Diffraction theory of the impulse mirage effect

Abstract

A diffraction theory of the mirage effect is derived for the case of impulse excitation of a thin planar heat flux source located at the surface of an irradiated solid sample. A Fresnel diffraction theory is derived to predict optical deflection and diffraction of a probe laser beam directed over the surface of the sample, through an adjacent fluid phase. A closed-form analytical expression for the perturbed electric field distribution of a probe beam intersecting a 1-D mirage element is derived and used to compute beam profile changes, changes in the beam’s central moment, and point differences in the intensity change measured in the detector plane. Photothermally induced changes in the probe beam’s central moment are found to give a robust measure of the photothermal deflection effect and are substantially insensitive to photothermal diffraction. Photothermally induced diffraction effects are resolved by computing point changes in the probe beam intensity. The photothermal deflection effect is found to give a maximum sensitivity with the mirage region centered at the waist of the probe beam and detection in the far field. The photodeflection effect dominates the mirage signal when the thermal diffusion length of the mirage element is comparable to or greater than the probe beam radius. Photothermal diffraction effects are significant when the thermal diffusion length is much smaller than the probe beam radius and when detection occurs in the near field. With far-field detection using a bicell, photothermal diffraction effects are, in general, significant only at early times past excitation. A quantitative correction for the diffractive effect is possible using the current theory.