Transfer Matrix Formulation With Optical Penetration for Axisymmetric Thermoelastic Wave Propagation in Films

Using Laplace and Hankel integral transforms in time and the radial coordinate, a fully-coupled thermoelastic formulation based on the equation of motion and heat equation is developed to study the effects of axial optical penetration on axisymmetric wave propagation in thermoelastic layers and/or layered structures. It is demonstrated that the optical penetration has no effect on the entries of the sextic transfer matrix, however it introduces an equivalent forcing term for all state variables for both surfaces of a thermoelastic layer as opposed to the surface heating case in which the heating effect is localized in the heating volume (the thermal skin). The thickness of thermal skin depends on the light intensity modulation frequency while the optical penetration typically depends only on the wavelength of the light. This additional forcing vector is a function of the light intensity modulation frequency, the radial wave number, penetration decay rate, as well as thermoelastic material properties. Complexities in wavefields due to the nature of the forcing term are demonstrated and discussed. A thin copper layer with hypothetical penetration properties is considered for the demonstration of the current formulation.