Extended Data Fig. 7: Measurements and simulations of the mechano-optical response of single (15% Tm³⁺) piezochromic ANPs.

Measured 800 nm / 700 nm -emission ratio (a) and percent change of the 800 nm / 700 nm -emission ratio (b) versus applied force, for 5 compression cycles originating from 5 different piezochromic ANPs (excitation intensity: 1,131 ± 46 kW cm⁻²). Integration time per data point was: 3 s (NP #1), 3 s (NP #2), 3 s (NP #3), 30 s (NP #4), and 50 s (NP #5). While their initial 800 nm / 700 nm -emission ratios differ by up to ±25% (full statistics in Extended Data Fig. 8), their mechanical response is similar. c. Photon avalanche DRE model simulations of the 15% Tm³⁺ piezochromic ANP force response. All DRE parameters are listed in Supplementary Note 6, Table S3. Zero-force simulation parameters are derived from fitting the excitation (at 1064 nm) versus emission (at 800 nm) data measured for piezochromic ANPs at ambient conditions (Supplementary Note 6, Fig. S5c). Force dependence of all of the nonradiative relaxation and cross-relaxation rates are derived from the equations listed in Supplementary Note 6. Calculations were performed for excitation intensities ca. 20-fold higher than threshold intensities, in line with the excitation power densities used for the piezochromic ANP measurements in this study.