Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Two-step four-photon absorption

Bing Gu, Wei Ji

Published Jun 24, 2008• 22 citations
Publisher

Abstract

We report a theoretical investigation of effective four-photon absorption (4PA) process and propose a two-step 4PA model of three-photon- induced excited-state absorption (ESA). Based on three-level rate-equation theory, we find an analytical result for the effective 4PA coefficient that depends on the three-photon absorption (3PA) cross-section, excited-state photophysical properties, and laser pulse duration. We present the analytical theory of the z-dependent nonlinear transmission for straightforwardly yet unambiguously evaluating the 3PA and effective 4PA coefficients simultaneously.

DOI
10.1364/oe.16.010208

Related papers

Dynamics of two-photon-induced three-photon absorption in nanosecond, picosecond, and femtosecond regimes

Bing Gu, Kai Lou, Hui‐Tian Wang +1 more

Based on five-level rate-equation theory, we develop the laser-pulse-duration dependence of two-photon-absorption-induced singlet and triplet excited-state absorptions (ESAs). We present analytical expressions for the effective three-photon absorption coefficients caused by both singlet and triplet ESAs under the pulsed excitation on time scales from femtoseconds to microseconds. We demonstrate that the triplet ESA is predominant with longer laser pulses (microseconds to tens of nanoseconds) and that the resultant nonlinear absorption (NLA) can be adequately interpreted by a simplified four-level model. Under the excitation of picosecond laser pulses, generally speaking, the competition between singlet and triplet ESAs is observable. In this instance, the photodynamics of the system can be understood by a five-level model. In the femtosecond regime, however, a three-level model is validated in the prediction of NLA, because the triplet ESA becomes negligible.

Optics Letters•Jan 28, 2010•30 citations

Theory of three-step absorption of three light pulses

Inna Rebane

The theory of the absorption of three light pulses with an arbitrary duration in four-level systems is proposed. The pulses are in resonance with the corresponding transitions. By using the time-dependent perturbation theory the probability that the fourth level is excited at the moment t is found. The possible absorption lines and parameters on which their widths depend on are analysed.

Journal of Physics Conference Series•May 19, 2017•0 citations

Analytical approach to dynamics of reverse saturable absorbers

Andrey E. Kobyakov, David J. Hagan, Eric W. Van Stryland

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.

Journal of the Optical Society of America B•Nov 1, 2000•36 citations

Time-dependent theory of three-step absorption of three light pulses; pp. 54–63

Inna Rebane

The time-dependent theory of the three-step absorption of three different light pulses in the electronic four-level systems is considered using the time-dependent perturbation theory. The first, the second, and the third pulse are in resonance with transitions from level 0 to level 1, from level 1 to level 2, and from level 2 to level 3, respectively. The spectral and temporal behaviour of the probability that the fourth level is excited at the moment of time t depends on the energy relaxation constants of the excited electronic levels, the frequencies of the maxima, the spectral widths (and so the durations) of the light pulses, and the time delays between the pulses. To conclude, there are 12 parameters that affect the spectra in the simple model used. We calculate and analyse the case where the frequencies of the maxima of the first and the second pulse are fixed and the frequency of the maximum of the third pulse varies. On the whole, three lines may exist, one of which corresponds to the coherent contribution and the others do not.

Proceedings of the Estonian Academy of Sciences•Jan 26, 2017•1 citation

Identification of strong one-step two-photon absorption in a cascade three-level system

Ji‐Cai Liu, Lei Chen, Ye-Qi Zhang

The ultrafast one-step and two-step two-photon absorption processes in a cascade three-level system induced by a strong femtosecond laser pulse is studied. The strong change of the population in the two-photon absorption state at the zero points of the first derivative of the population in the real intermediate state shows straightforwardly in time domain the footprint of the coherent one-step two-photon absorption.

Journal of Physics Conference Series•Apr 10, 2014•0 citations

Excited-state nonlinear absorption and its application in photonic technology

Li Chun-Fei, Jinhai Si, Yang Miao +1 more

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.

Acta Physica Sinica (Overseas Edition)•Aug 1, 1995•5 citations
We report a theoretical investigation of effective four-photon absorption (4PA) process and propose a two-step 4PA model of three-photon- induced excited-state absorption (ESA). Based on three-level rate-equation theory, we find an analytical result for the effective 4PA coefficient that depends on the three-photon absorption (3PA) cross-section, excited-state photophysical properties, and laser pulse duration. We present the analytical theory of the z-dependent nonlinear transmission for straightforwardly yet unambiguously evaluating the 3PA and effective 4PA coefficients simultaneously.
Based on five-level rate-equation theory, we develop the laser-pulse-duration dependence of two-photon-absorption-induced singlet and triplet excited-state absorptions (ESAs). We present analytical expressions for the effective three-photon absorption coefficients caused by both singlet and triplet ESAs under the pulsed excitation on time scales from femtoseconds to microseconds. We demonstrate that the triplet ESA is predominant with longer laser pulses (microseconds to tens of nanoseconds) and that the resultant nonlinear absorption (NLA) can be adequately interpreted by a simplified four-level model. Under the excitation of picosecond laser pulses, generally speaking, the competition between singlet and triplet ESAs is observable. In this instance, the photodynamics of the system can be understood by a five-level model. In the femtosecond regime, however, a three-level model is validated in the prediction of NLA, because the triplet ESA becomes negligible.
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.
The time-dependent theory of the three-step absorption of three different light pulses in the electronic four-level systems is considered using the time-dependent perturbation theory. The first, the second, and the third pulse are in resonance with transitions from level 0 to level 1, from level 1 to level 2, and from level 2 to level 3, respectively. The spectral and temporal behaviour of the probability that the fourth level is excited at the moment of time t depends on the energy relaxation constants of the excited electronic levels, the frequencies of the maxima, the spectral widths (and so the durations) of the light pulses, and the time delays between the pulses. To conclude, there are 12 parameters that affect the spectra in the simple model used. We calculate and analyse the case where the frequencies of the maxima of the first and the second pulse are fixed and the frequency of the maximum of the third pulse varies. On the whole, three lines may exist, one of which corresponds to the coherent contribution and the others do not.
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.