnyje Polarizacjonnyje Ustrojstva (Tiechnika, Kijev, U.S.S.R., 1984).

G. N. Ramachadran, S. Ramaseshan, “The theory of propagation of light in anisotropic media,” in Handbuch der Physik, S. Flugge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, pp. 76–85.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957), Sec. XIV.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1977), Sec. 2.10, pp. 119–122.

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Figures (9)

Fig. 1
Fig. 1

Orientation of the phase plate.

Fig. 2
Fig. 2

Dependence of the first eigenvector ellipticity angle θf on the angle Θ between the propagation axis and the optical axis in quartz.

Fig. 3
Fig. 3

Phase difference δ versus normalized thickness D: no multiple reflections. Solid curve, linear birefringence; long-dashed curve, elliptical birefringence; short-dashed curve, near-circular birefringence.

Fig. 4
Fig. 4

Difference Δδ of the phase shift resulting from multiple reflections versus normalized thickness D.

Fig. 5
Fig. 5

Ellipticity angle θ versus normalized thickness D: no multiple reflections. Curves as in Fig. 3.

Fig. 6
Fig. 6

Difference Δθ of the ellipticity angle resulting from multiple reflections versus normalized thickness D. Curves as in Fig. 3.

Fig. 7
Fig. 7

Azimuth angle α versus normalized thickness D: no multiple reflections. Curves as in Fig. 3.

Fig. 8
Fig. 8

Difference Δα of the azimuth angle resulting from multiple reflections versus normalized thickness D: (a) linear birefringence, (b) long-dashed curve, elliptical birefringence; short-dashed curve, near-circular birefringence.

Fig. 9
Fig. 9

Transmittance T versus normalized thickness D. Curves as in Fig. 3.

Equations (19)

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E i = ( E i x E i y ) ,
J = [ j 11 j 12 j 21 j 22 ] = [ cos 2 β + sin 2 β exp ( - i γ ) sin β cos β [ 1 - exp ( - i γ ) ] exp ( - i δ f ) sin β cos β [ 1 - exp ( - i γ ) ] exp ( i δ f ) sin 2 β + cos 2 β exp ( - i γ ) ] ,
γ = 2 π λ ( n s - n f ) d ,
E t = J · E i .
J + = J ( + β ) ;
J - = J ( - β ) ;
T 1 = [ T 1 x 0 0 T 1 y ] = [ 2 1 + n f 0 0 2 1 + n s ] ;
T 2 = [ T 2 x 0 0 T 2 y ] = [ 2 n f 1 + n f 0 0 2 n s 1 + n s ] ;
R = [ R x 0 0 R y ] = [ n f - 1 n f + 1 0 0 n s - 1 n s + 1 ] .
E t = T 2 · J + · ( n = 0 M n ) · T 1 · E i ,
n = 0 M n = 1 1 - M ,
B = T 2 · J + · ( 1 - M ) - 1 · T 1 ,
E t = B · E i ,
T 1 x = T 1 y = T 1 , T 2 x = T 2 y = T 2 , R x = R y = R ,
B = T 1 T 2 C [ j 11 + Δ j j 12 j 21 j 22 - Δ j ] ,
Δ j = cos ( 2 β ) R 2 [ 1 - exp ( - i γ ) ] exp ( - i γ ) 1 - R 2 exp ( - i γ ) ,
C = [ 1 - R 2 exp ( - i γ ) ] [ 1 - ( Δ j exp ( - i γ ) R ) 2 ] .
E t = B · E i = m · J · E i ,
D = γ 2 π = d ( n s - n f ) λ .

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