Simultaneous measurement of real and imaginary parts of nonlinear susceptibility for the verification of the Kramers Kronig relations in femtosecond spectroscopy

摘要

Summary form only given. Recently, spectral interferometry has been developed to study the ultrafast dynamics in nonlinear materials and enables us to obtain both real and imaginary parts of nonlinear refractive index change which corresponds to the third-order nonlinear susceptibility. They are related through the KK relations and many discussions were reported in nonlinear optical systems. In time-resolved spectroscopy, the KK relations are not generally satisfied, however, we reported that the KK relations are strictly satisfied in the following special cases: (A) /spl Delta/N(t) is constant (quasi-steady state). (B) Excitation pulse is a /spl delta/ function. (C) /spl Delta/N(t)=0 over t>0 (negative delays). (D) /spl Delta/N(t)=0 over t<0 (positive delays) and /spl chi/(/spl omega/) is constant. Here /spl Delta/N(t) and /spl chi/(/spl omega/) represent the population difference caused by the pump and linear susceptibility, respectively.