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

Journal of Nonlinear Optical Physics & Materials

ALL-OPTICAL POWER LIMITING

Mary J. Potasek, S. Kim, David W. McLaughlin

Published Sep 1, 2000• 12 citations
Publisher

Abstract

We derived a numerical technique for the propagation of the electromagnetic field in a five-level reverse saturable absorber including the nonlinear Kerr effect and dispersion. The numerical method combines the split step beam propagation method and the Crank–Nicholson method. Using our numerical technique we observed new behavior, not previously observed nor predicted to our knowledge, including the temporal splitting caused by the dynamics of the carrier densities in a reverse saturable absorber and the enhancement of absorption due to the Kerr nonlinearity. Our numerical calculation enables the prediction of nonlinear absorption using material parameters such as the absorption cross-sections and decay rates. We can also investigate the interplay between the optical pulse properties such as the temporal pulse width, spatial radius, incident energy and the carrier dynamics and nonlinear absorption of the reverse saturable absorber.

DOI
10.1142/s0218863500000224

Related papers

Propagation of the electromagnetic field in optical-limiting reverse-saturable absorbers

S. Kim, David W. McLaughlin, Mary J. Potasek

Reverse-saturable absorbers are of considerable interest for optical limiting. Using the electric dipole perturbation, we derived the rate equation for a five-level system describing reverse-saturable absorbers. Traditional theories for the propagating laser beam in these materials are expressed in terms of the optical intensity. However, with the introduction of high-power short-pulsed lasers, the propagation of light in these materials may be subject to nonlinear phenomena such as self-focusing and self-phase modulation. Furthermore, conventional theories treat the laser light as a continuous wave or as a very broad temporal pulse in which dispersive effects are neglected. In order to incorporate these other nonlinear or dispersive effects, and therefore determine their influence in reverse-saturable absorbers, we derived an equation for the propagation of the electromagnetic field, rather than the intensity, coupled to the rate equations for a five-level system. We also coupled our theory to experimentally measurable parameters for these materials and detailed the various physical approximations used to obtain the rate equations.

Physical Review A•Jan 11, 2000•13 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

Picosecond optical limiting in reverse saturable absorbers: a theoretical and experimental study

Richard S. Lepkowicz, Andrey E. Kobyakov, David J. Hagan +1 more

We theoretically and experimentally study absorption of picosecond laser pulses in materials described by a four-level system that exhibit reverse saturable absorption (RSA). Using an approximate solution to the rate equations, we derive, analyze, and verify, numerically and experimentally, a single dynamical equation for the spatial evolution of the pulse fluence that includes both the rate equations and the propagation equation. This analytical approach considerably simplifies the study of optical limiting with picosecond pulses and helps to predict the behavior of the nonlinear transmittance, the level of output signal clamping, and a possible turnover from RSA to saturable absorption that restricts the performance of optical limiters based on RSA. The results obtained can also be used to characterize RSA materials by the pump–probe technique.

Journal of the Optical Society of America B•Jan 1, 2002•37 citations

Optical limiting with reverse saturable absorbers

Stephen W. McCahon, Lee W. Tutt, Marvin B. Klein +1 more

We have used a physically realistic model to investigate the spatial and temporal behavior of reverse saturable absorption and optical limiting in organometallic cluster compounds. An algorithm was developed to solve numerically the model and is used for the case of a collimated beam to determine various material parameters by fitting theory to experimental optical limiting data. Using these parameters, the algorithm was then extended to the case of converging and/or diverging beams.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 1, 1990•9 citations

Propagation of optical pulses in a saturable absorber

L. Davis, Yung‐Sen Lin

The coupled Maxwell-Schrodinger equations are used to describe propagation of a pulse in a nonlinear absorbing medium. The absorber is assumed to be comprised of a homogeneously broadened system of two-level atoms that are exactly resonant with the field. Numerical calculations have been performed for incident pulses of hyperbolic-secant shape and of duration that is long compared to the atomic phase-memory time. Selected values of input intensity are considered. For intensities below a certain level the calculations nearly agree with rate-equation predictions, but as the incident intensity is increased we find that optical nutation comes into play. The nutation effect leads to pulse breakup as the packet penetrates into the medium. An analytical calculation, for the case of an applied optical field of step-function form, has been performed in order to provide additional insight about the intensity threshold for nutation.

IEEE Journal of Quantum Electronics•Dec 1, 1973•7 citations

Effect of laser pulse shape on optical limiting properties of reverse saturable absorbers

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

Using an analytical approach we quantitatively estimate the effects of the pulse shape and material parameters on the intensity-dependent transmittance of reverse saturable absorbers. Irradiance levels required to fully exploit the nonlinearity are estimated.

Nonlinear Optics•Jan 1, 2000•0 citations
We derived a numerical technique for the propagation of the electromagnetic field in a five-level reverse saturable absorber including the nonlinear Kerr effect and dispersion. The numerical method combines the split step beam propagation method and the Crank–Nicholson method. Using our numerical technique we observed new behavior, not previously observed nor predicted to our knowledge, including the temporal splitting caused by the dynamics of the carrier densities in a reverse saturable absorber and the enhancement of absorption due to the Kerr nonlinearity. Our numerical calculation enables the prediction of nonlinear absorption using material parameters such as the absorption cross-sections and decay rates. We can also investigate the interplay between the optical pulse properties such as the temporal pulse width, spatial radius, incident energy and the carrier dynamics and nonlinear absorption of the reverse saturable absorber.
Reverse-saturable absorbers are of considerable interest for optical limiting. Using the electric dipole perturbation, we derived the rate equation for a five-level system describing reverse-saturable absorbers. Traditional theories for the propagating laser beam in these materials are expressed in terms of the optical intensity. However, with the introduction of high-power short-pulsed lasers, the propagation of light in these materials may be subject to nonlinear phenomena such as self-focusing and self-phase modulation. Furthermore, conventional theories treat the laser light as a continuous wave or as a very broad temporal pulse in which dispersive effects are neglected. In order to incorporate these other nonlinear or dispersive effects, and therefore determine their influence in reverse-saturable absorbers, we derived an equation for the propagation of the electromagnetic field, rather than the intensity, coupled to the rate equations for a five-level system. We also coupled our theory to experimentally measurable parameters for these materials and detailed the various physical approximations used to obtain the rate equations.
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.
We theoretically and experimentally study absorption of picosecond laser pulses in materials described by a four-level system that exhibit reverse saturable absorption (RSA). Using an approximate solution to the rate equations, we derive, analyze, and verify, numerically and experimentally, a single dynamical equation for the spatial evolution of the pulse fluence that includes both the rate equations and the propagation equation. This analytical approach considerably simplifies the study of optical limiting with picosecond pulses and helps to predict the behavior of the nonlinear transmittance, the level of output signal clamping, and a possible turnover from RSA to saturable absorption that restricts the performance of optical limiters based on RSA. The results obtained can also be used to characterize RSA materials by the pump–probe technique.
The coupled Maxwell-Schrodinger equations are used to describe propagation of a pulse in a nonlinear absorbing medium. The absorber is assumed to be comprised of a homogeneously broadened system of two-level atoms that are exactly resonant with the field. Numerical calculations have been performed for incident pulses of hyperbolic-secant shape and of duration that is long compared to the atomic phase-memory time. Selected values of input intensity are considered. For intensities below a certain level the calculations nearly agree with rate-equation predictions, but as the incident intensity is increased we find that optical nutation comes into play. The nutation effect leads to pulse breakup as the packet penetrates into the medium. An analytical calculation, for the case of an applied optical field of step-function form, has been performed in order to provide additional insight about the intensity threshold for nutation.