A Theoretical and Experimental Study of Time-Resolved Thermal Mirror with Non-Absorbing Heat-Coupling Fluids

Abstract

A theoretical and experimental study taking sample-fluid heat coupling into account in time-resolved photothermal mirror experiments is presented. Thermoelastic equations were solved to obtain a semi-analytical solution to the phase shift induced by the sample and the surrounding fluid. The solution was used to model the thermal mirror effects and found to be in excellent agreement with the finite element method analysis and experiment. Heat transferred to the air-coupling fluid did not introduce important effects in the phase shift when compared with the solution obtained, without considering heat flux. However, when using water as the fluid, heat coupling led to a significant effect in fluid phase shift. Experimental results using stainless steel in air and water were used to demonstrate the potentiality of the thermal mirror technique to determine the thermal properties of both the sample and the fluid.

Laser induced thermoelastic surface displacement in solids detected simultaneously by photothermal mirror and interferometry

“…The last term on the right-hand side of the thermoelastic equation represents the inertia term yielding elastic wave motion. This term can be neglected [22] as the signal oscillations due to the inertia term are not observed experimentally considering the relatively long detector response time [23]. The z-component (normal) of the displacement vector at the sample surface for a semi-infinite sample is [8] and λ p is the probe beam wavelength.…”

“…(6) can be concurrently measured by the TM and the interferometer. The TM detection is performed by analyzing the on-axis intensity change of the central portion of the probe beam reflected from the sample surface at the far field photodetector [11,22]. The centers of both the pump and the probe beams overlap at the sample surface.…”

“…Additional phase shift to the probe beam as a consequence of the thermal lens (TL) effect created in the surrounding air by heat coupling to the sample is given by [22]…”

Influence of edge effects on laser-induced surface displacement of opaque materials by photothermal interferometry

“…with proper boundary and initial conditions as given in Ref. 37. D i = k i /ρ i c pi is the thermal diffusivity, k i is the thermal conductivity, ρ i is the mass density and c pi is the specific heat for the sample (i = s) and fluid (i = f ).…”

“…7represents the inertia term yielding elastic wave motion. This term can be neglected 37 as the elastic waves described by the inertia term are not observed experimentally since the detector averages them out due to its relatively long response time 35 . The normal component of the displacement vector at the sample surface, u z (r, z = 0,t), in null flux approximation, can be written for the semi-infinite sample as…”