Abstract

Theoretical formulas are presented for calculating the trajectory of the extraordinary ray at the back of a rotating uniaxial birefringent plate.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, Optical Waves in Layered Media (Wiley, Chinchester, UK, 1988), Chap. 9.
  2. J. Mentel, E. Schmidt, T. Mavrudis, “Birefringent filter with arbitrary orientation of the optic axis: an analysis of improved accuracy,” Appl. Opt. 31, 5022–5029 (1992).
    [CrossRef] [PubMed]
  3. X. Zhu, “Explicit Jones transformation matrix for a tilted birefringent plate with its optic axis parallel to the plate surface,” Appl. Opt. 33, 3502–3506 (1994).
    [CrossRef] [PubMed]
  4. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 27.
  5. Z. Shao, C. Yi, “Behavior of extraordinary rays in uniaxial crystals,” Appl. Opt. 33, 1209–1212 (1994).
    [CrossRef] [PubMed]
  6. E. Cojocaru, “Direction cosines and vectorial relations for extraordinary-wave propagation in uniaxial media,” Appl. Opt. 36, 302–306 (1997).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. 14.
  8. Ref. 7, Section 1.6.
  9. R. C. Weast, S. M. Selby, eds., Handbook of Tables for Mathematics (Chemical Rubber Company, Cleveland, Ohio, 1970), p. 524.

1997 (1)

1994 (2)

1992 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. 14.

Cojocaru, E.

Mavrudis, T.

Mentel, J.

Schmidt, E.

Shao, Z.

Siegman, A.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 27.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. 14.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, Chinchester, UK, 1988), Chap. 9.

Yi, C.

Zhu, X.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Refraction of light incident upon a negative uniaxial plane-parallel plate (no > ne) within an isotropic ambient medium. The upper left corner shows the orientation of the unit vector ŵ along the optic axis direction, which is defined by angles θ and ϕ.

Fig. 2
Fig. 2

Traces of the eo ray on the back surface of the uniaxial plate at z = d for different incidence angles θ1 (a) when θ = π/2 and (b) when θ ≠ π/2 (θ = 44.07°) in the x′–y′ plane with the o ray as origin. Negative uniaxial crystals with d = 10 mm, no = 1.658, and n e = 1.486 are considered in air (n1 = 1).

Fig. 3
Fig. 3

Coordinates x+′, x-′, and y+′ as functions of incidence angle θ1 (a) when θ = π/2 and (b) when θ ≠ π/2. The maximum yM′ of y′ when θ ≠ π/2 is also plotted as a function of θ1 in view (b). Crystal parameters are the same as in Fig. 2.

Equations (22)

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

¯=CT¯pC,
C=cos θ cos ϕcos θ sin ϕ-sin θ-sin ϕcos ϕ0sin θ cos ϕsin θ sin ϕcos θ.
33ζeo2+2ξ13ζeo+ξ211-oe=0.
ÊĤŜ=cos δ0-sin δ010sin δ0cos δ-cos αsin α0-sin α-cos α0001×cos θeo0-sin θeo010sin θeo0cos θeoxˆŷzˆ
sin α=c32/sin γ,
cos α=c33 sin θeo-c31 cos θeo/sin γ,
sin δ=Δ sin γ cos γ/o2 sin2 λ+e2 cos2 γ1/2,
cos δ=o+Δ cos2 γ/o2 sin2 γ+e2 cos2 γ1/2.
cos γ=c31 sin θeo+c33 cos θeo.
x=dcos δ sin θeo-cos α sin δ cos θeo/cos δ cos θeo+cos α sin δ sin θeo,
y=d sin α sin δ/cos δ cos θeo+cos α sin δ sin θeo,
x=da1 cos ϕ+a21+a3 cos2 ϕ/a4-a5 cos2 ϕ1/2,
y=d sin ϕa1+a2a3 cos ϕ/a4-a5 cos2 ϕ1/2,
a1=Δ cot θ/o+e cot2 θ,
a2=oξ1+cot2 θ,
a3=Δ/o+e cot2 θ,
a4=oe-ξ21+cot2 θo+e cot2 θ,
a5=oΔξ21+cot2 θ.
x2+y2+A2=Cx2x2+y2+B,
A=ξ2d2/o,
B=d21+e/o,
C=ξ2o+e-ξ2/oe.

Metrics