Finite-size effect on the surface deformation thermal mirror method

Direct measurement of photo-induced nanoscale surface displacement in solids using atomic force microscopy

“…The problem is treated in cylindrical coordinates due to the axially symmetric radial nature of the Gaussian pump laser beam. Introducing the scalar displacement potential and the Love function [22], the displacement z-component at the sample surface for an arbitrary temperature profile is [12]:…”

“…Applying the temperature in the Hankel-Fourier cosine space and performing the integral over, k the z-component of the displacement at the sample surface is given, in a good approximation to moderate optical absorbing material, by [12]:…”

“…The relative far-field intensity at the detector plane, I(t), of the center of the probe beam spot is given by [11,12]:…”

“…The methods employ coherent or incoherent light sources to heat up a material. From changes in the thermal state of the absorbing sample or its adjacent fluid, several effects can be monitored individually by measuring infrared emission, temperature change, acoustic waves, refractive index change, and surface displacement [2][3][4][5][6][7][8][9][10][11][12]. A laser-induced surface displacement, for instance, can be analyzed by probing the time-dependent intensity of a laser reflected off of the surface using the thermal mirror (TM) technique.…”

“…A laser-induced surface displacement, for instance, can be analyzed by probing the time-dependent intensity of a laser reflected off of the surface using the thermal mirror (TM) technique. TM has been used to investigate transparent and opaque materials, and is sensitive to deformation on the order of a few nanometers [11][12][13]. In addition, the pump-probe remote characteristics of this technique allow temperature scanning during measurements [14].…”