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Laser Physics

Theoretical study on nonlinear properties of four level systems under nano-second illumination

Srinivasa Rao Allam

Published Apr 9, 2015• 12 citations
Publisher

Abstract

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.

DOI
10.1088/1054-660x/25/5/055701

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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 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.
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.
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.