Wavelength Dispersion of Optical Power Limiting in Stilbene3 Analyzed within a Three Level Model
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'Laboratoire de Spectrom6trie Physique, Univ. J.Fourier, BP 87, 38402 St Martin d'Hbres (France).
ABSTRACT Nonlinear transmission in a dye (stilbene3) exhibiting two-photon absorption (TPA) has been studied has a function of wavelength, in the visible range using nanosecond laser pulses. The results have been analyzed within a three level model: the first excited one is populated by TPA and is excited toward an upper level (excited state absorption, ESA). The TPA and ESA spectra obtained by optical limiting (6~10-46 cm 4s photon'molecule'; 7_ 10-116 cm 2-) are in good agreement with those determined by two-photon fluorescence and Kerr ellipsometry. Thus, nonlinear transmission appears as a useful technique to estimate the TPA and ESA contributions in optical limiting. INTRODUCTION Since two decades, much work have been devoted to optical limiting, and entire conferences have been dedicated to that subject."' Different phenomena are used for optical limiting, such as light scattering due to refractive index inhomogeneities induced by solvent vaporization around small absorbing particles (Carbon Black Suspensions), beam fanning in
photorefractive materials, nonlinear absorption in absorbing materials (Reverse Saturable Absorption, RSA) or in transparent ones (Two-Photon Absorption,) materials. Though RSA materials have a rather high limiting power extending to pulses of few microsecond duration, the, have the drawback of high absorbing and highly colored,5 unless mixtures are used. On the opposite hand, TPA materials are transparent and colorless or have a faint yellow color. The magnitude of their two-photon absorption has been studied experimentally 6 and theoretically.' In the first studies, the nonlinear transmission was interpreted in terms of pure TPA and it was pointed out that the TPA cross-section values differed from nearly two orders of magnitude between picosecond and nanosecond laser pulses. It was latter recognized that not only TPA was involved in nonlinear transmission but that there was a very strong contribution of the reabsorption of the excited state (ESA), populated by TPA. 8 The dependence of the effective TPA cross-section upon laser pulse duration originates from the fact that it needs tens or hundredths of picoseconds to populate significantly this state. In a previous paper9 we have described optical limiting wavelength dependence of Stilbene3 in the visible range under nanosecond pulses and have analyzed the results within a phenomenological three-photon absorption model. In the present work we have re-interpreted them within a three level model, and compared the TPA and ESA spectra with those obtained by the two-photon fluorescence and the Kerr ellipsometry techniques'° respectively. 357 Mat. Res. Soc. Symp. Proc. Vol. 597 @2000 Materials Research Society
THEORY Phenomenological model The nonlinear transmission can be described from a phenomenological point of view by expanding the attenuation into successive powers of the intensity: z 2 3
Assuming I to be constant (top hat beam) and
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