Abstract

A general description is given of a long-neglected use for the piezo-optic or photoelastic effect (stress-induced birefringence). An acoustic vibration, such as a fundamental extensional mode in a bar or long thin plate, is set up in a block of isotropic transparent material, such as glass or fused silica; the vibration is sustained by a transducer. The resulting modulated birefringence can be used in a variety of ways, notably to produce a beam of alternately left- and right-circularly polarized light for circular-dichroism measurements. Strains of the order 10−5 are required, considerably below the breakage point for most materials. Because advantage is taken of the high Q of the vibrational modes, typically 103 to 104, very small transducer power is needed, usually less than 1 W. The literally enormous useful angular aperture, of the order 50° total cone angle, makes the device far superior to Pockels or Kerr cells for many applications. Reference is made to current practical realizations and to present and future uses of the device.

© 1969 Optical Society of America

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References

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  1. H. J. Jessop, in Encyclopedia of Physics, Vol. VI, S. Flügge, Ed. (Springer-Verlag, Berlin, 1958). This is a review and includes references to books on mechanical engineering applications.
  2. M. Billardon and J. Badoz, Compt. Rend. 262, 1672 (1966); Compt. Rend. 263, 139 (1966).
  3. A review of modern polarization devices is given by W. A. Shurcliff, Polarized Light (Harvard Univ. Press, Cambridge, 1962). For the state of the art in electro-optic devices see R. S. Ploss, Opt. Spectry. 3,(1)63 (1969).
  4. A. Sommerfeld, Optics (Academic Press Inc., New York, 1964); Ch. IV.
  5. R. W. Dixon, IEEE J. Quant. Electr.,  QE-3, 85 (1967).
    [Crossref]
  6. K. Vedam and S. Ramaseshan, in Progress in Crystal PhysicsR. S. Krishnan, Ed. (S. Viswanathan, Madras, India, 1958). Some photoelastic data are given in terms of the stress-optical constants qij, essentially the pij times elastic constants. Data for glasses and fused quartz are compiled in Landolt-Bornstein Tables, (Springer-Verlag, Berlin, 1962), Vol. II, Part 8, pp. 3–542; these are generally in terms of a stress-optical constant C0, related for practical purposes to constants we use by Δn/n= rσ= (C0Y/n)σ= (n/2) × (p11 − p12)σ, where Y is Young’s modulus and σ is a uniaxial strain.
  7. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics (D. Van Nostrand Co., Inc., New York, 1950); Ch. XV.
  8. L. F. Mollenauer, D. Downie, H. Engstrom, and W. B. Grant, Appl. Opt. 8, 661 (1969).
    [Crossref] [PubMed]

1969 (1)

1967 (1)

R. W. Dixon, IEEE J. Quant. Electr.,  QE-3, 85 (1967).
[Crossref]

1966 (1)

M. Billardon and J. Badoz, Compt. Rend. 262, 1672 (1966); Compt. Rend. 263, 139 (1966).

Badoz, J.

M. Billardon and J. Badoz, Compt. Rend. 262, 1672 (1966); Compt. Rend. 263, 139 (1966).

Billardon, M.

M. Billardon and J. Badoz, Compt. Rend. 262, 1672 (1966); Compt. Rend. 263, 139 (1966).

Dixon, R. W.

R. W. Dixon, IEEE J. Quant. Electr.,  QE-3, 85 (1967).
[Crossref]

Downie, D.

Engstrom, H.

Grant, W. B.

Jessop, H. J.

H. J. Jessop, in Encyclopedia of Physics, Vol. VI, S. Flügge, Ed. (Springer-Verlag, Berlin, 1958). This is a review and includes references to books on mechanical engineering applications.

Mason, W. P.

W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics (D. Van Nostrand Co., Inc., New York, 1950); Ch. XV.

Mollenauer, L. F.

Ramaseshan, S.

K. Vedam and S. Ramaseshan, in Progress in Crystal PhysicsR. S. Krishnan, Ed. (S. Viswanathan, Madras, India, 1958). Some photoelastic data are given in terms of the stress-optical constants qij, essentially the pij times elastic constants. Data for glasses and fused quartz are compiled in Landolt-Bornstein Tables, (Springer-Verlag, Berlin, 1962), Vol. II, Part 8, pp. 3–542; these are generally in terms of a stress-optical constant C0, related for practical purposes to constants we use by Δn/n= rσ= (C0Y/n)σ= (n/2) × (p11 − p12)σ, where Y is Young’s modulus and σ is a uniaxial strain.

Shurcliff, W. A.

A review of modern polarization devices is given by W. A. Shurcliff, Polarized Light (Harvard Univ. Press, Cambridge, 1962). For the state of the art in electro-optic devices see R. S. Ploss, Opt. Spectry. 3,(1)63 (1969).

