How to Compute Wall-Plug Efficiency from an LIV Curve

Scope

This article describes the procedure for computing wall-plug efficiency ${\eta }_{\text{WPE}}$ (the total electrical-to-optical conversion efficiency) of a semiconductor laser diode from LIV measurement data. Coverage includes the peak-WPE operating point identification, the relationship between ${\eta }_{\text{WPE}}$ and the other quantum efficiencies, and typical values across device classes. Calculation of WPE for systems including drive electronics, optical isolators, and packaging losses is outside scope.

Wall-plug efficiency formula

Wall-plug efficiency is defined as the ratio of optical output power to total input electrical power:

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

where $I$ is the drive current, $V(I)$ is the forward voltage at that current, and $P_{\text{out}}(I)$ is the corresponding optical output. The quantity is dimensionless and conventionally expressed as a percentage.

Unlike slope efficiency and differential quantum efficiency, which describe the marginal conversion of additional electrical power above threshold, wall-plug efficiency is the total conversion at a given operating point. It is the relevant metric for power-budget calculations, thermal management design, and overall system efficiency.

Relationship to other efficiencies

The wall-plug efficiency depends on three contributing factors:

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

where:

• ${\eta }_d$ is the external differential quantum efficiency (photons out per electron above threshold)
• $h\nu \mathrm{/}(qV)=(1.24\mu \text{m}\cdot \text{V}\mathrm{/}\lambda )\cdot 1\mathrm{/}V$ is the photon-to-electron-energy ratio, accounting for the fact that the junction voltage exceeds the bandgap voltage
• $(1-I_{\text{th}}\mathrm{/}I)$ is the lasing fraction, which approaches 1 at high $I\mathrm{/}{I}_{\text{th}}$ but penalizes operation near threshold

Three regimes:

Near threshold ($I\approx I_{\text{th}}$): ${\eta }_{\text{WPE}}\to 0$ because nearly all the electrical power goes to maintaining the threshold current rather than to additional photon production.

Moderate current (several times $I_{\text{th}}$): ${\eta }_{\text{WPE}}$ reaches a peak. The lasing fraction $(1-I_{\text{th}}\mathrm{/}I)$ approaches 1 while the voltage has not yet risen significantly above the bandgap.

High current ($I\gg I_{\text{th}}$): ${\eta }_{\text{WPE}}$ declines because the forward voltage $V$ rises due to series resistance, while ${\eta }_d$ may also decrease from thermal rollover or carrier leakage.

For linear L–I and V–I characteristics, with $V=V_0+I{R}_s$, the peak wall-plug efficiency ${\eta }_{\text{WPE,max}}$ lies at

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

which is $1+\sqrt{1+V_0\mathrm{/}(I_{\text{th}}{R}_s)}$ times threshold: the smaller the resistive drop at threshold compared with the turn-on voltage, the further above threshold the peak lies. For the worked example below the formula gives 48 mA, six times threshold; self-heating, which it leaves out, moves the measured peak to 46 mA.

Typical wall-plug efficiency by device class

Telecom DFB lasers have substantially lower WPE than equally-developed pump diodes because they are designed for spectral purity and direct modulation rather than for raw efficiency. Quantum cascade lasers have the lowest WPE of the classes listed. Their upper laser level is emptied by optical-phonon scattering in about a picosecond, so a high current density is needed to reach threshold, and each stage of the cascade drops more voltage than the energy of the photon it emits.

For comparison, wall-plug efficiency of the entire optical link (laser + drive electronics + fiber coupling + receiver) is substantially lower than the laser-alone ${\eta }_{\text{WPE}}$.

Required measurements

A standard LIV measurement provides all required data. No special instrumentation is needed beyond what is described in the LIV curve glossary entry and the bench setup article:

• Drive current $I$ swept through the operating range
• Forward voltage $V(I)$ measured by 4-wire Kelvin sense
• Optical output $P_{\text{out}}(I)$ measured by calibrated detector (integrating sphere preferred)

The current sweep should extend from well below threshold to at least $5I_{\text{th}}$ (and ideally beyond the peak-WPE operating point) so that the peak can be identified from the data rather than extrapolated.

For accurate peak-WPE measurement, the sweep must use small enough current steps that the peak is well-resolved, typically 50–100 points spanning the lasing region. The current source compliance voltage must exceed the maximum forward voltage at the highest sweep current, including margin for any series resistance.

