Z-scan study of the thermo-optical effect

Abstract

In the case of cw Gaussian illumination, the thermo-optical n₂ cannot be characterised by a constant value. It is shown that, if absorption has both linear and nonlinear contributions, the thermo-optical n₂ consists of a position- and power-dependent term. Hence analytical formulae that assume a constant n₂ are no longer valid for the Z-scan fitting. In this paper a new Z-scan theory is introduced, which is applicable to the thermo-optical effect in the presence of both linear and nonlinear absorption and an arbitrary extent of optical nonlinearity. The calculation technique can be used for large sample thickness too, by dividing it into thin slices. It was found that inside one slice, the distribution of the light-induced refraction is similar to that for the case of graded index media. The propagation can be described through the transformation of the q-parameter. It is demonstrated that the Z-scan technique makes the sensitive measurement of the linear absorption coefficient possible. The linear and nonlinear absorption coefficients were experimentally determined for Mg doped LiNbO₃ to be α=0.6 m^-1 and β=2.9×10^-9 m/W, respectively.