Reverse Polarizability of Rare Earth Ions (La³⁺, Gd³⁺, Lu³⁺, Y³⁺) in Tellurite Glasses and Glass Ceramics for Optical Limiting

All-optical modulation using inherent third-order optical nonlinearity of a medium has garnered considerable interest in photonics and optoelectronics. Herein, nonlinear optical (NLO) properties of tellurite glasses and glass ceramics (GCs) containing four different rare earths (RE = La, Gd, Lu, and Y) have been deliberated in near-infrared regions under an ultrafast regime. The La-based glass exhibits ∼10 times higher nonlinear refraction (n₂) and absorption (α₂) than reported NLO materials. The NLO susceptibility [χ⁽³⁾] trend in the studied glasses is La > Gd > Lu > Y, matching with RE³⁺ polarizability. Furthermore, Ln₂Te₆O₁₅ nanocrystallite-embedded transparent GCs exhibit a larger NLO coefficient due to the enhanced local field from oxygen vacancies in crystallites. Interestingly, the trend of χ⁽³⁾ in GCs follows the sequence of Y > Lu > Gd > La, precisely opposite to the glasses. This observation challenges the general polarizability approach of RE³⁺ ions, emphasizing that quadratic hyperpolarizability of RE³⁺ is pivotal for NLO properties of GCs. Among the studied matrices, Y-containing GCs showed the lowest optical limiting (OL) threshold (5.4 mJ/cm² at 800 nm), much lower than those of the reported NLO materials, suggesting its potential as a femtosecond NIR-laser safety material. A combination of large α₂ and n₂ from the studied matrices indicates their advantage for harmonic generation, potentially aiding in the design of ultrafast signal processing devices.