Unfolding The Origin of Titanium Nitride’s Ultrafast Optical Nonlinearity

In the last decade, Titanium Nitride (TiN) has been brought into the spotlight as a promising alternative plasmonic material to noble metals, such as gold and silver [1]. Indeed, it boasts a refractory character, CMOS- and bio-compatibility, tunable permittivity at the synthesis stage, and epsilon-near-zero properties at optical wavelengths. On top of that, TiN shows an extremely rapid hot-electron relaxation time (&lt; 100 fs), one order of magnitude lower than noble metals such as, e.g., gold [2]. This property is extremely appealing to exploit TiN as a novel material in devices for all-optical-modulation. Nevertheless, in order to perform device design, the bare knowledge of the hot-carriers cooling time is not sufficient. A comprehensive model, able to predict how the broadband dielectric properties of the material are modulated, upon ultra-rapid photoexcitation, is essential.<br/>In this work, we develop an original numerical model, able to disclose the origin of TiN’s giant optical nonlinearity. Starting from a rate-equation model, we evaluate the increments in carrier and lattice temperatures following photoexcitation. Then, we manage to disentangle the interband and intraband contributions to the permittivity modulation, on a broad spectral domain, pointing out the key role of interband transitions in the first instants (&lt; 150 fs) of TiN optical dynamics. The calculations are validated on ultrafast pump-probe spectroscopy experiments, starting from the simplest TiN structure: a 200 nm-TiN film on glass. The sample is excited with an ultrashort pump at ~ 500 nm, and probed with a broadband pulse, having a temporal resolution of ~ 100 fs [3]. The model is then implemented to study the ultrafast optical nonlinearity in TiN nanostructures. Specifically, we focus on a lattice of TiN nanodisks in air and on a colloidal solution of TiN nanospheres in water. For both systems, the comparison with ultrafast pump-probe measurements [4],[5] shows accurate results. As a further step, we aim at studying the hot-carriers induced optical nonlinearity on a even more complex structure, namely a TiN-based metasurface.<br/>Our work provides a powerful tool: indeed, starting from the actual experimental conditions, such as the pump fluence or the nanostructure geometry, we are able to predict the ultrafast optical properties of virtually any TiN-based sample over a broad spectral range. This paves the way to the design and demonstration of new TiN-based devices for ultrafast plasmonics applications.<br/><br/><br/>References:<br/>[1] G.V. Naik <i>et al.</i>, Adv. Mater., 25, 3264 (2013).<br/>[2] B.T. Diroll, <i>et al.,</i> Adv. Opt. Mater., 8, 2000652 (2020).<br/>[3] S. Rotta Loria <i>et al</i>., Adv. Optical Mater., 11, 2300333 (2023).<br/>[4] T. Reese <i>et al.</i>, ACS Photonics, 8, 1556 (2021).<br/>[5] S. Adhikari<i> et al., </i>Phys. Rev. Appl., 15, 024032 (2021).