Abstract

A method for determining the individual strain-optic coefficients of transparent materials is described. It utilizes a composite piezoelectric resonator inserted in one arm of a Mach-Zehnder interferometer to give rise to a time varying interference pattern. The coefficients are deduced from the modulation of the interference pattern. The Pockels elastooptic constants for several optical glasses at 6328 Å have been found by this method and these values have been analyzed in terms of nonlinear polarizabilities and lattice contributions. An estimate of the nonlinear strain polarizabilities for the oxygen, sulfur, and lead ions has been obtained.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957), p. 249.
  2. M. Born, K. Huang, Dynamic Theory of Crystal Lattices (Clarendon Press, Oxford, 1954), p. 376.
  3. W. W. Lester, J. Acoust. Soc. Amer. 38, 931(A) (1965); J. Acoust. Soc. Amer. 40, 1260(A) (1966).
    [CrossRef]
  4. R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Letters 13, 479 (1964).
    [CrossRef]
  5. G. W. Morey, Properties of Glass (Reinhold Publishing Corporation, New York, 1938), p. 428.
  6. C. Schaefer, H. Nassenstein, Z. Naturforsch. 8a, 90 (1953).
  7. J. Marx, Rev. Sci. Instrur. 22, 503 (1951).
    [CrossRef]
  8. W. G. Cady, Piezoelectricity (Dover Publications, Inc., New York, 1964), p. 397.
  9. W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
    [CrossRef]
  10. K. Vedam, E. D. D. Schmidt, R. Roy, J. Amer. Ceram. Soc. 49, 531 (1966).
    [CrossRef]
  11. H. Mueller, J. Amer. Ceram. Soc. 21, 27 (1938).
    [CrossRef]
  12. J. R. Tessman, A. H. Kahn, W. Shockley, Phys. Rev. 90, 890 (1953).
    [CrossRef]
  13. R. C. Miller, Appl. Phys. Letters 5, 17 (1964).
    [CrossRef]

1966

K. Vedam, E. D. D. Schmidt, R. Roy, J. Amer. Ceram. Soc. 49, 531 (1966).
[CrossRef]

1965

W. W. Lester, J. Acoust. Soc. Amer. 38, 931(A) (1965); J. Acoust. Soc. Amer. 40, 1260(A) (1966).
[CrossRef]

1964

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Letters 13, 479 (1964).
[CrossRef]

R. C. Miller, Appl. Phys. Letters 5, 17 (1964).
[CrossRef]

1959

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

1953

J. R. Tessman, A. H. Kahn, W. Shockley, Phys. Rev. 90, 890 (1953).
[CrossRef]

C. Schaefer, H. Nassenstein, Z. Naturforsch. 8a, 90 (1953).

1951

J. Marx, Rev. Sci. Instrur. 22, 503 (1951).
[CrossRef]

1938

H. Mueller, J. Amer. Ceram. Soc. 21, 27 (1938).
[CrossRef]

Born, M.

M. Born, K. Huang, Dynamic Theory of Crystal Lattices (Clarendon Press, Oxford, 1954), p. 376.

Cady, W. G.

W. G. Cady, Piezoelectricity (Dover Publications, Inc., New York, 1964), p. 397.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Letters 13, 479 (1964).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Letters 13, 479 (1964).
[CrossRef]

Huang, K.

M. Born, K. Huang, Dynamic Theory of Crystal Lattices (Clarendon Press, Oxford, 1954), p. 376.

Kahn, A. H.

J. R. Tessman, A. H. Kahn, W. Shockley, Phys. Rev. 90, 890 (1953).
[CrossRef]

Lester, W. W.

W. W. Lester, J. Acoust. Soc. Amer. 38, 931(A) (1965); J. Acoust. Soc. Amer. 40, 1260(A) (1966).
[CrossRef]

Marx, J.

J. Marx, Rev. Sci. Instrur. 22, 503 (1951).
[CrossRef]

Miller, R. C.

R. C. Miller, Appl. Phys. Letters 5, 17 (1964).
[CrossRef]

Morey, G. W.

G. W. Morey, Properties of Glass (Reinhold Publishing Corporation, New York, 1938), p. 428.

Mueller, H.

H. Mueller, J. Amer. Ceram. Soc. 21, 27 (1938).
[CrossRef]

Nassenstein, H.

C. Schaefer, H. Nassenstein, Z. Naturforsch. 8a, 90 (1953).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957), p. 249.

Post, D.

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

Primak, W.

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

Roy, R.

K. Vedam, E. D. D. Schmidt, R. Roy, J. Amer. Ceram. Soc. 49, 531 (1966).
[CrossRef]

Schaefer, C.

C. Schaefer, H. Nassenstein, Z. Naturforsch. 8a, 90 (1953).

Schmidt, E. D. D.

K. Vedam, E. D. D. Schmidt, R. Roy, J. Amer. Ceram. Soc. 49, 531 (1966).
[CrossRef]

Shockley, W.

J. R. Tessman, A. H. Kahn, W. Shockley, Phys. Rev. 90, 890 (1953).
[CrossRef]

Tessman, J. R.

J. R. Tessman, A. H. Kahn, W. Shockley, Phys. Rev. 90, 890 (1953).
[CrossRef]

Townes, C. H.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Letters 13, 479 (1964).
[CrossRef]

Vedam, K.

