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Applied Optics

Nonsteady-state molecular luminescence behavior under narrowband laser excitation

G. D. Boutilier, Nicolo’ Omenetto, J. D. Winefordner

Published Jun 1, 1980• 7 citations
Publisher

Abstract

The time behavior of a two- and a three-level molecular system under narrowband pulsed-laser excitation is discussed, and relations are presented for the temporal variation of the concentrations of the levels involved. It is shown that if saturation is approached, the response time of the molecular system is strictly related to the pumping time, which is given by the reciprocal of the product of the laser spectral density and the Einstein coefficient of stimulated absorption. Typical calculations of the fractional number densities of the levels are presented as a function of the value of the laser spectral density required to achieve saturation for a few typical molecules such as benzophenone, fluorene, and rhodamine 6G.

DOI
10.1364/ao.19.001838

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Excitation of transitions between atomic or molecular energy levels by monochromatic laser radiation - II. Excitation under conditions of strictly inhomogeneous line broadening and mixed homogeneous and inhomogeneous broadening

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Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly inhomogeneous line broadening due to such causes as doppler shift arising from translational velocity. The ratio of the number of molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width ∆, where E0 is the amplitude of the electric field in the incident radiation and is the dipole moment matrix element for the transition. Excitation functions obtained in a previous paper (I) for various values of the ratio γ/β, where γ is the half line-width in the absence of inhomo­geneous broadening, are used to obtain the variation of N2/N with time under conditions of mixed broadening for various values of the ratio γ/∆ and γ/β, when the exciting radiation is in exact resonance with the central frequency of the transition.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jun 30, 1978•12 citations
The time behavior of a two- and a three-level molecular system under narrowband pulsed-laser excitation is discussed, and relations are presented for the temporal variation of the concentrations of the levels involved. It is shown that if saturation is approached, the response time of the molecular system is strictly related to the pumping time, which is given by the reciprocal of the product of the laser spectral density and the Einstein coefficient of stimulated absorption. Typical calculations of the fractional number densities of the levels are presented as a function of the value of the laser spectral density required to achieve saturation for a few typical molecules such as benzophenone, fluorene, and rhodamine 6G.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
A new theoretical model describing the emission and absorption dynamics in an ensemble of molecules under intense coherent pulsed pumping is developed on the basis of the concepts of cooperative light-induced luminescence (CLIL). The CLIL development is described within the framework of formalism of the system density matrix in the space of photon wave functions. It is shown that the fast growth of CLIL relates to the development of coherent states of the quantum field in the area of efficient cooperative interactions of molecules (coherence volume). A system of equations for the calculation of CLIL energy, population of excited states, and optical absorption of the system in dependence on the laser pump energy density is solved. The theoretical results obtained are in good agreement with the experimental data.
We consider the nonlinear propagation of an intense short pulse of polarized light through a molecular medium with ground- and excited-state absorption, excited-state emission, and fluorescence from the excited state to the ground state and possibly to a lower-lying excited state. We incorporate the effects of saturation, field-induced alignment, and rotational diffusion of the molecules in the medium. Our approach uses a slowly varying envelope approximation for the light propagation and rate equations for the effective parallel and perpendicular (and higher-multipole) population components of the molecular states. The time dependence of the anisotropy of the fluorescence occurring after preparation of the medium by the intense short pulse is determined. We can treat propagation through an optically nonthin medium wherein the intensity of the pulse decreases while propagating through the medium. An example of a 100-ps pulse propagating through a sample of Rhodamine-6G is presented. We compare our method with others used to describe intense-short-pulse propagation in molecular media.
The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.
Three typical excited-state nonlinear absorption effects in molecular systems with weak ground-state absorption (at 532 nm) are experimentally demonstrated: (a) reverse saturable absorption (RSA) caused by strong triplet first-to-second excited-state absorption in a copper phthalocyanine solution with 15-ns laser pulses; (b) RSA caused by strong singlet first-to-second excited-state absorption in a C60{\mathrm{C}}_{60}C60​ solution with 21-ps laser pulses; (c) the RSA-SA turnover caused by strong singlet first-to-second excited-state absorption and weak singlet second-to-third excited-state absorption in a metallo-porphyrin-like solution with 21-ps laser pulses. To simulate these excited-state nonlinear absorption behaviors we propose a general ten-level density-matrix model and its simplified models for the three cases. All simulations are in good agreement with the experimental results.
Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly inhomogeneous line broadening due to such causes as doppler shift arising from translational velocity. The ratio of the number of molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width ∆, where E0 is the amplitude of the electric field in the incident radiation and is the dipole moment matrix element for the transition. Excitation functions obtained in a previous paper (I) for various values of the ratio γ/β, where γ is the half line-width in the absence of inhomo­geneous broadening, are used to obtain the variation of N2/N with time under conditions of mixed broadening for various values of the ratio γ/∆ and γ/β, when the exciting radiation is in exact resonance with the central frequency of the transition.