Tip-enhanced four-wave mixing internally illuminated by an ultrafast vector light field

A tip nanofocusing light field, with high electric-field intensity and nanoscale mode volume, can significantly improve nonlinear light scattering efficiency, thereby greatly promoting the development of strong-field nano-optics. Here, tip-enhanced four-wave mixing (FWM) is theoretically analyzed through two ultrafast radial vector beams internally illuminating an Ag-coated silica tip (ACST). Two femtosecond pulses, with radial electric vectors and pulse width of 100 fs, are adopted as excitation sources to illuminate the ACST. Degenerate tip-enhanced FWM (ω_FWM= 2ω₁-ω₂) with a nonlinear conversion efficiency of ∼10^-5 is achieved. The peak electric-field amplitude of the two pump pulses is 5 × 10⁷ V/m, which is two orders of magnitude lower than that of the external excitation method. Further theoretical analysis shows that the conversion efficiency of the tip-enhanced FWM has strict frequency detuning dependence characteristics, and is closely related to the frequency response of the tip nanofocusing light field. This plasmonic tip provides an approach for enhancing nonlinear nano-optics, and may be used in the field of tip-based FWM nanoscopy.