R-hyperbolic functions - A new tool for description of thermalwaves

Abstract
A general new method of description of thermal waves for the case of samples placed on a different backing material is presented and discussed. New functions of the R-hyperbolic type useful for the proper description of the periodical temperature fields and periodical photoacoustic and piezoelectric signais are proposed and described. They were applied for a description of several cases most frequently met in photoacoustic and photothermal methods. The paper comprises among others general equations for the ratio of the magnitudes and the phase-lag between the front and rear photoacoustic signals, instantaneous temperature spatial distributions in a sample and the equations describing the piezoelectric signal. All these formula are expressed in a domain of R-hyperbolic functions. This paper presents in general a strong influence of the backing material on photothermal characteristics.