Linewidth enhancement factor (α)

The linewidth enhancement factor, also called the Henry factor (after C. H. Henry, 1982), is defined as

where $n'$ and $n''$ are the real and imaginary parts of the refractive index, $N$ is the carrier density, and $g = -(4\pi/\lambda_0) n''$ is the optical gain. The minus sign makes $\alpha$ positive for normal semiconductor materials (refractive index decreases with increasing carrier density).

$\alpha$ enters the modified Schawlow–Townes formula for semiconductor laser linewidth:

For $\alpha = 3$, the linewidth is 10× the Schawlow–Townes value. The factor also governs:

• Frequency chirp during direct modulation — current changes carrier density, which changes $n'$ and thus the lasing frequency
• Filamentation in broad-area lasers — refractive index hot spots concentrate the optical field
• Susceptibility to optical feedback — back-reflection at $\alpha \gtrsim 1$ produces strong dynamics including coherence collapse

Typical values:

Measurement: $\alpha$ can be extracted from small-signal modulation response (FM/AM ratio), from chirp during pulsed operation, or from the asymmetry of injection-locking range.

Lower-$\alpha$ designs reduce linewidth, chirp, and feedback sensitivity simultaneously. Quantum dot lasers were originally developed in part to exploit their intrinsically lower $\alpha$, though achieving the theoretically-predicted $\alpha = 0$ in practical devices has remained difficult.