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Journal of the Optical Society of America B

Theory and analysis of excitation–probe studies of induced-absorption three-level molecular systems

Steve Hughes, Brian S. Wherrett, G. Spruce

Published Mar 1, 1997• 0 citations
Publisher

Abstract

The theory of dual-beam excitation-probe measurements for induced absorption three-level systems is presented, including third-order and fifth-order (excited-state absorption saturation) responses, molecular reorientational effects, and optical coherence effects. Negative coherent artifacts are predicted for the self-diffraction configurations and verified experimentally for the induced-absorptive dye 1, 3, 3, 1′, 3′, 3′-hexamethylindotricarbocyanine iodide. We obtain the reorientational times and the recombination lifetimes of the first and the second excited states of the material. These lifetimes are important to the design and exploitation of induced absorbers for optical limiting. The ratio between off-diagonal and diagonal χ(3) tensor elements is also obtained from the modeling.

DOI
10.1364/josab.14.000526

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Journal of the Optical Society of America B•Jun 1, 1993•22 citations
The theory of dual-beam excitation-probe measurements for induced absorption three-level systems is presented, including third-order and fifth-order (excited-state absorption saturation) responses, molecular reorientational effects, and optical coherence effects. Negative coherent artifacts are predicted for the self-diffraction configurations and verified experimentally for the induced-absorptive dye 1, 3, 3, 1′, 3′, 3′-hexamethylindotricarbocyanine iodide. We obtain the reorientational times and the recombination lifetimes of the first and the second excited states of the material. These lifetimes are important to the design and exploitation of induced absorbers for optical limiting. The ratio between off-diagonal and diagonal χ(3) tensor elements is also obtained from the modeling.
Picosecond measurements of the optical response of chloroaluminum phthalocyanine in solutions are presented. The observed nonlinearities are modeled and interpreted theoretically by rate-equation and density-matrix techniques within a three-level model. Single-pulse power limiting is observed at 532 nm, and the absorption cross section of the first excited state is determined to be 15 times that of the ground state. From time-resolved excitation–probe measurements we determine an excited-state recombination time of 7 ns and a reorientational time of 7 ps. Further, the observation of the associated optical coherence effects, which are manifested as a negative coherent artifact, allow us to obtain an 8ps coherence time.
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.
The saturation behavior of molecular absorbers characterized by absorption coefficients expressible as the ratio of two polynomials in the intensity is analyzed. Two cases are considered in detail. In the first, the absorption coefficient is the ratio of a linear equation in I to a quadratic equation in I. In the second, the highest order of the intensity occurring in both numerator and denominator is increased by two. The absorption coefficients are derived from two specific five-level models which are pertinent to the interpretation of the absorption of CO2 laser radiation at 937 cm−1 by SF6, but the analysis of the saturation curves is independent of the models from which they are derived. The saturation curves display as many as three extrema and provide considerable flexibility for fitting complicated experimental data. Both five-level models include excited-state absorption with the terminal level of the ground-state absorption distinct from the initial level of the excited-state absorption. Each of the five levels can be considered as a composite of many rotational states which interact in a like manner with the incident radiation. In one of the models the ratio of the excited-state and ground-state absorption cross sections is taken to be intensity dependent.
The main achievements in our research on the physical phenomena of the excited-state nonlinear absorption in a molecular system and its applications in photonic technology are described. In the first part of this paper, some energy-level models and rate-equations are used to explain various mechanisms of the excited-state nonlinear absorption under different conditions, such as reverse saturable absorption caused by the triplet and/or the singlet excited-state absorption; saturable absorption due to the first and/or the second singlet excited-state absorption; and the excited-state nonlinear absorption induced by two-photon absorption. The experimental results for metal-organic and C 60 materials irradiated by ps and ns laser pulses are consistent with the simulated curves of the transmittance versus fluences. In the second part, the applications of excited-state nonlinear absorption in photonic techniques including optical bistability, optical switching, optical limiting, optical modulation, optical logic and optical storage are introduced. The working principles of the photonic devices based on the excited-state nonlinear absorption are presented. The experimental characteristic curves are found in good agreement with the theoretical simulations for these devices.
We develop an analytical approach to the dynamics of band populations of reverse saturable absorbers modeled by the three-level approximation of the five-level rate equations. We find high-accuracy approximate solutions to these rate equations, taking into account the temporal shape of the incident laser pulse for different regimes of excitation. The results obtained are confirmed by direct numerical integration of the rate equations and are verified by solution of the full system of the rate and the propagation equations. The validity ranges of the approximations are determined. We also prove that for input pulses that are much longer than the lifetime of the first excited state the ground-state depletion obeys the same functional dependence on the input fluence as in the case of rectangular input pulses. The dynamics of the excited states, however, explicitly depends on the pulse shape. We quantitatively estimate the effect of various parameters on the nonlinear absorption coefficient and discuss implementation of the approach by a beam propagation method to reduce the computational time.
Phase conjugation by degenerate four-wave mixing in a saturable absorbing medium with a relatively long-lived excited state is analyzed; the analytical results are compared with experimental results. We propose a four-level model and take into account the effects of both excited-state absorption and pump propagation to explain the experimental results, which could not be explained by the models proposed previously. The numerical result predicts that the value of the phase-conjugate reflectivity as a function of the pump intensity is maximum at a certain absorbance (as absorbance increases) that is dependent on the cross section of the excited-state absorption. The present analysis explains most observations in the experiment, which was performed with a saturable-dye-doped polymer film as the saturable absorbing medium.