Fig. 4.

Two-photon-absorption-induced photoluminescence and two-photon absorption dispersion of n = 4. a PL spectra from n = 4 under two-photon absorption (2PA) for different excitation wavelengths from 1.0 μm (black) to 1.7 μm (grey) at increments of 0.1 μm (ascending wavelengths correspond to the color sequence black, red, green, yellow, blue, purple, cyan, grey). The major exciton PL (vertically translated for clarity) is identified by spectral subtraction, which is essentially the same as the one-photon-absorption-induced photoluminescence (PL, dashed trace) using frequency-tripled Nd:YAG radiation (355 nm). b Amplified spontaneous emission of the sharp peak (~ 790 nm) from the low-energy shoulder of n = 4 when the exciton state is resonantly excited by 2PA with excitation energy ranging from 10 μJ (black) to 40 μJ (blue) at increments of 10 μJ (ascending excitation energies correspond to the color sequence black, red, green, yellow, blue). c Experimental β(λ) (dots) where error bars arise from uncertainty in the powder size. The theoretical β(λ) (red curve) corresponds to Eq. (4) using K = 5000 and the fundamental bandgap, E _g = 1.89 eV. The dashed curve is Eq. (4) using the optical gap (~ 1.70 eV) as a band-dispersion parameter with K = 3500