Materials Science and Engineering B 165 (2009) 182–185 Contents lists available at ScienceDirect Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb Effects of nonlinear absorption on the Z-scan technique through beam dimension measurements G. Tsigaridas a,b,∗ , P. Persephonis a , V. Giannetas a a Department of Physics, University of Patras, GR-26504 Patras, Greece b Technological and Educational Institute of Lamia, 3rd Km of Lamia-Athens, Old National Road, GR-35100 Lamia, Greece article info Article history: Received 21 August 2008 Received in revised form 21 August 2009 Accepted 2 September 2009 Keywords: Optical properties Optical non-linearity Z-scan abstract Recently we have proposed a novel Z-scan technique for measuring refractive nonlinearities, based on the direct measurement of the variations of the beam dimensions in the far field. In the present work this approach is extended to the case of simultaneous presence of nonlinear refraction and absorption, enabling the complete characterization of the materials regarding their nonlinear optical properties. In more detail we have found that nonlinear absorption induces asymmetry on the peak-valley configuration of the Z-scan curves, both in the cases of circular and elliptic Gaussian beams. We have also shown that this asymmetry grows exponentially with the values of the nonlinear phase shift and the nonlinear absorption coefficient. Further, we have found that the effects of nonlinear absorption on the Z-scan curves can be suppressed by multiplying the radius Z-scan plot with an open Z-scan curve. This result can be used for determining the nonlinear refractive index of the material through a simplified relation. © 2009 Elsevier B.V. All rights reserved. 1. Introduction A sensitive and experimentally simple method for measuring nonlinear refraction and absorption is the well-known open Z-scan technique, introduced by Sheik-Bahae et al. [1] in 1990, and further elaborated by many other authors [2–24]. Other techniques have also been developed for measuring third-order optical nonlinear- ities as third harmonic generation [25,26], degenerate four-wave mixing [27,28], interferometric techniques [29], beam self-bending [30], etc. The configuration of a Z-scan experiment is shown in Fig. 1.A thin sample of the material is moved across the focus of a Gaussian laser beam and the transmittance is recorded as a function of the sample position relative to the beam focus. Due to the refractive non-linearity the material acts as a thin lens changing the beam dimensions as the sample moves across the focus. These changes are translated into variations of the beam energy transmitted through the pinhole and provide information for determining the nonlinear refractive index of the material. On the other hand, if the pinhole is removed, the variations of the transmitted energy due to nonlinear absorption provide adequate information for determin- ing the nonlinear absorption coefficient of the material. However, the original Z-scan technique has some serious drawbacks as ∗ Corresponding author. E-mail address: gtsig@upatras.gr (G. Tsigaridas). 1. High sensitivity in beam pointing instability and energy fluctu- ations (due to the use of the pinhole). 2. Complexity in the calculations for determining the nonlinear optical coefficients (because integration is required to calculate the transmitted energy). 3. Restriction to the case of circular Gaussian beams (because the pinhole cannot follow the changes in the shape of the beam). Therefore, a novel Z-scan technique has been introduced based on the direct measurement of the beam dimensions in the far field [23,24]. The experimental setup for this technique is shown in Fig. 2. In this case the measured quantities are the beam dimensions in the far field, defined as the distances from the beam cen- ter to the points where the intensity drops to a certain fraction q of its on-axis value. Thus, in the case of a circular Gaussian beam the measured quantity is the beam radius, while in the case of an elliptic Gaussian beam the measured quantities are the lengths of the principal semiaxes. The intensity profile of the beam was obtained from the electricfield profile through the relation I(x,y;z,t) = cε 0 n 0 |E(x,y;z,t)| 2 /2, where c is the speed of light in the vacuum, ε 0 the permittivity of the vacuum, and n 0 the linear refrac- tive index of the medium where the beam propagates. The electric field of the beam after passing through the nonlinear material and propagated to a desired distance D was calculated using the Gaus- sian decomposition method, as described in the articles [9,10,24]. Some characteristic curves, both for circular and elliptic Gaus- sian beams are shown in Fig. 3. It should be noted that in the case of an elliptic (astigmatic) Gaussian beams two Z-scan curves are 0921-5107/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2009.09.001