Sommerfeld, A.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1964); Ch. IV.

Vedam, K.

K. Vedam and S. Ramaseshan, in Progress in Crystal PhysicsR. S. Krishnan, Ed. (S. Viswanathan, Madras, India, 1958). Some photoelastic data are given in terms of the stress-optical constants qij, essentially the pij times elastic constants. Data for glasses and fused quartz are compiled in Landolt-Bornstein Tables, (Springer-Verlag, Berlin, 1962), Vol. II, Part 8, pp. 3–542; these are generally in terms of a stress-optical constant C0, related for practical purposes to constants we use by Δn/n= rσ= (C0Y/n)σ= (n/2) × (p11 − p12)σ, where Y is Young’s modulus and σ is a uniaxial strain.

Appl. Opt. (1)

Compt. Rend. (1)

M. Billardon and J. Badoz, Compt. Rend. 262, 1672 (1966); Compt. Rend. 263, 139 (1966).

IEEE J. Quant. Electr. (1)

R. W. Dixon, IEEE J. Quant. Electr.,  QE-3, 85 (1967).
[Crossref]

Other (5)

K. Vedam and S. Ramaseshan, in Progress in Crystal PhysicsR. S. Krishnan, Ed. (S. Viswanathan, Madras, India, 1958). Some photoelastic data are given in terms of the stress-optical constants qij, essentially the pij times elastic constants. Data for glasses and fused quartz are compiled in Landolt-Bornstein Tables, (Springer-Verlag, Berlin, 1962), Vol. II, Part 8, pp. 3–542; these are generally in terms of a stress-optical constant C0, related for practical purposes to constants we use by Δn/n= rσ= (C0Y/n)σ= (n/2) × (p11 − p12)σ, where Y is Young’s modulus and σ is a uniaxial strain.

W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics (D. Van Nostrand Co., Inc., New York, 1950); Ch. XV.

A review of modern polarization devices is given by W. A. Shurcliff, Polarized Light (Harvard Univ. Press, Cambridge, 1962). For the state of the art in electro-optic devices see R. S. Ploss, Opt. Spectry. 3,(1)63 (1969).

A. Sommerfeld, Optics (Academic Press Inc., New York, 1964); Ch. IV.

H. J. Jessop, in Encyclopedia of Physics, Vol. VI, S. Flügge, Ed. (Springer-Verlag, Berlin, 1958). This is a review and includes references to books on mechanical engineering applications.

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Figures (3)

Fig. 1
Fig. 1

The piezo-optical birefringence modulator in rudimentary form. A simple extensional vibration is set up in a transparent bar, sustained by an acoustic transducer (not shown). Incident light I0 linearly polarized at 45° to the bar axis is rendered alternately right- and left-circularly polarized by the alternating birefringence, if the peak birefringence corresponds to λ/4 retardation; this output (I1) can be used in circular-dichroism measurements. Addition of P′, or of a stationary λ/4 plate followed by P′, permits flux modulation at frequencies 2ω or ω, respectively.

Fig. 2
Fig. 2

The output flux I2 of Fig. 1, as a function of time (a); the time-averaged mean flux as a function of the retardation amplitude ϕ0 is shown in (b). The (+) and (−) peaks in (a) correspond to the senses of elliptic or circular polarizations in the beam incident on P′ in Fig. 1, for the case 0 < ϕ0 < π.

Fig. 3
Fig. 3

Geometry for angular-aperture considerations. In the stressed plate of isotropic material, with peak stress-induced retardation of the order one wave, the double-refraction separation s between extraordinary and ordinary exit waves is of the order one wavelength, and is therefore greatly exaggerated in the figure. An upper limit for the retardation increase with θ is given by the simple path increase, secθ or secθ′ in (b).

Equations (5)

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I 2 ( t ) = I 0 [ sin ( ϕ 0 sin ω t ) ] 2 = I 0 { 1 2 [ 1 - J 0 ( ϕ 0 ) ] + J 2 ( ϕ 0 ) cos ( 2 ω t ) + J 4 ( ϕ 0 ) cos ( 4 ω t ) + } ,
Δ n ( θ , α ) / n [ Δ n ( 0 , 0 ) / n ] ( 1 - sin 2 θ cos 2 α ) .
W = 1 2 ρ u max 2 d x d y d z = 1 4 ρ ω 2 δ 0 2 w t l
P = π 16 w ρ v s 3 λ 0 2 m 2 t n 2 r 2 Q .
w = 12 mm , t = 6 mm ( w / t = 2 ) ρ = 2.3 gm / cm 3 ; v s = 5 × 10 5 cm / sec n = 1.5 ; λ 0 = 5000 Å ; r 0.1 } P 1000 m 2 / Q ( W )