Abstract

When an ordinary or extraordinary ray that propagates through a birefringent crystal is reflected it gives rise to two reflected rays whose directions may be calculated with formulas similar to Snell’s law for refraction. When the reflection angle is greater than the incidence angle there is a critical angle for which the reflected ray is grazing, and for values of the incidence angle greater than this critical value the reflected ray no longer exists. We call this phenomenon inhibited reflection. We show how the critical angles may be calculated, and an experiment that visualizes the phenomenon shows good agreement with theory.

© 1989 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  2. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  3. M. C. Simon, R. M. Echarri, Appl. Opt. 25, 1935 (1986).
    [Crossref] [PubMed]
  4. M. C. Simon, R. M. Echarri, Appl. Opt. 26, 3878 (1987).
    [Crossref] [PubMed]

1987 (1)

1986 (1)

Born, M.

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

Echarri, R. M.

Simon, M. C.

Wolf, E.

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

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).

Appl. Opt. (2)

Other (2)

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

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

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Figures (3)

Fig. 1
Fig. 1

Coordinate system z3 is in the xz plane, and δ is the angle between the incidence plane and the xz plane.

Fig. 2
Fig. 2

Scheme of the experiment, α is the angle between the incident ray and the normal to face a.

Fig. 3
Fig. 3

Photographs of the experimental arrangement and resulting rays, (a) γo = 62.6°, γe = 61.2°; (b) γo = 65.5°, γe = 64.5°; (c) γo = 69.7°, γe = 69.23°.

Tables (1)

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Table 1 Relative Intensities of the Four Reflected Rays

Equations (17)

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sin γ u o = sin γ u ,
sin γ = u o u sin γ c = 1 .
u 2 = [ 1 ( N e z 3 ) 2 ] u e 2 + ( N e z 3 ) 2 u o 2 ,
( N e z 3 ) = ( z 3 x ) cos γ c + ( z 3 z ) sin γ c cos δ ,
A c sin 4 γ c + B c sin 2 γ c + C c = 0 ,
A c = cos 4 δ b o 2 [ 1 ( z 3 x ) 2 ] 2 + cos 2 δ 2 b o × [ 1 ( z 3 x ) 2 ] 2 + [ 1 + b o ( z 3 x ) 2 ] 2
B c = 2 { cos 2 δ b o [ 1 ( z 3 x ) 2 ] [ u e 2 u o 2 b o ( z 3 x ) 2 ] [ 1 + b o ( z 3 x ) 2 ] [ u e 2 u o 2 b o ( z 3 x ) 2 ] } ,
C c = [ u e 2 u o 2 + b o ( z 3 x ) 2 ] 2 ,
b 0 = u o 2 u e 2 u o 2 .
( R o x ) = 0 ,
R o = 1 f n [ u e 2 N o + ( u o 2 u e 2 ) ( N o z 3 ) z 3 ] ,
cot γ RR = b * cos δ ( z 3 z ) ( z 3 x ) 1 + b * ( z 3 x ) 2 ,
b * = ( u o 2 u e 2 1 ) .
sin γ L u o = sin γ RR u ,
sin 2 γ L = ( n e / n o ) 2 [ 1 + b * cos 2 δ ( Ζ 3 Ζ ) 2 1 + b * ( Ζ 3 Χ ) 2 ] ,
γ L = 67 . 1 ± 0 . 2 .
γ L = 67 . 4 ± 0 . 5 .

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