Herbert S. Bennett and Richard A. Forman, "Absorption coefficients in highly transparent solids: barothermal theory for cylindrical configurations," Appl. Opt. 14, 3031-3037 (1975)
The development of highly transparent solids requires improved methods to measure very low absorption coefficients at laser wavelengths. For the case in which a laser beam passes through a weakly absorbing solid that is surrounded by a confined, nonabsorbing gas, the temperature profiles in the solid and the temperature and pressure profiles in the gas have been calculated. Our calculations suggest that sufficient heat transfers from the solid into the gas to produce an easily detected pressure rise in the gas.
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The relative pressure is (p∞/p0); the relative steady-state temperature at r = 0 is [υs(0)/T0], the radius of the laser beam is rl, the radius of the solid is rs = 0.5 cm and the radius of the outer cylindrical surface is ri. The radii are in cm, and the relative quantities are dimensionless. The ambient temperature and pressure are, respectively, T0 = 300 K and p0 = 1.013 × 105 N/m2 (1 atm).
The radius of the solid sample is rs = 0.5 cm, and the radius of the laser beam is rl = 0.45 cm. The radius of the outer cylindrical surface is ri; the times tj in s are given by Eq. (35); the relative pressure at time 2t1 is [p(2t1)/T0] and is given by Eq. (44); and the relative temperature at time 2t1, and at r = 0 is [Ts(0,2t1)/T0] and is given by Eq. (42). The jth value ξj in cm−1 is the jth solution to Eq. (34), and the coefficients (Aj/T0) are given by Eq. (41). The relative pressure, the relative temperature, and the coefficients (Aj/T0) are all dimensionless.
The relative pressure is (p∞/p0); the relative steady-state temperature at r = 0 is [υs(0)/T0], the radius of the laser beam is rl, the radius of the solid is rs = 0.5 cm and the radius of the outer cylindrical surface is ri. The radii are in cm, and the relative quantities are dimensionless. The ambient temperature and pressure are, respectively, T0 = 300 K and p0 = 1.013 × 105 N/m2 (1 atm).
The radius of the solid sample is rs = 0.5 cm, and the radius of the laser beam is rl = 0.45 cm. The radius of the outer cylindrical surface is ri; the times tj in s are given by Eq. (35); the relative pressure at time 2t1 is [p(2t1)/T0] and is given by Eq. (44); and the relative temperature at time 2t1, and at r = 0 is [Ts(0,2t1)/T0] and is given by Eq. (42). The jth value ξj in cm−1 is the jth solution to Eq. (34), and the coefficients (Aj/T0) are given by Eq. (41). The relative pressure, the relative temperature, and the coefficients (Aj/T0) are all dimensionless.