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Optics and Spectroscopy

Mathematical simulation of dual fluorescence quenching

V. A. Morozov, Nikolai D. Chuvylkin, Evgenii A. Smolenskii

Published Mar 1, 2014• 1 citation
Publisher

Abstract

The dynamic quenching of dual fluorescence is simulated based on solving a system of equations for matrix elements of the statistical operator of a five-level model molecule three levels of which belong to its excited states. It is assumed that one of the excited states is resonantly populated by monochromatic irradiation, while the other two states are populated as a result of subsequent relaxation processes. These two states are initial states for transitions that emit dual fluorescence photons. Expressions for the population of the excited molecular states in the case of steady-state fluorescence are obtained taking into account their decay (quenching) due to collisions with foreign molecules of the environment. As applied to molecules with intramolecular hydrogen bonds, the dual fluorescence quenching is described more completely and in more detail compared to the description given in the literature based on the molecular model with two excited levels.

DOI
10.1134/s0030400x1403014x

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The dynamic quenching of dual fluorescence is simulated based on solving a system of equations for matrix elements of the statistical operator of a five-level model molecule three levels of which belong to its excited states. It is assumed that one of the excited states is resonantly populated by monochromatic irradiation, while the other two states are populated as a result of subsequent relaxation processes. These two states are initial states for transitions that emit dual fluorescence photons. Expressions for the population of the excited molecular states in the case of steady-state fluorescence are obtained taking into account their decay (quenching) due to collisions with foreign molecules of the environment. As applied to molecules with intramolecular hydrogen bonds, the dual fluorescence quenching is described more completely and in more detail compared to the description given in the literature based on the molecular model with two excited levels.
The dynamics of transformation of a light pulse by a five-level model molecule whose secondary emission spectrum can contain two fluorescence bands is simulated. The system of equations that determine the time behavior of the matrix elements of the statistical operator of the molecule interacting with the light pulse is numerically solved. From this solution, the time dependences of the populations of the molecular states are determined for different values of the parameters of the irradiation pulse, which is described in terms of the classical theory, and of the parameters that characterize the rates of radiative and nonradiative spontaneous transitions of the molecule. Based on particular examples of the choice of these parameters, it is demonstrated that the mechanism by which dual fluorescence occurs in molecules with intramolecular hydrogen bonds can be efficiently established from the numerically simulated intramolecular dynamics.
Numerical simulations of the excitation spectra of resonant fluorescence bound by the dynamic interaction of two different two-level nanoparticles have been performed. We considered the excitation of one of the particles by monochromatic light with a frequency close to the transition frequency of this particle, at an irradiation intensity leading to a small population of its excited state. The formalism for the description of resonance fluorescence by the Heitler--Ma method was applied to a complete compound system of the marked particle pair and quantized emission field. The resulting expressions for the excitation spectrum reflect consideration of the absorption of the fluorescence photon without attributing it to the emission of any one particle. Expressions for the excitation spectra when taking into account such absorption of the fluorescence photon that allows us to attribute it to the radiation of one or another of the particles were obtained by solving a modified system of equations of the Heitler--Ma method, which reflects the addition of non-interfering amplitudes of the emission field states of each particle. It was found that the shape of the excitation spectra of the stationary resonance fluorescence of the particles in question is determined by the shape of the corresponding intensity spectra of the spontaneous fluorescence of these particles. Keywords: mathematical modeling, interacting two-level nanoparticles, resonant fluorescence, excitation spectrum.
A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.
Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.
Abstract Mathematical modeling of the excitation dynamics of an isolated two-level particle under bichromatic irradiation is carried out on basis of solutions of the Schrödinger equation for the probability amplitudes of the states of the composite system of the particle and an interaction two-mode quantized radiation field, with the photons for each of which in a superposition state at the initial time. An analytical expression describing the change in the time of the population of the excited state of a particle in the adsorption of one of the irradiation photons in the simplest case when the irradiation is a sequence of identical pulses of a sinusoidal form is obtained. The obtained time dependence is compared with the time dependence of the diagonal matrix element of the statistical operator of the particle in the excited state found on the basis of the numerical solution of the system of the optical Bloch equations, with the corresponding irradiation described by the classical theory. Examples of significant differences in the type of these compared time dependences for a number of characteristic cases of irradiation are given.
Abstract A system of equations is obtained for describing the dynamics of the secondary photoreaction of two-level molecules emitting spontaneous fluorescence at initial excitation of one of them. The system is derived using the Schrödinger equation for the compound system of a reagent molecule, a reaction product molecule, and a quantized radiation field. Unlike those commonly used in similar modeling, optical Bloch equations describing the dynamics of a non-selective (collective) population of the ground states of two molecules (i.e., the total number of molecules of a pair in their ground states), the system of equations (and its generalization allowing for the longitudinal and transverse relaxation of excited states of molecules) allows estimates of the relative number of reagent molecules and the product in their ground states, the use of which provides a complete idea of the effectiveness of the reaction.