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

Abstract

Simultaneous measurement of continuous spectra of real and imaginary parts of complex nonlinear optical susceptibility was performed for porphyrin J-aggregates with sharp absorption peaks using a femtosecond Sagnac interferometer. A nonresonant component ( χ (3) NR) due to a solvent and a resonant component ( χ (3) R) due to the porphyrin J-aggregates are observed. The real and imaginary parts are compared using the Kramers–Kronig (KK) relations, which are valid for linear optical susceptibility. It is shown that χ (3) R satisfies the KK relations at all delay times. On the other hand, χ (3) NR does not satisfy the KK relations at zero delay time. The validity of the KK relations, which have been reported in previous papers by our group, are verified for the first time experimentally using continuous spectra.