Photoacoustic methods for measuring surface and bulk absorption coefficients in highly transparent materials: theory...

Researchers seek improved ways to measure the surface absorption and the bulk absorption coefficients of highly transparent materials. Procedures are presented here by which one may determine separately the surface absorption and the bulk absorption coefficients. For the case in which a laser beam modulated at angular frequency omega passes through the weakly absorbing windows of a gas cell containing a nonabsorbing gas, the temperature profiles in the cell windows and the temperature and acoustic pressure or stress profiles in the gas have been calculated. These calculations indicate that for sufficiently low frequencies and high ambient gas pressure, enough heat transfers from the cell windows to the gas to produce a detectable acoustic pressure signal at angular frequency omega in the gas. These calculations also enable us to state the necessary measurements for determining the surface and bulk absorption coefficients. Measuring the acoustic stress amplitude at the fundamental and higher harmonic frequencies and measuring the phase shifts of the frequency components of the acoustic stress with respect to the modulated laser beam give sufficient data by which one can determine the surface and bulk absorption coefficients. Numerical examples for a representative laser glass and air (nitrogen) are given.