Procedure

1. Acquire LIV with sufficient range and resolution

Sweep current from 0 to at least $5I_{\text{th}}$ in steps that resolve the curvature of ${\eta }_{\text{WPE}}(I)$, typically 50–100 points across the lasing region. Record $V(I)$ and $P_{\text{out}}(I)$ at each point.

For a typical telecom DFB with $I_{\text{th}}=10$ mA, this requires a sweep extending to at least 50 mA with $\sim 0.5$ mA steps in the lasing region. For a high-power pump diode with $I_{\text{th}}=200$ mA, the sweep extends to several amperes with proportionally larger steps.

2. Compute WPE at each operating point

For each measurement point:

$${\eta }_{\text{WPE,i}}=\frac{P_{\text{out,i}}}{I_i\cdot V_i}\mathrm{.}$$

In SI units with $P$ in watts, $I$ in amperes, and $V$ in volts, ${\eta }_{\text{WPE}}$ is dimensionless. Multiply by 100 to express as a percentage.

3. Identify the peak

The peak of ${\eta }_{\text{WPE}}(I)$ is typically a smooth maximum. Locate the maximum from the discrete data; for finer resolution, fit a low-order polynomial near the apparent peak and locate the maximum of the fit.

The peak operating current $I_{\text{peak}}$ and the peak efficiency value ${\eta }_{\text{WPE,max}}$ together specify the device's best operating point for raw efficiency.

4. Report

The Wall-Plug Efficiency Calculator accepts LIV data in (current, voltage, power) format and produces the WPE curve with peak identification.

Report:

• ${\eta }_{\text{WPE,max}}$ (percentage)
• $I_{\text{peak}}$ at which the peak occurs
• The ratio $I_{\text{peak}}\mathrm{/}{I}_{\text{th}}$
• $V$ and $P_{\text{out}}$ at $I_{\text{peak}}$
• The measurement temperature (heatsink setpoint)
• The full WPE-vs-I curve, since peak operation is one point and many applications operate near (but not at) the peak

If the application requires operation at a specified current rather than at peak efficiency (e.g., for a datacom transmitter required to produce a fixed optical power), report ${\eta }_{\text{WPE}}$ at the actual operating current rather than at the peak.

Worked example

The 1310 nm InP Fabry–Pérot laser used in the other LIV articles, with a high-reflection coating on its rear facet, is swept CW at a 25 °C heatsink from 0 to 100 mA in 2 mA steps. The values below come from the same model as the continuous-wave curve in the pulsed vs CW article: a threshold of 8.05 mA once self-heating is included, a forward voltage of $0.95\text{ V}+5\mathrm{\Omega }\times I$ and a thermal resistance of 50 K/W. Selected points:

The largest value in the 2 mA sweep is ${\eta }_{\text{WPE}}=37.8\mathrm{\%}$ at $I_{\text{peak}}=46$ mA, where $V=1.180$ V and $P_{\text{out}}=20.53$ mW, so $I_{\text{peak}}\mathrm{/}{I}_{\text{th}}\approx 5.7$. The peak is broad: every point from 34 to 66 mA is within one percentage point of it. Above the peak the efficiency falls mainly because the forward voltage keeps rising through the series resistance, from 1.18 V at the peak to 1.45 V at 100 mA, while the lasing fraction is already close to 1. Self-heating adds a smaller loss: at 100 mA the CW output is 4% below the pulsed value.

A peak of 37.8% is high for a 1310 nm InP laser. It follows from the example's slope efficiency, 0.55 W/A from the front facet, which the high-reflection rear coating makes possible, and from its low threshold. Telecom DFB lasers, designed for single-frequency operation and modulation rather than for efficiency, reach the lower values in the table above.

Sources of error

Voltage measurement contaminated by IR drops. As discussed in the bench setup article, 2-wire voltage measurement includes cable and contact resistance, producing apparent voltage higher than the true junction value. This biases WPE low. 4-wire Kelvin sense is required.

Optical power calibration error. Detector calibration errors translate directly to WPE errors at the same fractional magnitude. A 10% detector calibration error produces a 10% error in WPE. Verify detector calibration against NIST-traceable reference for accurate WPE values.

Self-heating in CW measurements. Self-heating raises the threshold and lowers the slope efficiency, depressing ${\eta }_{\text{WPE}}$ at high currents; the forward voltage at a given current, if anything, falls slightly as the bandgap narrows with temperature. For accurate high-current WPE, pulsed measurement removes this contribution; see the pulsed vs CW LIV article.

