THE SOCIETY FOR PHOTONICS NEWS Chaotic Microcavity Lasers Discrete Optics in Liquid Crystalline Lattices

We report a sensitive single-beam technique for measuring both the nonlinear refractive index and nonlinear absorption coefficient for a wide variety of materials. We describe the experimental details and present a comprehensive theoretical analysis including cases where nonlinear refraction is accompanied by nonlinear absorption. In these experiments, the transmittance of a sample is measured through a finite aperture in the far field as the sample is moved along the propagation path (z) of a focused Gaussian beam. The sign and magnitude of the nonlinear refraction are easily deduced from such a transmittance curve (Z-scan). Employing this technique, a sensitivity of better than λ/300 wavefront distortion is achieved in n2 measurements of BaF2 using picosecond frequencydoubled Nd:YAG laser pulses. In cases where nonlinear refraction is accompanied by nonlinear absorption, it is possible to separately evaluate the nonlinear refraction as well as the nonlinear absorption by performing a second Z scan with the aperture removed. We demonstrate this method for ZnSe at 532 nm where two-photon absorption is present and n2 is negative. Introduction Recently we reported a single-beam method for measuring the sign and magnitude of n2 that has a sensitivity comparable to interferometric methods [1]. Here, we describe this method in detail and demonstrate how it can be applied and analyzed for a variety of materials. We also extend this method to the measurement of nonlinear refraction in the presence of nonlinear absorption. Thus, this method allows a direct measurement of the nonlinear absorption coefficient. In addition, we present a simple method to minimize parasitic effects due to the presence of linear sample inhomogeneities. Previous measurements of nonlinear refraction have used a variety of techniques including nonlinear interferometry [2], [3], degenerate four-wave mixing [4], nearly degenerate three-wave mixing [5], ellipse rotation [6], and beam distortion measurements [7], [8], The first three methods, namely, nonlinear interferometry and wave mixing, are potentially sensitive techniques, but all require relatively complex experimental apparatus. Beam distortion measurements, on the other hand, are relatively insensitive and require detailed wave propagation analysis. The technique reported here is based on the principles of spatial beam distortion, but offers simplicity as well as very high sensitivity. We will describe this simple technique, referred to as a “Z-scan,” in Section II. Theoretical analyses of Z-scan measurements are given in Section III for a “thin” nonlinear medium. It will be shown that for many practical cases, nonlinear refraction and its sign can be obtained from a simple linear relationship between the observed transmittance changes and the induced phase distortion without the need for performing detailed calculations. In Section IV, we present measurements of nonlinear refraction in a number of materials such as CS2 and transparent dielectrics at wavelengths of 532 nm, 1.06 μm, and 10.6 μm. In CS2 at 10 μm, for example, both thermooptical and reorientational Kerr effects were identified using nanosecond and picosecond pulses, respectively. Furthermore, in Section V, we will consider the case of samples having a significant absorptive nonlinearity as well as a refractive one. This occurs in, for example, two-photon absorbing semiconductors. It will be shown that both effects can easily be separated and measured in the Z-scan scheme. We also show how effects of linear sample inhomogeneities (e.g., bulk index variations) can be effectively removed from the experimental data. The Z-Scan Technique Using a single Gaussian laser beam in a tight focus geometry, as depicted in Fig. 1, we measure the transmittance of a nonlinear medium through a finite aperture in the far field as a function of the sample position z measured with respect to the focal plane. The following example will qualitatively elucidate how such a trace (Zscan) is related to the nonlinear refraction of the sample. Assume, for instance, a material with a negative nonlinear refractive index and a thickness smaller than the diffraction length of the focused beam (a thin medium). This can be regarded as a thin lens of variable focal length. Starting the scan from a distance far away from the focus (negative z), the beam irradiance is low and negligible nonlinear refraction occurs; hence, the transmittance (D2/D1, in Fig. 1) remains relatively constant. As the sample is brought closer to focus, the beam irradiance increases, leading to self-lensing in the February 2007 IEEE LEOS NEWSLETTER 17 Sensitive Measurement of Optical Nonlinearities Using a Single Beam Special 30th Anniversary Feature Mansoor Sheik-Bahae, Member, IEEE, Ali A. Said, Tai-Huei Wei, David J. Hagan, Member, IEEE and E. W. Van Stryland, Senior Member, IEEE MANUSCRIPT RECEIVED NOVEMBER 6, 1989. THIS WORK WAS SUPPORTED BY THE NATIONAL SCIENCE FOUNDATION UNDER GRANT ECS-8617066, THE DARPA/CNVEO, AND THE FLORIDA HIGH TECHNOLOGY AND INDUSTRY COUNCIL. THE AUTHORS ARE WITH THE CENTER FOR RESEARCH IN ELECTRO-OPTICS AND LASERS (CREOL), UNIVERSITY OF CENTRAL FLORIDA, ORLANDO. FL 32826. IEEE LOG NUMBER 8933825. Figure 1: The Z-scan experimental apparatus in which the ratio D2/D1 is recorded as a function of the sample position z. BS Sample Aperture D1 −Z +Z D2 21leos01.qxd 1/31/07 5:05 PM Page 17