“…Considering the average reported value of the strain-induced Raman shift of ∼1.700 cm –1 /GPa in bulk sapphire, 77 this difference in the Raman shift of ∼−1.256 cm –1 (from 755.630 to 754.374 cm –1 ) corresponds to a tensile stress change of ∼−0.74 GPa, as found for typical luminescent Nd:YVO4, Nd:YAG, and Cr:YAG analogs. 34,82,83 In contrast, one can reasonably estimate the thermally induced residual stress, σ, in the sapphire core in terms of Young’s modulus ν, Poisson’s ratio E , core-to-clad volume fraction f , TEC α, and temperature change Δ T using the following relation 84
where
Assuming that the physical properties of the micrometer-sized fiber are similar to those of the millimeter-sized bulk sample, the values of ν, E , and α for the c axis sapphire core are 0.23, 400 GPa, and 4.5 × 10 –6 °C –1 , 85,86 respectively. Furthermore, f = (20 μm) 2 /(160 μm) 2 = 1/64, and typically, Δ T = 525–25 °C = 500 K (i.e., the transition temperature for borosilicate glass is 525 °C).…”