I fitted the dominant peak in each spectrum with a Lorentzian plus linear baseline, over 1.24–1.44 eV. The table gives the fitted peak intensity and center \(x_c\) for each power.

| Power (µW) | Peak intensity | \(x_c\) (eV) |
|---:|---:|---:|
| 5 | 122.2 | 1.31689 |
| 10 | 224.8 | 1.32216 |
| 15 | 316.0 | 1.32417 |
| 20 | 404.9 | 1.32593 |
| 25 | 496.6 | 1.32736 |
| 30 | 590.8 | 1.32830 |
| 35 | 665.5 | 1.32887 |
| 40 | 788.4 | 1.33018 |
| 45 | 849.3 | 1.33046 |
| 50 | 943.4 | 1.33150 |
| 60 | 1129.4 | 1.33197 |
| 70 | 1321.4 | 1.33327 |
| 80 | 1505.8 | 1.33347 |
| 90 | 1729.4 | 1.33416 |
| 100 | 2000.2 | 1.33480 |

The plots and full fit results are available here:

- [Intensity and peak position plots with allometric fits](allometric_fits.png)
- [Lorentzian fit parameters for each power](lorentzian_peak_fits.csv)

For \(y=aP^b\), the fitted intensity exponent is \(b=0.9232\pm0.0119\). The corresponding peak-position exponent is \(b=0.004386\pm0.000090\).

RESULT: b = 0.9232 ± 0.0119