Determination of nonlinear absorption and refraction by single Z-scan method

We report a simplified Z-scan technique based on a study on the symmetric features of a typical Z-scan curve. The contributions from the two-photon absorption (TPA) and the nonlinear refraction (NLR) are easily separated from a closed-aperture Z-scan curve using this method. And the determination of the two nonlinearities is simplified and unambiguous. We demonstrate this method on ZnSe, CdS, and ZnTe semiconductors with 120-fs laser pulses. And the influence from the uncertainty of the focal plane (Z = 0) position is discussed. It is also found that the TPA coefficient can be obtained independently without knowing the exact location of the focal point. PACS: 42.65.An; 78.20.Ci; 78.40.Fy Materials that possess third-order optical nonlinearities have been investigated extensively, for their application to highspeed all-optical switching devices [1]. To assess a material for the above application, one must characterize its index of non-linear refraction (NLR) and two-photon absorption (TPA) coefficient [2]. These two parameters may be determined by Z-scan technique [3], in which a sample is scanned near the focal region of a focused laser beam. As the sample is moved along the propagation direction of the laser beam, Z-axis, it consequently experiences a phase and intensity modulation, which can be observed on its transmittance measured as a function of the sample position (z). If all the transmitted light is measured, only TPA affects the Z-scan. In this case, it refers to as open-aperture Z-scan. If part of the transmitted light is detected due to the presence of an aperture in front of the detector, both NLR and TPA manifest themselves on a so-called closed-aperture Z-scan. To extract the NLR index, one must take the TPA value that is obtained from an open-aperture Z-scan, into the account in the closedaperture Z-scan modeling [3]. In this paper, we present a general study on Z-scan curves measured with the aperture. We have found that, for laser ∗Corresponding author. beams with circular symmetry and low irradiances, the normalized transmittance T(z) can be expressed by 1+T∆Φ(z)+ T∆Ψ (z), where T∆Φ(z) originating from NLR is an odd function of z; and T∆Ψ (z) caused by TPA is an even function of z. Consequently, T∆Φ(z) and T∆Ψ (z) are easily separated from a closed-aperture Z-scan, T(z), by the operations of [T(z)− T(−z)]/2 and [T(z)+ T(−z)]/2− 1, respectively. Thus, instead that both openand closed-aperture Z-scans must be performed [3], one can obtain information on the NLR index (γ ) and TPA coefficient (β) only from a single closedaperture Z-scan. This simplified method is demonstrated on ZnSe, CdS, and ZnTe semiconductors. We also discuss possible sources for experimental errors in implementation and how to minimize these errors.