The influence of finite bandwidth excitation sources in degenerate four-wave mixing spectroscopy

Abstract

The effects of finite-bandwidth excitation are incorporated into the theoretical treatment of degenerate four-wave mixing (DFWM) spectroscopy by employing a general description of applied electromagnetic fields, thereby permitting the transient nature of typical laser sources to be taken explicitly into account. A computationally efficient perturbative (weak-field) formalism is developed by exploiting exponentially-decaying wave forms as a flexible basis for expanding the temporal envelope functions of incident quasimonochromatic pulses. This approach has the distinct advantage of yielding time-domain response integrals that can be evaluated analytically since they are almost as simple in form as their monochromatic counterparts. The resulting frequency-domain expressions for the induced DFWM signal polarization reflect the pronounced influence of finite-bandwidth excitation without needing to cobble such behavior into phenomenological rates for population decay and coherence dissipation. Spectral line shapes are examined for both stationary and nonstationary ensembles of isolated (gas-phase) target molecules, with the latter analyses demonstrating the systematic degradation of spatial discrimination introduced by nonmonochromatic implementations of the sub-Doppler (phase-conjugate) four-wave mixing scheme. In keeping with recent experimental findings, the precipitous drop in signal intensity accompanying the action of collisional dephasing processes is predicted to be tempered greatly by the use of short-duration excitation pulses.