Time Domain Observation of the Lorentz - Local Field

The resonance frequency of an atom in an ensemble is shifted from that for an isolated atom due to the net polarization of the ensemble. This shift, ∆ω L , was first derived by Lorentz [1] and Lorenz [2] independently, thus it is known as the Lorentz–Lorenz shift and is given by where N is the number density and µ is the dipole moment. The corresponding modification to the dielec-tric constant (or index of refraction) is also known as the Clausius–Mossotti formula as Clausius [3] and Mossotti [4] previously derived it for the static case. Despite this long history, the Lorentz–Lorenz shift proved difficult to verify experimentally. Since the only free parameter is N , a system where N can be varied is essential. Atomic vapors are ideal since µ can be determined very accurately and N varied. However at sufficiently high densities for ∆ω L to be significant compared to the linewidth, the absorption is so strong that the vapor is opaque on resonance. Significant theoretical work on ways to observe the Lorentz–Lorenz shift using frequency domain spectroscopy was undertaken to overcome these difficulties [5–7]. Experimental verification of the Lorentz–Lorenz shift finally came in the 1990s [8–12]. The Lorentz–Lorenz shift is also important in solids , particularly in semiconductors, which can have a very high optical density on the exciton resonance. Because relaxation times in semiconductors are typically " ultrafast, " i.e., in the picosecond to femtosecond regime, time-domain spectroscopic techniques are preferred that utilize ultrashort optical pulses [13], as opposed to the frequency domain techniques [8–12] favored by atomic physicists. Although the Lorentz– Lorenz formula is for a frequency shift, the Lorentz local field that gives rise to it is also observable in the time-domain technique of transient-four-wave-mixing (TFWM) [14]. Specifically, it gives rise to signal for the " wrong " time ordering of the pulses.