Abstract

Details of the growth morphology at the interface surface of birefringent crystals growing from the melt can be observed by an interferometry technique using laser light to produce fringes which can be observed directly or recorded holographically. The fringes define contour lines of constant crystal thickness. The contour separation varies with the orientation of the crystal. For sodium nitrate the separation of adjacent fringes represents about 4-μm thickness difference, for optic axis orientation perpendicular to the incident light. Direct observation of the fringe development rate can be used to determine crystal growth rate precisely.

© 1970 Optical Society of America

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References

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  1. R. H. McFee, J. Appl. Phys. 40, 3873 (1969).
    [CrossRef]
  2. S. N. Komnik, V. I. Startsev, J. Cryst. Growth 5, 207 (1969).
    [CrossRef]
  3. C. D. West, J. Opt. Soc. Amer. 35, 26 (1945).
    [CrossRef]
  4. T. Yamaguti, J. Phys. Soc. Japan 7, 113 (1952).
    [CrossRef]
  5. S. Mallick, M. F. Roblin, Appl. Phys. Lett. 14, 61 (1969).
    [CrossRef]
  6. M. Francon, in Advanced Optical Techniques, A.C.S. van Heel, Ed. (North-Holland Publ. Co., Amsterdam, 1937), p. 39.

1969

R. H. McFee, J. Appl. Phys. 40, 3873 (1969).
[CrossRef]

S. N. Komnik, V. I. Startsev, J. Cryst. Growth 5, 207 (1969).
[CrossRef]

S. Mallick, M. F. Roblin, Appl. Phys. Lett. 14, 61 (1969).
[CrossRef]

1952

T. Yamaguti, J. Phys. Soc. Japan 7, 113 (1952).
[CrossRef]

1945

C. D. West, J. Opt. Soc. Amer. 35, 26 (1945).
[CrossRef]

Francon, M.

M. Francon, in Advanced Optical Techniques, A.C.S. van Heel, Ed. (North-Holland Publ. Co., Amsterdam, 1937), p. 39.

Komnik, S. N.

S. N. Komnik, V. I. Startsev, J. Cryst. Growth 5, 207 (1969).
[CrossRef]

Mallick, S.

S. Mallick, M. F. Roblin, Appl. Phys. Lett. 14, 61 (1969).
[CrossRef]

McFee, R. H.

R. H. McFee, J. Appl. Phys. 40, 3873 (1969).
[CrossRef]

Roblin, M. F.

S. Mallick, M. F. Roblin, Appl. Phys. Lett. 14, 61 (1969).
[CrossRef]

Startsev, V. I.

S. N. Komnik, V. I. Startsev, J. Cryst. Growth 5, 207 (1969).
[CrossRef]

West, C. D.

C. D. West, J. Opt. Soc. Amer. 35, 26 (1945).
[CrossRef]

Yamaguti, T.

T. Yamaguti, J. Phys. Soc. Japan 7, 113 (1952).
[CrossRef]

Appl. Phys. Lett.

S. Mallick, M. F. Roblin, Appl. Phys. Lett. 14, 61 (1969).
[CrossRef]

J. Appl. Phys.

R. H. McFee, J. Appl. Phys. 40, 3873 (1969).
[CrossRef]

J. Cryst. Growth

S. N. Komnik, V. I. Startsev, J. Cryst. Growth 5, 207 (1969).
[CrossRef]

J. Opt. Soc. Amer.

C. D. West, J. Opt. Soc. Amer. 35, 26 (1945).
[CrossRef]

J. Phys. Soc. Japan

T. Yamaguti, J. Phys. Soc. Japan 7, 113 (1952).
[CrossRef]

Other

M. Francon, in Advanced Optical Techniques, A.C.S. van Heel, Ed. (North-Holland Publ. Co., Amsterdam, 1937), p. 39.

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Figures (7)

Fig. 1
Fig. 1

Principal section of birefringent crystal slab with parallel beam incident normally on plane face. Optic axis direction is indicated as OA.

Fig. 2
Fig. 2

Variation of thickness change between fringes with crystal optic axis orientation.

Fig. 3
Fig. 3

Crystal-growing furnace.

Fig. 4
Fig. 4

Optical system for hologram recording and reconstruction.

Fig. 5
Fig. 5

Hologram reconstruction of growing NaNO3 crystal, showing interface fringes δ = 2.5 μm.

Fig. 6
Fig. 6

Hologram reconstruction of growing NaNO3 crystal, showing interface fringes δ = 5.4 μm.

Fig. 7
Fig. 7

Hologram reconstruction of growing NaNO3 crystal, showing interface fringes δ = 5.4 μm.

Equations (13)

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Δ = n o t n e ω t / cos α ,
I = I o cos 2 ( π Δ / λ ) ,
I = I o cos 2 [ π t λ ( n o n e ω cos α ) ] .
π t λ ( n o n e ω cos α ) = ( 2 m 1 ) 2 π ( m = integer )
t = 1 2 ( 2 m 1 ) λ cos α / ( n o cos α n e ω ) .
t o = λ cos α / 2 ( n o cos α n e ω ) .
t 1 = t o + δ = 3 λ cos α 2 ( n o cos α n e ω ) ,
δ = t 1 t o = λ cos α n o cos α n e ω
δ / λ = cos α / ( n o cos α n e ω ) .
tan α = ( n o 2 n e 2 ) sin 2 ω 2 ( n o 2 sin 2 ω + n e 2 cos 2 ω ) α .
n e ω 2 [ ( sin 2 ω / n e 2 ) + ( cos 2 ω / n o 2 ) ] = 1 ,
n e ω = n o n e ( n o 2 sin 2 ω + n e 2 cos 2 ω ) 1 2 .
δ λ = ( n o 2 sin 2 ω + n e 2 cos 2 ω ) 1 2 cos [ ( n o 2 n e 2 ) sin 2 ω 2 ( n o 2 sin 2 ω + n e 2 cos 2 ω ) ] n o ( n o 2 sin 2 ω + n e 2 cos 2 ω ) 1 2 cos [ ( n o 2 n e 2 ) sin 2 ω 2 ( n o 2 sin 2 ω + n e 2 cos 2 ω ) ] n o n e .

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