Nonlinear optical response of Ge nanocrystals in a silica matrix

Time-resolved degenerate-four-wave-mixing measurements were used to study the nonlinear optical response (intensity-dependent refractive index) of Ge nanocrystallites embedded in a silica matrix. Nanocrystals were fabricated by ion-implanting silica with 1.0 MeV Ge ions to fluences in the range from 0.6 to 3 × 10¹⁷ Ge cm^-2, followed by annealing at 1100°C for 60 min. For the highest fluence, this resulted in nanocrystals with a log-normal size distribution, having a geometric mean diameter of 3.0 nm and a dimensionless geometric standard deviation of 0.25. The intensity-dependent refractive index |n₂| was measured at a wavelength of 800 nm and found to increase linearly with increasing Ge fluence. For the highest fluence, |n₂| was determined to be in the range 2.7-6.9 × 10^-13 cm^-2 W^-1, depending on the duration of the excitation pulse; values were consistently smaller for shorter pulse lengths. Relaxation of the nonlinear response was found to have two characteristic time constants, one <100 fs and the other ∼1 ps.