Open Z-scan analytical model for multiphoton absorption
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RESEARCH ARTICLE
Open Z-scan analytical model for multiphoton absorption Ferhat Kessi1 • Hamadouche Naima2
Received: 21 December 2018 / Accepted: 17 May 2020 Ó The Optical Society of India 2020
Abstract We present an open-aperture elliptic Gaussian beam Z-scan theory for thin nonlinear optical material possesses simultaneous ðN nÞ nonlinear absorption processes with residual linear absorption. We show that an approximate analytical but closed-form expression for the normalized energy transmittance is possible by means of the weak nonlinearities approximation. The elaborate theory can be used to fit the open Z-scan traces allowing the determination of material’s nonlinear absorption coefficients and incident Gaussian beam parameters. The contribution of absorptions of distinct order can also be identified, separated and compared. Keywords Elliptic Gaussian beam Multiphoton absorption Nonlinear absorption coefficient Transmitted power Normalized transmittance
Introduction Multiphoton absorption is a nonlinear process in which two or more photons of indistinguishable or different frequencies are simultaneously absorbed by a material due its exposure to high intensity laser light [1]. We can have a single-photon process or many distinctive single-photon processes at the same time. In both cases, multiphoton & Ferhat Kessi [email protected] Hamadouche Naima [email protected] 1
Department of Technology, A. Mira University, Bejaia, Algeria
2
LAMOS, A. Mira University, Bejaia, Algeria
nonlinear make reference to the modification in transmittance of the material as a function of light intensity. Due to the many different effects it produces, multiphoton absorption is of particular interest for various scientific and technological applications such as laser-induced damage [2, 3], fluorescence microscopy [4], optical power limiting [5, 6], fluorescence up-conversion [7, 8], Up converting lasing [9], luminescence imaging [10] and multiphoton spectroscopy [11]. There are numerous experimental techniques for characterizing second-order nonlinear optical processes in materials such as nonlinear absorption. Among them, the open Z-scan method furnishes the simplest and most sensitive experimental technique. This technique initially designed for measurements of two-photon absorption remains valid for those of multiphoton absorption. The basic open Z-scan technique has been well described by Mansoor Cheikh-Bahae et al. [12–14], and a brief description of the technique is given here. Along the axis of a focused Gaussian beam assimilated to the Z direction of the laboratory reference frame, a thin sample is translated in the region around the laser beam’s focal point. In this procedure, the transmitted energy in the far field is measured for each position z of the sample. The term ‘‘open aperture’’ means that the detector collects the entire transmitted light from the sample. The adjustment of the obtained open Z-scan traces by a suitable theoretical expression preliminarily elaborated makes it possible in prin
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