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Science China Mathematics

Excited-state nonlinear absorption and its description using density matrix theory

Ruibo Wang

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

A density matrix theory with a ten-energy-level model in the molecular system irradiated bya pulsed laser at non-resonant wavelength is proposed. The reverse saturable absorption under ns and pspulses and the transformation from reverse saturable absorption to saturable absorption under strong ps pulses are described by this model. The correctness of the theoretical model is proved by experiments.

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Excited-state nonlinear absorption in multi-energy-level molecular systems

Chunfei Li, Jinhai Si, Yang Miao +2 more

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 ${\mathrm{C}}_{60}$ 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.

Physical Review A•Jan 1, 1995•45 citations

Excited-state nonlinear absorption and its application in photonic technology

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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.

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The transformation of density matrix of four-level system in solid laser

Tang Mei-juan

Solid laser is a four-level system.This paper utilizes theories of quantum mechanics and Kraus operator,to analysis the four-level system which in the case of absorption as well as radiation.The object of the research is to probe into the transformation properties of density matrix.The result shows that probability of absorption and radiation condition is satisfied,between the second excited state and the first excited state forms reversion of particles and prepares for producing laser.It also shows that when particles transform from the second excited state to the first excited state and the first excited state to the ground state at very high probability,the system produces laser.

Jiguang zazhi•Jan 1, 2006•0 citations
A density matrix theory with a ten-energy-level model in the molecular system irradiated bya pulsed laser at non-resonant wavelength is proposed. The reverse saturable absorption under ns and pspulses and the transformation from reverse saturable absorption to saturable absorption under strong ps pulses are described by this model. The correctness of the theoretical model is proved by experiments.
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 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.
The nonlinear absorption properties of organic materials in nanosecond (ns), picoseond (ps) and femtosecond (fs) regime were theoretically investigated by rate equations based on multilevel organic molecular system respectively. The results show that the reverse saturable absorption (RSA) phnomenon is mainly due to the absorption contribution of the triplet first excited state in the ns regime, and that of the singlet first excited state in the ps regime, both of which are a third-order nonlinear phenomena. The RSA phnomenon in fs regime is mainly due to the excited state absorption (ESA) induced by two-photon absorption (TPA), which is a fifth-order nonlinear phenomenon.
In this work, we report the theoretical results of the single beam transmittance of an absorber by employing the rate equation approach, utilizing 10 ns laser pulses. With the appropriate choice of lifetimes of the participating levels in the transition and their corresponding absorption cross-section, it is possible to control the onset of different phenomena like saturable absorption, reverse saturable absorption, and double saturable absorption. We discuss how to increase the saturable and optical limiting nature of the system by appropriate changes of spectroscopic parameters. We discuss the estimation of spectroscopic terms from their contribution in the single beam transmittance.
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.
Solid laser is a four-level system.This paper utilizes theories of quantum mechanics and Kraus operator,to analysis the four-level system which in the case of absorption as well as radiation.The object of the research is to probe into the transformation properties of density matrix.The result shows that probability of absorption and radiation condition is satisfied,between the second excited state and the first excited state forms reversion of particles and prepares for producing laser.It also shows that when particles transform from the second excited state to the first excited state and the first excited state to the ground state at very high probability,the system produces laser.