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Nonlinear Optics: Materials, Fundamentals, and Applications. Technical Digest. Postconference Edition. TOPS Vol.46 (IEEE Cat. No.00CH37174)

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

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

Published Nov 7, 2002• 0 citations
Publisher

Abstract

Using an analytical approach we quantitatively very estimate the effects of the pulse shape and of material parameters on the intensity-dependent transmittance of reverse saturable absorbers. Irradiance levels required to fully exploit the nonlinearity are estimated.
DOI
10.1109/nlo.2000.883619

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

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 21, 2016•4 citations
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.
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.
As a high-intensity monochromatic light pulse passes through a material containing two-level systems, saturable absorption or amplification of the radiation may occur. The resultant ``shaping'' of the intensity-vs-time curve as a function of distance into the sample is the subject of this paper. A theory is developed based on the Einstein rate equations, and pulse-shape functions are derived which depend on the absorption and loss coefficients of the material, the relaxation time of the systems, the input-pulse intensity and width, the initial ``state-of-pump'', and number density of absorbers in the sample.