Energy band-gap dependence of two-photon absorption

We present measurements of the two-photon absorption coefficients /2 of 10 different semiconductors having band-gap energies between 1.4 and 3.7 eV. We find that 12 varies as Eg- 3 , as predicted by theory. In addition, the absolute values of 02 agree with theory, which includes the effect of nonparabolic bands, the average difference being less than 26%. This agreement permits confident predictions of two-photon absorption coefficients of other materials at other wavelengths. The ever-increasing role of semiconductors in lightwave technology has created a pressing demand for the characterization of the nonlinear-optical properties of these materials. Semiconductors are attractive as elements in nonlinear-optical devices because of their large and potentially extremely fast optical nonlinearities. A careful study of these macroscopic nonlinearities should allow one to determine the dependence of these nonlinearities on fundamental microscopic mechanical and electronic material properties (e.g., band gap, carrier lifetime, carrier effective mass). The data base formed by this information would then allow one not only to tabulate the materials that exhibit large nonlinearities but also to predict the specific material parameters that give rise to these high nonlinearities. This predictive capability is extremely important from the standpoint of searching for materials with large nonlinearities. A study of the nonlinear-optical properties of several semiconductors is presented here, and a relationship between the two-photon absorption coefficient (/32) and other material properties is verified. Ten different materials were experimentally studied for which the incident photon energy hw is less than the direct band-gap energy Eg but greater than Eg/2, so that two-photon absorption (2PA) is allowed.' Both 1.06and 0.53-jum picosecond pulses are used in transmission experiments, similar to those used previously by Bechtel and Smith, 2 on semiconductors with Eg ranging from 1.4 to 3.7 eV. We find that 02 is given by