Silent breakdown of the perturbative polarization expansion in the terahertz regime

Abstract

Nonlinear optics expands the polarization in powers of the drive and retains only the lowest-order terms. This truncation is safe at optical frequencies, where the convergence field lies far above the damage threshold. In the terahertz regime, phonon polaritons enhance the nonlinear susceptibilities by orders of magnitude, lowering the convergence field into the sub-damage range and opening a window in which the expansion fails while the crystal remains recoverable. We term this window silent breakdown. At resonance, the nearest singularities of the driven lattice mode are a complex-conjugate pair of branch points below the multistability threshold, so the response remains smooth and single-valued even though the $χ^{\left( n \right)}$ description fails. The convergence field scales as $Q^{-3/2}$, so sharpening a resonance enhances the nonlinearity but narrows the range over which the expansion applies. It follows from the mode shift $S$ alone, $E_{\mathrm{conv}}=E_{\mathrm{ref}}(3\sqrt{3}QS)^{-1/2}$, giving 2$\sim$9 MV/cm for $\mathrm{LiNbO}_{3}$. Since resonant enhancement is central to terahertz nonlinear optics, this boundary defines the field range over which susceptibility-based descriptions are quantitatively reliable.