Abstract

A method for ray tracing in uniaxial crystals is presented. General formulas for the direction of extraordinary rays are obtained. The method used in this paper is simpler than the general method based on Huygens’s construction, and its physical picture is clearer.

© 1990 Optical Society of America

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References

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  1. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  2. M. C. Simon, “Ray Tracing Formulas for Monoaxial Optical Components,” Appl. Opt. 22, 354–360 (1983).
    [CrossRef] [PubMed]
  3. M. C. Simon, R. M. Echarri, “Ray Tracing Formulas for Monoaxial Optical Components: Vectorial Formulation,” Appl. Opt. 25, 1935–1939 (1986).
    [CrossRef] [PubMed]
  4. Z. X. Zhang, “The Trajectory of the Extraordinary Ray as the Crystal Rotates,” Acta Phys. Sin. 29, 1483–1486 (1980).
  5. J. P. Mathieu, Optics (Pergamon, Oxford, 1975), p. 86.
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, London1959), p. 665.

1986 (1)

1983 (1)

1980 (1)

Z. X. Zhang, “The Trajectory of the Extraordinary Ray as the Crystal Rotates,” Acta Phys. Sin. 29, 1483–1486 (1980).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London1959), p. 665.

Echarri, R. M.

Mathieu, J. P.

J. P. Mathieu, Optics (Pergamon, Oxford, 1975), p. 86.

Simon, M. C.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London1959), p. 665.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Zhang, Z. X.

Z. X. Zhang, “The Trajectory of the Extraordinary Ray as the Crystal Rotates,” Acta Phys. Sin. 29, 1483–1486 (1980).

Acta Phys. Sin. (1)

Z. X. Zhang, “The Trajectory of the Extraordinary Ray as the Crystal Rotates,” Acta Phys. Sin. 29, 1483–1486 (1980).

Appl. Opt. (2)

Other (3)

J. P. Mathieu, Optics (Pergamon, Oxford, 1975), p. 86.

M. Born, E. Wolf, Principles of Optics (Pergamon, London1959), p. 665.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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Figures (2)

Fig. 1
Fig. 1

Directions of the e-wave vector, the field vectors, and the e-ray.

Fig. 2
Fig. 2

Illustration of the extraordinary ray direction in uniaxial crystals.

Tables (1)

Tables Icon

Table I Extraordinary Ray Direction Cosines as Different Incident Angles

Equations (20)

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k 1 · r = k o · r = k e · r ,
n 1 sin θ 1 = n o sin θ o
n 1 sin θ 1 = n sin θ e
n = n o n e n o 2 sin 2 θ + n e 2 cos 2 θ ,
[ E D H ] = [ E o D o H o ] exp [ i ( k · r - ω t ) ] ,
S = E × H .
tan α = ( n e 2 - n o 2 ) tan θ n e 2 + n o 2 tan 2 θ .
D = ɛ o n 2 [ E - k ^ ( k ^ · E ) ] ,
D j = ɛ o k ^ j ( k ^ · E ) 1 ɛ r j - 1 n 2 ,             j = x , y , z ,
cos θ = x o cos θ e + y o sin θ e .
n = n o n e n o 2 [ 1 - ( x o cos θ e + y o sin θ e ) 2 ] + n e 2 ( x o cos θ e + y o sin θ e ) 2 .
[ n o 2 + x o 2 ( n e 2 - n o 2 ) ] cot 2 θ e + 2 x o y o ( n e 2 - n o 2 ) cot θ e + n o 2 + y o 2 ( n e 2 - n o 2 ) - n o 2 n e 2 sin 2 θ 1 = 0 ,
cot θ e = 2 x o y o ( n o 2 - n e 2 ) ± 2 n o n o 2 n e 2 + n e 2 x o 2 ( n e 2 - n o 2 ) sin 2 θ 1 - [ n o 2 - ( n e 2 - n o 2 ) ( x o 2 + y o 2 ) ] 2 [ n o 2 + x o 2 ( n e 2 - n o 2 ) ] .
S x cos θ e + S y sin θ e = cos α .
| S x S y S z x o y o z o cos θ e sin θ e 0 | = 0 ,
S x ( - z o sin θ e ) + S y ( z o cos θ e ) + S z ( x o sin θ e - y o cos θ e ) = 0.
S x 2 + S y 2 + S z 2 = 1.
S x = cos α cos θ e + sin θ e sin α ( x o sin θ e - y o cos θ e ) z o 2 + ( x o sin θ e - y o cos θ e ) 2 ,
S y = cos α sin θ e - cos θ e sin α ( x o sin θ e - y o cos θ e ) z o 2 + ( x o sin θ e - y o cos θ e ) 2 ,
S z = z o sin α z o 2 + ( x o sin θ e - y o cos θ e ) 2 .

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