Reverse Polarizability\nof Rare Earth Ions (La<sup>3+</sup>, Gd<sup>3+</sup>, Lu<sup>3+</sup>, Y<sup>3+</sup>) in Tellurite\nGlasses and Glass Ceramics for Optical Limiting

All-optical\nmodulation using inherent third-order optical nonlinearity\nof a medium has garnered considerable interest in photonics and optoelectronics.\nHerein, nonlinear optical (NLO) properties of tellurite glasses and\nglass ceramics (GCs) containing four different rare earths (RE = La,\nGd, Lu, and Y) have been deliberated in near-infrared regions under\nan ultrafast regime. The La-based glass exhibits ∼10 times\nhigher nonlinear refraction (<i>n</i><sub>2</sub>) and absorption\n(α<sub>2</sub>) than reported NLO materials. The NLO susceptibility\n[χ<sup>(3)</sup>] trend in the studied glasses is La > Gd\n>\nLu > Y, matching with RE<sup>3+</sup> polarizability. Furthermore,\nLn<sub>2</sub>Te<sub>6</sub>O<sub>15</sub> nanocrystallite-embedded\ntransparent GCs exhibit a larger NLO coefficient due to the enhanced\nlocal field from oxygen vacancies in crystallites. Interestingly,\nthe trend of χ<sup>(3)</sup> in GCs follows the sequence of\nY > Lu > Gd > La, precisely opposite to the glasses. This\nobservation\nchallenges the general polarizability approach of RE<sup>3+</sup> ions,\nemphasizing that quadratic hyperpolarizability of RE<sup>3+</sup> is\npivotal for NLO properties of GCs. Among the studied matrices, Y-containing\nGCs showed the lowest optical limiting (OL) threshold (5.4 mJ/cm<sup>2</sup> at 800 nm), much lower than those of the reported NLO materials,\nsuggesting its potential as a femtosecond NIR-laser safety material.\nA combination of large α<sub>2</sub> and <i>n</i><sub>2</sub> from the studied matrices indicates their advantage for harmonic\ngeneration, potentially aiding in the design of ultrafast signal processing\ndevices.