Confinement-Induced Nonlocality and Optical Nonlinearity of Transdimensional Titanium Nitride in the Epsilon-Near-Zero Region

Ultrathin plasmonic films that approach the trans-dimensional (TD) thickness limit provide a promising route for light_matter interaction control and manipulation, yet their nonlinear optical response near the epsilon_near_zero (ENZ) condition remains poorly understood. Here, we report the strongly enhanced optical nonlinearity for their typical representative high quality TiN epitaxial films with thicknesses down to a few nanometers. Systematic Z_scan measurements reveal a pronounced increase in nonlinear absorption with decreasing thickness. Especially in the ENZ spectral region, the TD TiN films exhibit nearly two orders of magnitude stronger nonlinear absorption over a broad range of incidence angles as compared to conventional thin films. The enhanced nonlinear absorption observed is well described by a nonlinear nonlocal electromagnetic response model that accounts for electron confinement effects unique to the TD plasmonic systems. Comparison with Ti1_xAlxN highlights the necessity of low-loss ENZ response for nonlinear enhancement. These findings identify TiN and similar TD plasmonic systems as a robust refractory platform for exploiting ENZ mediated nonlinear processes in ultrathin photonic material structures.

💡 Research Summary

This paper investigates the nonlinear optical response of ultrathin titanium nitride (TiN) films in the epsilon‑near‑zero (ENZ) spectral region, focusing on the so‑called transdimensional (TD) regime where the film thickness lies between three‑dimensional bulk and two‑dimensional monolayer limits. Using nitrogen plasma‑assisted molecular beam epitaxy (PA‑MBE), the authors grew high‑quality epitaxial TiN layers with thicknesses ranging from 2 nm to 50 nm on c‑plane sapphire substrates. Structural characterization (SEM, AFM, XRD) confirms atomically smooth surfaces (RMS ≈ 1.5 Å for 4 nm films) and excellent crystallinity, while spectroscopic ellipsometry and UV‑Vis measurements reveal a thickness‑dependent ENZ wavelength that red‑shifts from ~465 nm for 50 nm films to longer wavelengths as the film becomes thinner.

Nonlinear absorption is probed by open‑aperture Z‑scan using femtosecond pulses (5–40 GW cm⁻²) at wavelengths close to the ENZ point (480 nm, 500 nm, 520 nm). All samples display reverse‑saturable absorption (RSA), indicative of processes such as free‑carrier absorption, two‑photon absorption, and excited‑state absorption. The extracted nonlinear absorption coefficient β increases dramatically as the thickness is reduced, reaching values up to 10⁻⁶ cm W⁻¹ for the 2 nm film—almost two orders of magnitude larger than for the 50 nm counterpart. Importantly, β shows little dependence on the angle of incidence, confirming that the ENZ‑mediated enhancement is robust over a wide angular range.

To explain these observations, the authors extend the existing nonlocal linear electromagnetic model for TD plasmonic films to the third‑order nonlinear regime. Quantum confinement in the vertical direction modifies the electronic dispersion, leading to a thickness‑dependent effective mass and enhanced electron‑electron interaction. The derived third‑order susceptibility χ^(3) scales roughly as 1/d², yielding a β(d,θ) that matches the experimental thickness trend and angular invariance. This nonlocal nonlinear model captures the essential physics of confinement‑induced field enhancement in the ENZ region.

A comparative study with Al‑doped Ti₁₋ₓAlₓN films (x = 0.2–0.6) demonstrates that increased optical loss (larger ε’’) suppresses the nonlinear enhancement, underscoring the necessity of low‑loss ENZ response for achieving strong nonlinearity. Ultrafast pump‑probe measurements reveal an electron‑phonon coupling time of ~93 fs and phonon relaxation on the nanosecond scale, ensuring that the 1 kHz repetition‑rate Z‑scan measurements are free from cumulative heating effects.

Overall, the work establishes ultrathin TiN as a robust, refractory platform for ENZ‑enhanced nonlinear optics. The combination of strong confinement‑induced nonlocality, low intrinsic loss, and high thermal stability makes TD TiN attractive for integrated photonic devices such as ultrafast modulators, nonlinear metasurfaces, and on‑chip frequency converters. The authors suggest that extending this approach to other transition‑metal nitrides or hybrid 2D/3D heterostructures could further boost nonlinear efficiencies and enable active control of ENZ‑mediated phenomena.