Method: input.csv holds one merged spectrum per excitation power (5-100 uW, 15 columns) vs Energy (eV). Each spectrum shows a main peak near 1.32-1.34 eV (plus a rising feature above ~1.5 eV that I excluded). I fitted every spectrum in the window 1.20-1.45 eV with a Lorentzian plus constant offset, y = y0 + A/(1+((x-xc)/w)^2), with A the peak intensity and xc the peak position. Window choices 1.22-1.40 and 1.20-1.50 gave consistent results.

Fit results (power uW: intensity, xc in eV):
5: 116.8, 1.3195 | 10: 219.8, 1.3246 | 15: 310.6, 1.3266 | 20: 400.9, 1.3280 | 25: 491.4, 1.3292 | 30: 584.0, 1.3301 | 35: 659.4, 1.3306 | 40: 782.7, 1.3316 | 45: 842.6, 1.3319 | 50: 936.2, 1.3329 | 60: 1119.9, 1.3333 | 70: 1310.6, 1.3344 | 80: 1490.4, 1.3345 | 90: 1712.5, 1.3351 | 100: 1978.6, 1.3357

Two plots were made: intensity vs power and xc vs power, each fitted with an allometric (power-law) function y = a * P^b (nonlinear least squares).

Plot 1, intensity vs power: a = 19.05, b = 1.001 +- 0.019 (unweighted). This is essentially linear. With weighting by fit errors, b = 0.958 +- 0.002; a log-log fit gives 0.932 +- 0.010.
Plot 2, peak position vs power: a = 1.3123 eV, b = 0.0039 +- 0.0001 (a slight blue shift with power).

The primary result is the intensity exponent, the usual power-law exponent of the emission.

RESULT: b = 1.001 ± 0.019
