Femtosecond phase spectroscopy by use of frequency-domain interference

We present the principles, experimental procedures, applications, and theoretical analyses of femtosecond phase spectroscopy, which is complementary to femtosecond absorption spectroscopy. In femtosecond phase spectroscopy difference spectra of both phase and transmission are simultaneously measured with a frequency-domain interferometer, which is only slightly modified from the conventional pump-probe method. Femtosecond time-resolved dispersion relations for CdS_xSe_1-x-doped glass and CS₂ are obtained with transform-limited pulses of 60-fs duration and 620-nm center wavelength. The results are theoretically analyzed and are well reproduced by numerical simulations. Although time-resolved data are not expected to satisfy the Kramers-Kronig (K-K) relations, the degree of discrepancy from the K-K relations is more substantial for CS₂ than for CdS_xSe_1-x-doped glass. These results arise from the difference in the linear susceptibility and in the excited-population dynamics. The conditions for which the K-K relations are applicable to time-resolved spectra are obtained theoretically and verified experimentally. It is shown that induced amplitude and phase modulations of the probe pulses cause a deviation from the K-K relations.