Abstract
Asymptotic evolution equations are derived to describe the interaction between an optical field and a terahertz-frequency field copropagating in a χ(3) material. Second-order and fourth-order multiple-scale perturbation theory is utilized to derive a set of coupled equations for the optical and the terahertz fields. For the terahertz wave a modified Korteweg–de Vries equation is found; it is coupled to a nonlinear Schrödinger equation describing the dynamics of the optical field. This asymptotic regime is valid away from classical natural-oscillator-frequency or quantum-mechanical-transition resonances. Analytic solutions to the evolution equations are given that resemble solutions to coupled cross-phase-modulation equations usually obtained for two copropagating optical fields. The long- to short-wavelength resonance equations have distinctive features that enable the optical fields to respond to the low-frequency fields. Experimentally measurable quantities to detect these interactions are discussed.
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