K. Vedam, E. D. D. Schmidt, R. Roy, J. Amer. Ceram. Soc. 49, 531 (1966).
[CrossRef]

Appl. Phys. Letters

R. C. Miller, Appl. Phys. Letters 5, 17 (1964).
[CrossRef]

J. Acoust. Soc. Amer.

W. W. Lester, J. Acoust. Soc. Amer. 38, 931(A) (1965); J. Acoust. Soc. Amer. 40, 1260(A) (1966).
[CrossRef]

J. Amer. Ceram. Soc.

K. Vedam, E. D. D. Schmidt, R. Roy, J. Amer. Ceram. Soc. 49, 531 (1966).
[CrossRef]

H. Mueller, J. Amer. Ceram. Soc. 21, 27 (1938).
[CrossRef]

J. Appl. Phys.

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

Phys. Rev.

J. R. Tessman, A. H. Kahn, W. Shockley, Phys. Rev. 90, 890 (1953).
[CrossRef]

Phys. Rev. Letters

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Letters 13, 479 (1964).
[CrossRef]

Rev. Sci. Instrur.

J. Marx, Rev. Sci. Instrur. 22, 503 (1951).
[CrossRef]

Z. Naturforsch.

C. Schaefer, H. Nassenstein, Z. Naturforsch. 8a, 90 (1953).

Other

W. G. Cady, Piezoelectricity (Dover Publications, Inc., New York, 1964), p. 397.

G. W. Morey, Properties of Glass (Reinhold Publishing Corporation, New York, 1938), p. 428.

J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957), p. 249.

M. Born, K. Huang, Dynamic Theory of Crystal Lattices (Clarendon Press, Oxford, 1954), p. 376.

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 (6)

Fig. 1
Fig. 1

Schematic diagram of the composite resonator circuit.

Fig. 2
Fig. 2

Experimental arrangement for the determination of the birefringence coefficient.

Fig. 3
Fig. 3

|(nn)| for Code 8363 glass vs strain. The incident light was polarized at 45° with respect to the applied stress.

Fig. 4
Fig. 4

Experimental arrangement for the determination of the individual strain-optic coefficients.

Fig. 5
Fig. 5

|(nn0) and (nn0) for fused silica (Code 7940 glass) vs strain. The incident light was polarized perpendicular to and parallel to the applied stress, respectively.

Fig. 6
Fig. 6

Modulated light wave form for As2S3 glass as a function of strain. The incident light is polarized perpendicular to the applied stress. The maximum strain amplitudes are 1.89 × 10−5, 2.44 × 10−5, 3.25 × 10−5, and 3.79 × 10−5 for A, B, C, and D, respectively. The retardation was considered to have passed through 90° between C and D at a strain amplitude of 3.66 × 10−5.

Tables (6)

Tables Icon

Table I Results of the Various Strain-Optic Birefringence Determinations

Tables Icon

Table II Basic Data for the Glasses Used in This Work

Tables Icon

Table III Results of the Individual Strain-Optic Determinations Expressed in Several Formsa

Tables Icon

Table IV Pockels Strain-Optic Constants of Fused Silica

Tables Icon

Table V Constitution of the Individual Strain-Optic Coefficients

Tables Icon

Table VI Computed Nonlinear Polarizabilities (in Å3)at 6328 Å, Derived from Strain-Optic Data

Equations (20)

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

Δ ( 1 / κ i j ) = p i j k l k l ,
( x ) = d cos ( π x / l d ) ,
d = [ ( 2 ) 1 2 M l d f d ] - 1 ( V d / R ) ,
s = d l d / l s ,
s = [ ( 2 ) 1 2 M l d f d ] - 1 ( I 0 2 - I 1 2 ) 1 2 ,
T = sin 2 [ δ ( t ) / 2 - θ ] ,
δ / 2 = ( π d s / λ ) Δ n = - ( π d s / λ ) ( n 0 3 / 2 ) ( p 11 - p 12 ) ( 1 + σ ) s ,
I = I 0 cos 2 ( δ 0 / 2 ) .
T = cos 2 [ δ 0 / 2 + ( π / λ ) d s Δ n ( t ) + ( π / λ ) ( n 0 - 1 ) Δ d ( t ) ] ,
Δ d ( t ) = - σ s l s ,
Δ n ( t ) = - ( n 0 3 / 2 ) [ p 12 - σ ( p 11 + p 12 ) ] s ,
Δ n ( t ) = - ( n 0 3 / 2 ) ( p 11 - 2 σ p 12 ) s ,
π / λ [ d s Δ n ( t ) + ( n 0 - 1 ) Δ d ( t ) ] = π / 2.
E j loc = E i + ( 4 π / 3 ) ( δ i j + C i j k l k l ) P j ,             i , j = 1 , 2 , 3 ,
P j = N α j i E i loc ,
Δ n j = [ 4 π 3 n 0 2 + 2 6 n 0 N α i j - ( n 0 2 + 2 ) ( n 0 2 - 1 ) 6 n 0 + ( n 0 2 - 1 ) 6 n 0 C i j ] j ,         i , j = 1 , , 6 ,
C i j = ( - 4 / 5 2 / 5 2 / 5 2 / 5 - 4 / 5 2 / 5 0 2 / 5 2 / 5 - 4 / 5 - 3 / 5 - 3 / 5 0 - 3 / 5 ) ,
α i = α i 0 + α i j j ,
( p 11 p 12 ) = - 2 n 0 3 { 4 π 3 ( n 0 2 + 2 ) 2 6 n 0 i N i ( α 11 i α 12 i ) - ( n 0 2 + 2 ) ( n 0 2 - 1 ) 2 6 n 0 + ( n 0 2 - 1 ) 6 n 0 ( - 4 / 5 2 / 5 ) } .
Δ n / s = ( n 0 3 / 2 ) p 11 = n 0 2 q and Δ n / s = ( n 0 3 / 2 ) p 12 = n 0 2 p .

Metrics