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Journal of the Optical Society of America B

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

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

Published Jan 1, 2002• 37 citations
Publisher

Abstract

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.

DOI
10.1364/josab.19.000094

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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 dynamic processes of reverse saturable absorption (RSA) in a solution of C60 are studied in detail by use of rate equations and the light-propagation equation for a five-energy-level model. The RSA experimental results for C60 in toluene solution with a nanosecond–picosecond Nd:YAG laser at 532 nm are consistent with the theoretical simulations. Effects of sample concentration and thickness on RSA and contributions of the singlet and triplet excited states to RSA for various laser-pulse widths and wavelengths are also analyzed. Finally, an all-optical switch based on excited-state nonlinear absorption and the pump-probe technique is implemented.
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.
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.
The dynamic and steady-state processes of the reverse saturable absorption (RSA) and the related optical limiting (OL) and optical bistability (OB) in metallophthalocyanine have been studied in detail using rate equations and the light-propagation equation. The experiments for demonstrating RSA, OL, and OB in a copper phthalocyanine (CuPc) solution with a Q-switched, frequency-doubled neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser were accomplished. The experimental results were consistent with the dynamic theoretical simulations, also approximately in accordance with the expression of RSA derived from the same equations at the steady-state condition.
The nonlinear optical absorption of a probe field is investigated in a three-level V-type quantum system under a pump-probe configuration. It is demonstrated that the system exhibits saturable absorption (SA) behavior. By introducing an indirect incoherent pumping field on the probe transition, we show that the incoherent field critically influences the switching from SA to reverse saturable absorption (RSA). This switching enables the system to function as an optical limiter, protecting sensors and seekers against high-power optical pulses. The results reveal that key parameters-such as the intensity of the incoherent field, detuning, and coupling field strength-can be precisely tuned to modulate optical limiting characteristics, including threshold intensity and operational range. The underlying physical mechanism is elucidated through the derivation and analysis of an analytical expression for the nonlinear absorption. The output response is further validated through calculations based on the open-aperture Z-scan technique. Overall, this study highlights the crucial role of incoherent field engineering in tailoring optical limiting behavior, providing a versatile framework for advanced photonic applications.
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.