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Applied Optics

Approximate analytic solutions for the optical pumping of fluorescent dyes

N. M. Lawandy

Published Jan 15, 1979• 3 citations
Publisher

Abstract

A general technique for solving a system of rate equations describing the interaction of an electromagnetic field and a molecular system is presented. The method is used to obtain approximate time-dependent solutions for the upper-level populations of fluorescent dyes in the presence of a pump field.
DOI
10.1364/ao.18.000189

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The technique of stimulated emission depletion of fluorescence (STED) from a two photon excited molecular population is demonstrated in the S1 excited state of fluorescein in ethylene glycol and methanol. Two photon excitation (pump) is achieved using the partial output of a regeneratively amplified Ti:Sapphire laser in conjunction with an optical parametric amplifier whose tuneable output provides a synchronous depletion (dump) pulse. Time resolved fluorescence intensity and anisotropy measurements of the fluorescein emission are made using picosecond time-correlated single photon counting. Pump-dump time delayed fluorescence intensity measurements are used to characterise the response of the system and to provide additional data on saturation dynamics of the dump transition. Two photon STED is modelled using both approximate analytical techniques in the weak dump limit and by numerical solutions to the appropriate rate equations. The latter are used to fit experimental data from which it is possible to determine the cross-section for the stimulated transition and lifetime of the upper vibrational levels of the ground state.
Rate equations for the population dynamics of multilevel systems in laser-induced fluorescence spectroscopy are solved by the aid of perturbation theory. This leads to a general expression for the population of the level pumped by the laser radiation. Arbitrary laser pulse shapes as well as collisional processes are admitted. In the first-order approximation three functions depending on time and the properties of the laser pulse remain. These functions have been tabulated for a bell-shaped laser pulse. The results are used in several characteristic situations and are compared with the numerical solutions of the rate equations.