Wall-plug efficiency

Wall-plug efficiency (WPE), also called power conversion efficiency, is the fraction of the electrical power delivered to a laser that leaves it as light:

$${\eta }_{\text{WPE}}=\frac{P_{\text{out}}}{I\cdot V},$$

where $P_{\text{out}}$ is the optical output power, $I$ the drive current and $V$ the voltage across the device terminals. It is quoted at a stated current or output power and heatsink temperature, since it changes with both. The 1310 nm Fabry-Perot laser used as the example in the LIV curve entry reaches 37.8% at 46 mA on a 25 °C heatsink, and high-power diode laser bars near 970 nm have exceeded 70%.

The three factors

Above threshold the output is $P_{\text{out}}={\eta }_d(h\nu \mathrm{/}q)(I-I_{\text{th}})$, where ${\eta }_d$ is the external differential quantum efficiency, $h\nu$ the photon energy and $I_{\text{th}}$ the threshold current. Dividing by $IV$ splits the efficiency into three factors:

$${\eta }_{\text{WPE}}={\eta }_d\cdot \frac{h\nu }{qV}\cdot (1-\frac{I_{\text{th}}}{I})\mathrm{.}$$

The first is the fraction of the electrons above threshold that produce a photon leaving the laser. The second is the photon energy as a fraction of the energy each electron receives from the supply. The third is the fraction of the current that goes into lasing rather than into holding the carrier density at threshold. For the example laser at 46 mA they are 57.2%, 0.802 and 0.825, and their product is 37.8%. Slope efficiency, $dP\mathrm{/}dI$ in W/A, and the differential quantum efficiency describe only the increment above threshold and leave out the last two factors.

Where the peak lies

Near threshold the third factor is small. At high current the voltage keeps rising through the series resistance, $V=V_0+I{R}_s$, and the second factor falls. For linear L–I and V–I characteristics the efficiency peaks at

$$I_{\text{peak}}=I_{\text{th}}+\sqrt{I_{\text{th}}^2+I_{\text{th}}{V}_0\mathrm{/}{R}_s},$$

that is, at $1+\sqrt{1+V_0\mathrm{/}(I_{\text{th}}{R}_s)}$ times threshold. The ratio $V_0\mathrm{/}(I_{\text{th}}{R}_s)$ compares the turn-on voltage with the resistive drop at threshold, so the lower the resistance, the further above threshold the peak lies. For the example laser, with $V_0$ = 0.95 V, $R_s$ = 5 Ω and $I_{\text{th}}$ = 8.05 mA, the formula gives 48 mA, six times threshold; self-heating, which the formula leaves out, moves the measured continuous-wave peak to 46 mA. The peak is broad: the efficiency stays within one percentage point of it from 34 to 66 mA, and it has fallen only to 33.5% at 100 mA, where the voltage has risen from 1.18 V to 1.45 V.

Where the rest of the power goes

At the example's peak, 46 mA at 1.180 V, the 54.28 mW of electrical input divides as follows:

Apart from a little light from the rear facet and spontaneous emission that escapes, the remaining 33.75 mW ends as heat in the chip. The last line is small only because the example's turn-on voltage, 0.95 V, is almost equal to the photon energy divided by the electron charge, 0.946 V at 1310 nm; heterojunctions that add voltage above the photon energy add their excess voltage times the current to it.

Temperature and cooling

Heat lowers all three factors. The threshold rises and the slope falls with temperature, at rates given by the characteristic temperatures $T_0$ and $T_1$: 59.6 K and 143 K for the example laser. If those values held up to 85 °C, with $V_0$ and $R_s$ unchanged, the threshold would rise from 8.0 to 21.9 mA and the slope efficiency fall from 0.55 to 0.36 W/A, and the peak on the linear model would drop from 38.5% at 48 mA to 19.5% at 90 mA, half the value at 25 °C.

A cooler has a cost of its own. At 50 mA the example laser turns 60.0 mW of input into 22.66 mW of light and 37.3 mW of heat. A thermoelectric cooler with a coefficient of performance of 0.4, the value the cooler entry gives for a 40 K temperature difference, draws 93 mW to pump that heat away, so the efficiency counted at the package terminals falls from 37.8% to 15%, before any heat that leaks into the package from outside. Datasheets and system studies that quote a wall-plug efficiency including the driver and cooler, as for an external laser source, are therefore not comparable with values for the laser alone.

Reported values

The first two rows were record results when they were published. High-power lasers near 970 nm reach the highest values because they are designed for efficiency above all, with low internal loss and low series resistance; Crump and colleagues review the losses that remain. Telecom DFB lasers, designed for a single frequency and fast modulation, sit well below the Fabry-Perot example, and quantum cascade lasers lose efficiency because each stage of the cascade drops more voltage than the energy of the photon it emits. Typical ranges for each class of device are tabulated in Wall-plug efficiency from LIV data.

Measuring it

Wall-plug efficiency comes from an LIV sweep, dividing the power by the product of current and voltage at each point. The voltage is sensed with four wires at the device, so that the leads do not add resistance, and the detector must collect the whole beam; both errors bias the result low. The Wall-Plug Efficiency Calculator computes the curve from pasted LIV data and locates the peak, and the article above gives the procedure and the checks.

Common questions

What is wall-plug efficiency?

The fraction of the electrical input power that a laser converts into optical output, $P\mathrm{/}(IV)$, at a stated current and temperature.

How is wall-plug efficiency different from slope efficiency?

Slope efficiency is the increase in output per unit increase in current above threshold, $dP\mathrm{/}dI$ in W/A. Wall-plug efficiency divides the total output by the total electrical input, so it also counts the power spent on the threshold current and on the voltage. The example laser has a slope efficiency of 0.55 W/A and a peak wall-plug efficiency of 37.8%.

Why does wall-plug efficiency fall at high current?

The voltage keeps rising through the series resistance while the output grows only in proportion to the current, and self-heating lowers the slope. In the example the efficiency falls from 37.8% at 46 mA to 33.5% at 100 mA.

What is the highest wall-plug efficiency of a laser?

Above 70% for high-power diode lasers near 970 nm at room temperature: 73% for a bar emitting 50 W continuously (Kanskar et al., 2005).

References: L. A. Coldren, S. W. Corzine, and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012). P. Crump et al., "Efficient high-power laser diodes," IEEE Journal of Selected Topics in Quantum Electronics 19, 1501211 (2013). M. Kanskar et al., "73% CW power conversion efficiency at 50 W from 970 nm diode laser bars," Electronics Letters 41, 245 (2005). R. Jäger et al., "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electronics Letters 33, 330 (1997). Y. Bai et al., "Room temperature quantum cascade lasers with 27% wall plug efficiency," Applied Physics Letters 98, 181102 (2011).