Steady-state absorption rate models for use in relaxation rate studies with continuous laser excited photothermal lens spectrometry

Abstract

This paper examines the solutions of kinetic rate equations for prediction of the photothermal lens signals under irradiance conditions that can lead to optical saturation or bleaching. The relaxation kinetics resulting from forcing excited state populations in multiple levels by high excitation irradiance continuous lasers is examined and irradiance-dependent photothermal lens signals are predicted. The analyses described in this paper are based on simple kinetic models for optical excitation and subsequent excited state relaxation. Dark-state relaxation is assumed to be extremely fast compared to limiting kinetics resulting in simplified excited state models. Kinetic models are derived for two, four and five active level molecular systems. Gaussian laser beam profiles are assumed and time dependent photothermal lens signals are calculated. Models account for excitation laser profile, thermal relaxation of the spatially and temporally distorted heating rate distribution resulting from nonlinear absorption, and metastable state relaxation. This heating rate is used to calculate the temperature change distribution and subsequently the optical elements needed to model the experimental photothermal signals.