Terahertz (THz) waves, bridging microwaves and infrared light, are a rapidly developing field with applications in various technologies. While THz nonlinear optics has seen breakthroughs in areas like high-harmonic generation and phonon modulation, the Terahertz Kerr Effect (TKE) remains underdeveloped. The Kerr effect is crucial for technologies such as optical solitons, supercontinuum spectra, and frequency combs, but its THz counterpart lags. While some materials like water and silicon have shown some TKE, the effect is weak, limiting practical applications. For visible and near-infrared light, Kerr nonlinearity stems mainly from electronic nonlinearity, but for THz waves, ionic contributions, particularly stimulated phonon polaritons (SPhPs), are significant. SPhPs, excited when THz waves strongly couple with polar optical phonons in ionic crystals, dramatically enhance THz nonlinear effects. This research demonstrates a giant TKE in a chip-scale lithium niobate (LN) Fabry-Pérot microcavity facilitated by SPhPs, significantly enhancing the nonlinear response for practical applications. This is achieved by designing a microcavity to generate and enhance the effect of SPhPs.

Previous research demonstrated high nonlinear refractive index coefficients in water at THz frequencies due to molecular vibrations. Studies in silicon suggested that thermal effects or carrier acceleration could increase TKE nonlinearity at high THz intensities, but the effect remained weak. THz pulses have also been shown to induce or enhance the Kerr effect of visible and infrared light in various materials, but the nonlinearity remained weak. Theoretical predictions suggest that ionic nonlinearity contributes more than electronic nonlinearity at microwave and THz frequencies, with SPhPs dominating THz nonlinear effects. The unique light-matter interaction mediated by SPhPs, characterized by remarkable delocalization and coherence, significantly enhances THz nonlinear effects. This work builds upon these findings to demonstrate and characterize significantly enhanced TKE.

A Fabry-Pérot microcavity was fabricated on a lithium niobate (LN) slab waveguide using femtosecond laser direct writing. The microcavity was sandwiched between two distributed Bragg reflectors (DBRs) acting as mirrors, enabling the creation of a single-mode microcavity resonating at 0.63 THz. THz waves were generated within the microcavity using femtosecond laser pulses via optical rectification. A pump-probe technique was employed to measure the generated THz waves; the pump beam generated THz waves, and the probe beam, delayed and frequency-doubled, measured the THz field via the electro-optic effect. The time-resolved spatiotemporal evolution of the THz waves was captured by a CCD camera after passing through a phase-contrast system. Experiments were conducted with varying pump laser powers to observe the power-dependent frequency shifts of the resonant mode. The initial peak amplitude of the generated THz waves was observed to be proportional to the pump power. The frequency shift, caused by the TKE, was then used to calculate the third-order nonlinear susceptibility (χ(3)). Finite element method simulations (COMSOL Multiphysics) were used to verify the experimental results using the calculated nonlinear susceptibility. Nonlinear Huang equations were employed to theoretically model the contribution of SPhPs to the giant TKE.

The experiments revealed a significant frequency shift (10 GHz or about 1.5%) in the single-mode microcavity’s resonant frequency with changing pump power, indicating a positive Kerr coefficient. The third-order nonlinear susceptibility (χ(3)) was calculated to be greater than 2.21 × 10⁻¹⁵ m²⋅V⁻², which is over four orders of magnitude larger than that observed for visible light in LN. This translates to a nonlinear refractive index (n₂) greater than 7.09 × 10⁻¹⁴ m²⋅W⁻¹. The experimental results are consistent with simulations using COMSOL Multiphysics, which modeled the frequency shift based on the calculated nonlinear susceptibility. The giant TKE observed is attributed to the excitation of SPhPs. The nonlinear Huang equations successfully explained the enhanced nonlinearity resulting from the interaction of THz waves and SPhPs, quantitatively matching the experimental observations.

The observed giant TKE in the lithium niobate microcavity, mediated by stimulated phonon polaritons, significantly advances THz nonlinear optics. The magnitude of the nonlinear susceptibility, several orders of magnitude larger than those reported for visible or infrared light, makes this approach highly promising for practical applications. The agreement between experimental findings, COMSOL simulations, and theoretical predictions using nonlinear Huang equations provides strong evidence supporting the mechanism of SPhP-enhanced TKE. The results suggest that this approach can lead to the development of compact and efficient THz devices for applications in high-speed communications, high-rate computing, and other areas.

This research demonstrates a giant terahertz Kerr nonlinearity mediated by stimulated phonon polaritons in a lithium niobate microcavity. The nonlinear coefficient is orders of magnitude larger than in visible or infrared light, enabling potential breakthroughs in THz technologies. Future research could explore other materials and microcavity designs to further enhance the TKE and investigate its applications in various THz devices.

The current study focuses on a specific microcavity design and material. The generalizability of the findings to other materials and cavity geometries needs further investigation. While the study provides a lower limit estimate for the nonlinear susceptibility, refining the analysis to account for non-resonant contributions and temporal evolution of the THz field could provide a more precise value.