Glossary entry

Differential quantum efficiency

The number of photons a laser emits for each additional electron injected above threshold, η_d = (q/hν)·dP/dI. It is the slope efficiency expressed in photons per electron, and equals the internal efficiency times the fraction of the light that leaves through the mirrors.

Lasers & gainUpdated October 2026

The differential quantum efficiency $η_{d}$ of a laser diode is the number of photons it emits for each additional electron injected above threshold: the slope of its light-current curve expressed in photons per electron,

η_{d} = \frac{q}{h ν} \frac{d P}{d I} = \frac{q λ}{h c} η_{s},

where $η_{s} = d P / d I$ is the slope efficiency in W/A, $q$ the electron charge and $h ν$ the photon energy. A slope efficiency of 0.25 W/A at 1550 nm is an $η_{d}$ of 31%. Because it counts photons rather than watts, $η_{d}$ compares lasers at different wavelengths directly: an $η_{d}$ of 50% is 0.63 W/A at 980 nm but 0.40 W/A at 1550 nm. For a laser with a single active junction, the total from both facets cannot exceed the internal quantum efficiency and so cannot exceed one.

Converting slope efficiency

Wavelength	$q λ / h c$ (multiply $η_{s}$ in W/A)	Slope efficiency at $η_{d} = 100 %$
850 nm	0.686 A/W	1.46 W/A
980 nm	0.790 A/W	1.27 W/A
1064 nm	0.858 A/W	1.17 W/A
1310 nm	1.057 A/W	0.95 W/A
1550 nm	1.250 A/W	0.80 W/A

The last column is the slope efficiency of a laser that turns every extra electron into an emitted photon, the ceiling for a single-junction device. Datasheets usually quote the slope efficiency of the front facet only. A chip with two uncoated facets splits its light equally between them, so its front-facet $η_{d}$ is half the total; with a high-reflection coating on the back facet, nearly all of the light leaves through the front.

Internal efficiency and cavity loss

Above threshold, a fraction $η_{i}$ of the extra electrons produce photons in the lasing mode, and those photons are either lost inside the cavity, at the rate of the internal loss $α_{i}$ , or leave through the mirrors, at the rate of the mirror loss $α_{m}$ . The efficiency is the product,

η_{d} = η_{i} \frac{α_{m}}{α_{i} + α_{m}}, α_{m} = \frac{1}{L} \ln \frac{1}{R},

for a cavity of length $L$ with two facets of reflectance $R$ . The fraction leaving through the mirrors falls as the cavity lengthens, which is the trade-off behind the choice of cavity length: long cavities have lower threshold gain but lower efficiency. For $η_{i} = 0.8$ , $α_{i} = 10$ cm⁻¹ and $R = 0.3$ :

Cavity length	$α_{m}$	$η_{d}$ , both facets	$1 / η_{d}$	Front-facet slope at 1550 nm
300 µm	40.1 cm⁻¹	0.640	1.56	0.256 W/A
600 µm	20.1 cm⁻¹	0.534	1.87	0.214 W/A
900 µm	13.4 cm⁻¹	0.458	2.18	0.183 W/A
1200 µm	10.0 cm⁻¹	0.401	2.50	0.160 W/A

Rearranged, the same relation is a straight line in the cavity length:

\frac{1}{η_{d}} = \frac{1}{η_{i}} + \frac{α_{i}}{η_{i} \ln (1 / R)} L .

Measuring $η_{d}$ on lasers cleaved to several lengths from the same wafer and fitting $1 / η_{d}$ against $L$ gives $η_{i}$ from the intercept and $α_{i}$ from the slope: the values in the table lie on a line with intercept 1.25 ( $η_{i} = 0.8$ ) and slope 10.4 cm⁻¹, from which $α_{i} = 10$ cm⁻¹. This is the standard way to separate the internal efficiency and loss of an active region; a single device cannot give them. The procedure and its pitfalls are covered in Slope efficiency and differential quantum efficiency from LIV measurements.

What lowers the efficiency

The efficiency falls with temperature, as carriers leak over the barriers of the active region, Auger recombination rises and free-carrier absorption increases the internal loss; it is often described by $η_{d} (T) = η_{d 0} \exp (- T / T_{1})$ , the companion of the characteristic temperature $T_{0}$ of the threshold. At high current, heating and carrier leakage lower $η_{i}$ further, and the light-current curve bends over. Current that flows around the active region rather than through it, and optical loss in doped cladding layers, lower $η_{d}$ at any temperature.

In quantum cascade lasers and lasers with several active regions joined by tunnel junctions, each electron passes through several stages and can emit a photon in each, so $η_{d}$ can exceed one. A value above one from an ordinary single-junction laser points to an error in the power or current measurement.

Common questions

How do you convert slope efficiency to differential quantum efficiency?

Multiply the slope efficiency in W/A by $q λ / h c$ , which is the wavelength in micrometers divided by 1.2398. At 1310 nm, 0.40 W/A is an $η_{d}$ of 42%.

What is the difference between differential and external quantum efficiency?

The external quantum efficiency is the ratio of all photons emitted to all electrons injected at an operating point, $(P / h ν) / (I / q)$ , so it includes the current spent reaching threshold. The differential efficiency counts only the increments above threshold and is the larger of the two on the linear part of the curve; near thermal rollover, where the slope falls below $P / I$ , it becomes the smaller. The internal efficiency $η_{i}$ counts photons generated inside the cavity, before the internal loss takes its share.

What limits the differential quantum efficiency?

The internal efficiency, and the ratio of mirror loss to total loss. Lowering the internal loss, shortening the cavity or lowering the facet reflectance raises $η_{d}$ , the last two at the cost of a higher threshold.

References: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012). G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).