Stress Birefringence in Optical Glass
Stress birefringence of optical glass: Δn = C(σ₁ − σ₂) and the retardance R = C d (σ₁ − σ₂) for fused silica and twelve Schott glasses, in nm/cm as glass catalogs quote it, with the stress that gives a half-wave retardance.
For uniaxial stress (σ₂ = 0), a positive value is tension and a negative one compression.
Stress-optic coefficient C
3.55 ×10⁻¹² Pa⁻¹
Jog 1957 (Filon & Harris), 649.5 nm
Birefringence Δn = C·σ
3.550e-5
signed
Phase Γ = 2πR/λ
3.524 rad
fringe order R/λ = 0.5608
Retardance R in 10 mm
355 nm
signed: flips between tension and compression
Retardance per cm
355 nm/cm
the unit glass catalogs use for stress birefringence
Stress for half-wave retardance
8.915 MPa
R = λ/2 at this thickness and wavelength
Retardance against stress
Glasses at 10 MPa
| Glass | C (×10⁻¹² Pa⁻¹) | R per cm (nm/cm) | Source |
|---|---|---|---|
| Fused silica | 3.55 | 355 | Jog 1957 (Filon & Harris), 649.5 nm |
| N-BK7 | 2.77 | 277 | Schott data sheet (N-BK7HT) |
| N-BAK4 | 2.9 | 290 | Schott data sheet |
| N-FK51A | 0.7 | 70 | Schott data sheet |
| F2 | 2.81 | 281 | Schott data sheet |
| SF10 | 1.95 | 195 | Schott data sheet |
| SF11 | 1.33 | 133 | Schott data sheet |
| N-SF11 | 2.94 | 294 | Schott data sheet |
| SF6 | 0.65 | 65 | Schott data sheet |
| N-SF6 | 2.82 | 282 | Schott data sheet |
| SF57 | 0.02 | 2 | Schott data sheet |
| N-SF57 | 2.78 | 278 | Schott data sheet |
| N-LASF9 | 1.72 | 172 | Schott data sheet |
Click a row to select the glass.
Model
R = C d (σ₁ − σ₂), Γ = 2πR/λ
The principal stress axes are the birefringence axes. C comes from the Schott data sheets (K in 10⁻⁶ mm²/N = 10⁻¹² Pa⁻¹; SF57's 0.02 is the near-zero-K lead glass used for polarization-preserving optics) and from Jog 1957 for fused silica (3.55 at 649.5 nm, rising to 3.75 at 460 nm). The sign of R flips between tension and compression.
Crystals are not listed because they have a stress-optic tensor, so their birefringence depends on the stress and light directions. Liquids carry no static shear stress.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Linear stress-optic law for isotropic glass at one wavelength (C varies a few percent across the visible; the page warns outside 0.4–2.5 µm). Crystals are not covered: they have a stress-optic tensor, so their birefringence depends on the stress and light directions.
- SCHOTT AG (2017). Optical glass data sheets, 2017-01-20: stress optical coefficient K. refractiveindex.info
- Jog E. S. (1957). The dispersion of the stress optical coefficient of vitreous silica. J. Indian Inst. Sci. 39(2), 93. Table I. journal.iisc.ac.in
- Dally J. W., Riley W. F. (2005). Experimental Stress Analysis, 4th ed. College House Enterprises. Theory of photoelasticity.