Series resistance overestimating peak WPE depression. External series resistance from cables, contact pads, and bonding contributes to the measured $V(I)$ but is not intrinsic to the device. For applications that will use a different bonding/contact configuration, the device-intrinsic series resistance must be separated from the bench-specific series resistance.

Operating point chosen outside the peak. Many devices are operated at constant power rather than peak efficiency. For datacenter optical modules, the required output power may correspond to an operating current well above the WPE peak. Report WPE at the actual operating current, not just the peak.

Comparison with system-level efficiency. Marketing or system-level documents sometimes quote "wall-plug efficiency" that includes the laser driver, cooling, and packaging. These values are not directly comparable to laser-alone WPE.

Validation

The peak WPE should fall within the typical range for the device class (table above). Values outside the typical range by more than 30% indicate either a non-standard device or measurement error.

The WPE curve should be smooth and have a single peak. Local non-monotonic behavior (apart from measurement noise) suggests mode hopping, kink-mode transitions, or instrument switching artifacts in the LIV.

At the peak, the lasing fraction $(1-I_{\text{th}}\mathrm{/}I)$ for a typical device is $0.7-0.9$, so peak WPE is approximately $0.7-0.9$ times the wall-plug efficiency that would be achieved if the threshold were zero. The three-factor product also gives a check, provided ${\eta }_d$ comes from the slope of the L–I curve rather than from the peak point itself, which would make the product equal the measured value by construction. In the worked example the slope just above threshold, 0.545 W/A between 10 and 20 mA, is ${\eta }_d=57.6\mathrm{\%}$ at 1310 nm; with $h\nu \mathrm{/}(qV)=0.946\mathrm{/}1.180=0.802$ and a lasing fraction of $1-8.05\mathrm{/}46=0.825$ at the peak, the product is 38.1%, within 1% of the measured 37.8%. The small shortfall is the self-heating that bends the CW curve below its low-current slope.

Common questions

What is wall-plug efficiency?

Wall-plug efficiency is the fraction of a laser's electrical input power that leaves as optical power, ${\eta }_{\text{WPE}}=P_{\text{out}}\mathrm{/}(IV)$ at a given drive current, usually quoted in percent. It is the total conversion at one operating point, whereas slope efficiency and differential quantum efficiency describe only the marginal conversion above threshold.

How do you calculate wall-plug efficiency from an LIV curve?

Sweep the current from below threshold to at least five times threshold, measuring the voltage by 4-wire sense and the optical power with a calibrated detector, and divide the optical power by the electrical power $IV$ at each point. Locate the maximum of the resulting curve, refined with a low-order polynomial fit near the peak if needed, and report it with its current, the ratio $I_{\text{peak}}\mathrm{/}{I}_{\text{th}}$ and the heatsink temperature.

What is a typical wall-plug efficiency for a laser diode?

Typical peak values are 0.5–4% for mid-infrared quantum cascade lasers, 8–18% for telecom DFB lasers, 30–45% for datacom VCSELs and high-power blue laser diodes, and 50–65% for high-power 980 nm pump diodes. The 1310 nm laser in the worked example peaks at 37.8%, a high value for an InP device.

At what current is wall-plug efficiency highest?

The peak lies at several times threshold: close to threshold most of the input power goes into sustaining the threshold current, and at high current the voltage drop across the series resistance keeps growing. For linear light-current and voltage-current curves with $V=V_0+I{R}_s$, the peak current is $1+\sqrt{1+V_0\mathrm{/}(I_{\text{th}}{R}_s)}$ times the threshold current; in the worked example that is 48 mA, and self-heating moves the measured peak to 46 mA, 5.7 times the 8.05 mA threshold.

What limits the wall-plug efficiency of a laser diode?

It is the product of three factors: the external differential quantum efficiency, the ratio $h\nu \mathrm{/}(qV)$ of photon energy to the energy supplied per electron, which stays below one because the forward voltage exceeds the bandgap voltage, and the lasing fraction $1-I_{\text{th}}\mathrm{/}I$. Series resistance and self-heating lower it further at high current.

References

For the textbook treatment of wall-plug efficiency in the context of semiconductor laser theory, see Coldren, Corzine, and Mašanović (2012), chapter 2. For the relationship between WPE and device material/structure choices in high-power laser design, see Crump et al. (2013) on broad-area diode laser efficiency optimization.

The wall-plug efficiency calculator runs this computation on pasted LIV data and locates the peak-efficiency current.