"Nonperturbative Nonlinearities": Perhaps Less than Meets the Eye

Abstract

We address challenges in characterizing changes in permittivity and refractive index beyond standard perturbative methods with special attention given to transparent conductive oxides (TCOs). We unveil a realistic limit to permittivity changes under high optical power densities. Our study covers both slow and ultrafast nonlinearities, demonstrating that all nonlinearities induce refractive index changes accurately described by a simple curve with saturation electric field (or irradiance) and maximum change of permittivity at saturation. Our model, grounded in material properties, like oscillator strength and characteristic times, offers a robust framework for understanding and predicting nonlinear optical phenomena in TCOs and other materials. We differentiate between the significance of higher-order nonlinear susceptibilities in ultrafast and slow nonlinear scenarios. We aim to provide valuable insights for researchers exploring strong light-matter interaction.

Figure 1

(a) Two-level system not far from resonance. (b) Susceptibility of the two-level system χ_2level(ω)=ε(ω) – n̅² as a function of the pump field. Solid line, exact; dashed line, perturbative approximation up to χ⁽⁷⁾.

Figure 2

(a) Dispersion E(k) of nonparabolic band. (b) Inverse effective transport mass m_t^–1 of a given electron state vs its energy E. (c) Average inverse effective mass ⟨m_t^–1⟩_E versus thermal energy of hot carriers per electron ΔE. (d) Permittivity ε(ω) as a function of optical power density. Dashed line, approximate expression; solid line, exact.

Figure 3

Negative ultrafast nonlinearity (“virtual saturation”). Coupled dressed states of the two-level system.

Figure 4

(a,b) Two contributions to ultrafast positive nonlinearity due to virtual two-photon processes. (c) The permittivity change as a function of the optical field. Solid line, exact result of eq 50; dashed line, perturbative approximation up to χ⁽⁷⁾; dot-dashed line, virtual saturation approximation of eq 33.