Giant Kerr nonlinearity of terahertz waves mediated by stimulated phonon polaritons in a microcavity chip

Terahertz (THz) waves bridge microwave and infrared regimes and enable emerging technologies in radiation sources, detection, imaging, and communications. Nonlinear THz optics has progressed (e.g., high-harmonic generation, induced ferroelectricity, carrier control, and phonon modulation), yet the terahertz Kerr effect (TKE) remains too weak for many applications due to low power densities and modest Kerr responses. In contrast to visible/near‑IR where electronic nonlinearities dominate, at THz frequencies ionic contributions become significant and are theoretically predicted to exceed electronic ones. In polar crystals, THz waves can strongly couple to optical phonons to form stimulated phonon polaritons (SPhPs), whose delocalization and coherence can dramatically enhance nonlinear interactions. The study investigates whether SPhP-mediated interactions in a lithium niobate (LN) microcavity can produce a giant TKE detectable via shifts in cavity resonance with THz intensity, potentially enabling practical THz nonlinear photonics for high-speed communications, computing, and chip-scale devices.

Prior work has reported enhanced TKE in water at THz frequencies due to molecular vibrations, and increases in silicon via thermal effects or carrier acceleration at high THz intensities; however, these responses remain too weak for applications. THz pulses can perturb the Kerr effect of visible/IR light in nonpolar liquids, air, and glasses, but with modest nonlinearity. Liquids can show giant THz Kerr coefficients but are impractical for devices; lactose powder exhibits a large nonlinear refractive index but is also device-unfriendly. Silicon’s Kerr enhancement at high THz intensities is still limited. Quartz exhibits a giant Kerr coefficient and ZnSe a moderate one with potential for THz photonics. Theoretically, for microwaves/THz the ionic nonlinear response can exceed the electronic contribution, and SPhPs in polar crystals are predicted to dominate THz nonlinear effects through a distinct light–matter interaction that greatly enhances nonlinearity. These gaps and predictions motivate exploring SPhP-mediated TKE in solid-state, chip-compatible platforms like LN.

A chip-scale one-dimensional Fabry–Pérot microcavity was fabricated on a 50 µm-thick x-cut MgO:LiNbO3 slab waveguide via femtosecond laser direct writing. The cavity is formed by two distributed Bragg reflectors (DBRs) comprising periodic air slots and LN pillars; DBR band structures are tuned by geometry. A single-mode cavity (length 245 µm) with resonance at 0.63 THz was designed; air slot width is 50 µm with 100 µm period. THz waves (0.2–1.2 THz) are generated in situ by optical rectification using 800 nm, 120 fs, 1 kHz pump pulses, cylindrically focused at the cavity center. Pump pulse energy is varied from 190 to 403 µJ. A 50 µJ probe beam, frequency-doubled and time-delayed, passes through the sample and experiences a phase shift via the electro-optic effect from the evolving THz-induced refractive index distribution. A phase-contrast imaging system converts phase to intensity, and a CCD captures spatiotemporal snapshots as the delay line scans, yielding the full time evolution of the THz electric field in the cavity. Fourier transformation of time-domain fields provides spectral content and resonance frequency. The Kerr nonlinearity modulates the effective refractive index n = n0 + n2 I, leading to power-dependent resonance shifts. The THz intensity is related to field amplitude by I = (1/2) ε0 c n0 |E|^2, and the Kerr response is parameterized by χ(3), with Δn ∝ χ(3) |E|^2/n0. The effective linear refractive index at 0.63 THz is taken as n0 = 4.20 from waveguide analysis. The initial peak THz field amplitude scales linearly with pump power due to optical rectification; measured peak field amplitudes are used to estimate a lower bound on χ(3), acknowledging THz field decay and contributions from non-resonant components early after generation. Finite element simulations (COMSOL Multiphysics) model the cavity with a field-dependent permittivity using the experimentally inferred χ(3) to reproduce resonance shifts versus THz field. Theoretical analysis employs nonlinear Huang equations including an SPhP-mediated coupling term in the ionic anharmonic oscillator model; solving yields χ(3)(ω1,−ω1,ω1,ω1) expressions dependent on material parameters, supporting the observed magnitude of the Kerr response in LN at 0.63 THz.

- Clear, power-dependent resonance frequency shifts are observed in the single-mode LN microcavity, with an example redshift of about 10 GHz (~1.5%). - The cavity resonance is at ~0.63 THz; the cavity quality factor is ~70 across pump powers. - The THz field amplitude inside the cavity scales linearly with pump laser power, consistent with optical rectification. - From the linear dependence of resonance frequency on THz field intensity, the third-order nonlinear susceptibility at 0.63 THz is inferred to be Re(χ(3)) > 2.21 × 10^−15 m^2·V^−2 (a lower bound), corresponding to a nonlinear refractive index n2 > 7.09 × 10^−14 m^2·W^−1 for z-polarized THz waves. - The extracted χ(3) is over four orders of magnitude larger than typical values at visible wavelengths in LN, evidencing a giant THz Kerr nonlinearity. - Finite element simulations incorporating the measured nonlinearity reproduce the observed redshift with increasing THz field, corroborating the experimental interpretation. - Theoretical modeling with nonlinear Huang equations that include SPhP contributions predicts large χ(3) at THz frequencies, consistent with measurements.

The study demonstrates that in a polar crystal microcavity (LN), stimulated phonon polaritons mediate a strong ionic nonlinearity that drastically enhances the terahertz Kerr effect. Measuring resonance shifts versus THz intensity provides a sensitive, on-chip method to quantify the Kerr response. The observed redshift scaling and the large, lower-bound χ(3) directly support the hypothesis that SPhPs dominate THz nonlinearities and can boost Kerr effects by orders of magnitude beyond electronic contributions typical at optical frequencies. Agreement between experiment, electromagnetic simulations, and the nonlinear Huang-equation-based theory strengthens the attribution to SPhP-mediated anharmonic ionic motion. These results indicate practical pathways for THz nonlinear photonics, enabling intensity-dependent refractive index control at modest THz field levels for functions such as switching, modulation, frequency comb dynamics, and potentially soliton formation in the THz band.

A chip-scale LN Fabry–Pérot microcavity exhibits a giant terahertz Kerr nonlinearity, evidenced by clear, power-dependent resonance redshifts. The extracted third-order nonlinearity at 0.63 THz exceeds visible/IR values by more than four orders of magnitude, consistent with theoretical predictions from nonlinear Huang equations that include stimulated phonon polariton contributions. The findings validate SPhP-mediated Kerr enhancement as a mechanism for strong THz nonlinear optics in solid-state, integrable platforms. Future work can optimize cavity designs (e.g., higher-Q, dispersion engineering), explore other polar materials and modal configurations (including multi-mode cross-modulation), quantify full tensor elements of χ(3), and develop THz Kerr-based devices for high-speed communications, on-chip computing, and sensing of systems with THz spectral fingerprints.

- The extracted χ(3) and n2 represent lower-bound estimates because initial peak THz field amplitudes were used while the field decays over time; the frequency-domain analysis integrates over the full time trace. - Non-resonant spectral components contribute to the measured frequency shift during early round-trips, potentially biasing the extraction of the strictly resonant Kerr response. - The cavity quality factor (~70) and spectral resolution may limit the precision of frequency-shift measurements and the accuracy of the derived nonlinear coefficients. - Generalization beyond the specific LN microcavity platform and polarization (z-polarized THz waves) is not established within the presented data.