Photoelastic Constants of α Quartz

T. S. Narasimhamurty

doi:10.1364/JOSA.59.000682

Journal of the Optical Society of America
Vol. 59,
Issue 6,
pp. 682-686
(1969)
•https://doi.org/10.1364/JOSA.59.000682

Photoelastic Constants of α Quartz

T. S. Narasimhamurty

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T. S. Narasimhamurty, "Photoelastic Constants of α Quartz," J. Opt. Soc. Am. 59, 682-686 (1969)

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Abstract

All of the stress-optical and strain-optical constants of α quartz have been determined by use of a Rayleigh compensator, a Babinet compensator, localized fringes, and ultrasonic excitation methods. The results agree with those obtained by Pockels (1889), but disagree with the results obtained by Günther (1932), who determined the constants for only one direction. The values of q_ij and p_ij at room temperature and for λ5893 Å are: q₁₁ = 1.35; q₁₂ = 2.69; q₁₃ = 1.94; q₁₄ = −0.11; q₃₁ = 3.11; q₄₁ = −0.34; q₃₃ = 0.07; q₄₄ = −1.13; (all in units of 10⁻¹³ cm²/dyn.) p₁₁ = 0.16; p₁₂ = 0.27; p₁₃ = 0.27; p₁₄ = −0.030; p₃₁ = 0.29; p41 = −0.047; p₃₃ = 0.10; p₄₄ = −0.079

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Equations (19)

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Direction of stress	Direction of observation	Nature of observation	Expression for path retardation δ₀
[100]	[001]	Relative	$\frac{1}{2} {n_{x}}^{3} (q_{11} - q_{12}) - s_{13} (n_{x} - n_{y})$
[100]	[010]	Relative	$\frac{1}{2} ({n_{x}}^{3} q_{11} - {n_{z}}^{3} q_{31}) - s_{12} (n_{x} - n_{z})$
[001]	[100]	Relative	$\frac{1}{2} ({n_{z}}^{3} q_{33} - {n_{x}}^{3} q_{13}) - s_{13} (n_{z} - n_{x})$
[001]	[010]	Relative	$\frac{1}{2} ({n_{z}}^{3} q_{33} - {n_{x}}^{3} q_{13}) - s_{13} (n_{z} - n_{x})$
[100]	M^a	Relative	$\frac{1}{2} {n_{x}}^{3} q_{11} - \frac{1}{4} {n_{y z}}^{3} (q_{12} + q_{31} - 2 q_{41}) - \frac{1}{2} (n_{x} - n_{y z}) (s_{12} + s_{13} - s_{14})$
[100]	M′^b	Relative	$\frac{1}{2} {n_{x}}^{3} q_{11} - \frac{1}{4} {n_{y z}}^{3} (q_{12} + q_{31} + 2 q_{41}) - \frac{1}{2} (n_{x} - n_{y z}) (s_{12} + s_{13} - s_{14})$
M	M′	Relative	$\frac{1}{8} {n_{y z}}^{3} (q_{11} + q_{13} - q_{14} + q_{31} + q_{33} + 2 q_{44} - 2 q_{41}) - \frac{1}{4} {n_{x}}^{3} (q_{12} + q_{13} + q_{14}) - \frac{1}{4} (n_{y z} - n_{x}) (s_{11} + 2 s_{13} + s_{33} - s_{44})$
M′	M	Relative	$\frac{1}{8} {n_{y z}}^{3} (q_{11} + q_{13} + q_{14} + q_{31} + q_{33} + 2 q_{44} + 2 q_{41}) - \frac{1}{4} {n_{x}}^{3} (q_{12} + q_{13} - q_{14}) - \frac{1}{4} (n_{y z} - n_{x}) (s_{11} + 2 s_{13} + s_{33} - s_{44})$
M′	M	Absolute	$\frac{1}{2} {n_{x}}^{3} (q_{12} + q_{13} - q_{14}) - \frac{1}{2} n_{x} (s_{11} + 2 s_{13} + s_{33} - s_{44})$ (for horizontal vibrations)
M′	M	Absolute	$\frac{1}{4} {n_{y z}}^{3} (q_{11} + q_{13} + q_{14} + q_{31} + q_{33} + 2 q_{44} + 2 q_{41}) - \frac{1}{2} n_{y z} (s_{11} + 2 s_{13} + s_{33} - s_{44})$ (for vertical vibrations)

No. of prism	Length		Breadth		Thickness
No. of prism	parallel to	mm	parallel to	mm	parallel to	mm
1.	[100]	9.96	[010]	4.50	[001]	2.53
2.	[100]	13.03	[010]	5.08	[001]	4.08
3.	[001]	13.80	[010]	5.45	[100]	6.80
4.	[100]	14.76	M′	6.50	M	5.96
5.	M	10.50	[100]	6.20	M′	5.67
6.	M′	10.65	[100]	6.45	M	3.85
7.	[001]	9.85	[100]	4.65	[010]	3.03

No. of prism	Direction of stress	Direction of observation	Actual value of δ
2.	[100]	[010]	−3.28
3.	[001]	[010]	−3.47
4.	[100]	M	−3.66
4.	[100]	M′	−2.36
5.	M	M′	−1.88
6.	M′	M	−2.82

Expression for R ratio of strain-optical constants	R by optical methods		R by ultrasonic methods by the author
Expression for R ratio of strain-optical constants	Pockels	author	R by ultrasonic methods by the author
p₁₂/p₁₁	1.87	1.67	1.57
p₃₁/p₁₁	1.86	1.78	2.00
p₁₃/p₃₃	2.63	2.67	2.81

Change in refractive index	Waxler and Weir	Vedam and Davis	Pockels	Author
Δn₀	1.03	1.03	1.00	1.08
Δn_e	1.07	1.07₅	1.04	1.16

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Tables (5)

Equations (19)

Journal of the Optical Society of America