Photoacoustic chopping frequency studies on sapphire

Experimental photoacoustic (PA) signal amplitude and phase angle data were obtained as a function of chopping frequency on single-crystal sapphire Al2O3 windows using a 1.3-μm laser with about 4 W incident power. The PA signal amplitude had a f−n dependence with n = 1.10 on one run and n = 1.07 on another. Somewhat noisy phase angle plots yielded a phase angle difference between 1000 and 100 Hz of 12 ° and 8.5 °; between 500 and 100 Hz of 10 ° and 7.5 °. Laser rate calorimetry on these samples yielded an average effective optical absorption coefficient βeff = βB +2βs /l = 0.745×10−3 cm−1. βB is the bulk optical absorption coefficient in cm−1 and βs the dimensionless surface optical absorption. l is the sample thickness = 0.78 cm. Theoretical calculations were made using several PA theories and parameters relevant to sapphire. The Rosencwaig-Gersho (R-G) theory calculations yielded results that differed greatly with experiment. Calculations using the McDonald-Wetsel composite-piston model, an extension of the R-G theory, yielded results closer to experiment. A comparison of various calculations using the Bennett-Forman theory indicated that the surface-to-bulk optical absorption ratio r≡βs /βB was between 0.015 and 0.020 cm. Using r = 0.020 cm yields βB = 0.709×10−3 cm−1 and βs = 0.000014. Thus for these samples 95% of the measured βeff is due to βB .