![Power Fit]([file link removed])

## Lorentzian Power-Dependence Results

**Pipeline:** despike (130 spikes removed) → Lorentzian fit on all 15 spectra (x-window 1.23–1.45 eV) → allometric fit I = a·P^b

### Per-power summary (all 15 points, Tier 1 HIGH)

| Power (µW) | xc (eV) | FWHM (meV) | Intensity | R² |
|---|---|---|---|---|
| 5 | 1.3206 | 62.4 | 99 | 0.887 |
| 10 | 1.3244 | 64.4 | 190 | 0.950 |
| 15 | 1.3264 | 64.1 | 268 | 0.958 |
| 20 | 1.3278 | 62.7 | 354 | 0.968 |
| 25 | 1.3290 | 61.7 | 425 | 0.973 |
| 30 | 1.3300 | 61.3 | 516 | 0.975 |
| 35 | 1.3304 | 60.8 | 565 | 0.978 |
| 40 | 1.3315 | 59.3 | 695 | 0.981 |
| 45 | 1.3318 | 59.1 | 739 | 0.981 |
| 50 | 1.3328 | 59.0 | 818 | 0.981 |
| 60 | 1.3332 | 58.0 | 936 | 0.982 |
| 70 | 1.3343 | 57.1 | 1140 | 0.983 |
| 80 | 1.3345 | 56.3 | 1265 | 0.983 |
| 90 | 1.3351 | 55.3 | 1538 | 0.984 |
| 100 | 1.3356 | 54.4 | 1715 | 0.984 |

### Allometric fit: I = a·P^b

- **a** = 16.28 ± 1.81
- **b** = 1.0048 ± 0.0261
- **R²** = 0.9951
- Interpretation: **~linear (excitonic)** regime

### Peak position trend

xc shifts from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — a **blueshift of ~15 meV** over the full power range (~5 meV per decade). This is consistent with band-filling / state-filling at higher excitation densities.

📥 [Download CSV results]([file link removed])

RESULT: b = 1.0048 ± 0.0261