Glossary entry

D-factor and MCEF

The two square-root-of-current slopes of laser speed: D relates resonance frequency to √(I−I_th); MCEF does the same for the 3-dB bandwidth. The standard 'GHz per √mA' figures of merit for directly modulated lasers.

Lasers & gainUpdated July 2026

Both of the numbers that describe how a laser's speed grows with drive current are square-root laws, and both get quoted as figures of merit.

The D-factor governs the relaxation-oscillation frequency:

f_r \;=\; D\,\sqrt{I - I_{th}}, \qquad D \;=\; \frac{1}{2\pi}\sqrt{\frac{\eta_i v_g a}{q V_a}}

\u2014 the physics of differential gain $a$ , active volume $V_a$ , and injection efficiency packed into one slope. Small active volumes and high differential gain make large D-factors: quantum-dot and short-cavity quantum-well lasers, and above all VCSELs, whose tiny mode volumes deliver D-factors of several GHz/\u221amA \u2014 multi-GHz resonances at sub-milliamp overdrives.

The MCEF (modulation current efficiency factor) applies the same form to the quantity engineers actually ship, the 3-dB bandwidth:

f_{3\mathrm{dB}} \;=\; \mathrm{MCEF}\,\sqrt{I - I_{th}}

In the lightly damped regime MCEF $\approx 1.55\,D$ ; as damping builds, MCEF falls below that ratio and eventually the K-factor ceiling takes over entirely. Reading a datasheet or paper, the pairing is diagnostic: D tells you about the gain medium and cavity design, MCEF about the deliverable bandwidth per unit of drive \u2014 and the gap between $1.55D$ and the measured MCEF tells you how much damping and parasitics are already eating.

Extraction is the same experiment as every other dynamic parameter: small-signal responses across bias, fit $f_r$ and $f_{3dB}$ , regress against $\sqrt{I-I_{th}}$ . Departures from straight-line behavior at high current flag thermal saturation of the differential gain \u2014 the point where pushing harder stops buying speed.