How to Measure Photodetector Bandwidth and Frequency Response

Scope

This article gives the procedures for measuring the small-signal frequency response of a photodiode or photoreceiver and extracting its 3 dB bandwidth. Three methods are covered: a network analyzer driving a calibrated modulator, optical heterodyning of two lasers, and the impulse response to short optical pulses. It also covers de-embedding the RF path, and the dependence of the result on bias and photocurrent. The physical limits on bandwidth (RC time constant, transit time and diffusion) are set out in Photodetector Characterization, which also covers responsivity and noise-equivalent power; the noise side is computed by the Photodiode Noise Calculator.

What is being measured

The frequency response $H(f)$ is the RF photocurrent (or output voltage, for a receiver with a transimpedance amplifier) produced per unit of optical power modulation at frequency $f$, normalized to its low-frequency value. The 3 dB bandwidth is the frequency where the RF output power has fallen by half, which is where $20\log_{10}|H(f)| = -3$ dB and the photocurrent amplitude has fallen to 0.707 of its low-frequency value. The measurement is small-signal: the optical modulation must be small enough, and the photocurrent low enough, that the detector responds linearly.

Method 1: network analyzer with a calibrated modulator

A vector network analyzer (VNA) drives an electro-optic modulator; the modulated light falls on the detector; the detector's RF output returns to the VNA. The measured $S_{21}$ is the product of the modulator's response, the detector's response, and the responses of the cables, probes and bias tee in the path, so in dB:

$$S_{21} \;=\; H_\text{mod} + H_\text{PD} + H_\text{path}.$$

The detector's response is found by subtracting the other terms in dB. The RF path is removed by the VNA's own calibration to the planes where the modulator and detector connect (coaxial calibration standards, or on-wafer standards for probed devices). The modulator's response must come from its own calibration, which is where the method depends on a reference: commercial lightwave component analyzers are built around a modulator and receiver whose responses are calibrated at the factory, usually by the heterodyne method below. A modulator whose response is not known cannot be used to measure a detector whose response is not known.

Procedure

1. Calibrate the VNA to the reference planes: the modulator's RF input and the detector's RF output connectors or probe tips.
2. Bias the modulator at its linear operating point (quadrature for a Mach-Zehnder) and set the RF drive low enough that the response does not change when the drive is lowered by a few dB.
3. Set the optical power at the detector to a photocurrent well below the level where the response begins to depend on it (see below), and apply the detector's operating bias through a bias tee.
4. Sweep $S_{21}$ from the lowest frequency the bias tee passes to beyond the expected bandwidth.
5. Subtract the modulator's calibrated response and any path not removed by the VNA calibration, and normalize to the low-frequency value.
6. Read the 3 dB frequency, and keep the full curve: a response with peaking or a slow roll-off at low frequency says more about the device than a single number.

Method 2: optical heterodyne

Two single-frequency lasers are combined in a fiber coupler and fall on the detector. Their beat, the same effect used in heterodyne detection, produces a photocurrent at the difference frequency, and tuning one laser sweeps that frequency. With equal polarizations and powers $P_1$ and $P_2$, the photocurrent has an AC amplitude

$$i_\text{ac} \;=\; 2\,\mathcal{R}\sqrt{P_1 P_2}$$

at frequencies well below the detector's bandwidth, where $\mathcal{R}$ is the responsivity. The modulation depth is 100% when $P_1 = P_2$, and no modulator is involved, so the method needs no optical reference: only the RF power sensor or spectrum analyzer, and the cable or probe between it and the detector, have to be calibrated. It is the standard method for calibrating the references used by method 1.

For $\mathcal{R}$ = 0.8 A/W and 1 mW from each laser, $i_\text{ac}$ = 1.6 mA, which delivers $i_\text{ac}^2 R_L/2$ = 64 μW (−11.9 dBm) into a 50 Ω load. A detector with its own internal 50 Ω termination splits the current between the two resistors and delivers a quarter of that, −18.0 dBm. The measured RF power divided by the low-frequency expectation, frequency by frequency, is $|H(f)|^2$.

At 1550 nm the beat frequency changes by 125 MHz for each picometre of wavelength difference, so 100 GHz corresponds to 0.80 nm.

Procedure

1. Combine the two lasers in a polarization-maintaining coupler, or set their polarizations equal with a polarization controller while watching the beat power.
2. Record the DC photocurrent throughout. It gives $P_1 + P_2$ at the detector and lets each reading be normalized for power drift.
3. Tune one laser to set the beat frequency, find the beat on a spectrum analyzer or read it with a calibrated RF power sensor, and record its power. The lasers' frequency jitter spreads the beat; a spectrum analyzer's resolution bandwidth must contain it, or a power sensor must be used.
4. Step across the frequency range and repeat, correcting each point for the calibrated loss of the RF cable or probe at that frequency.
5. Normalize to the low-frequency points and read the 3 dB frequency.

Method 3: impulse response

A train of optical pulses much shorter than the detector's response time (femtosecond or picosecond pulses from a mode-locked laser) falls on the detector, and a sampling oscilloscope records the output pulse. The Fourier transform of the recorded pulse, divided by the transforms of the optical pulse and of the oscilloscope's own response, gives $H(f)$. The method captures the whole response in one acquisition and shows slow tails from diffusion directly in the time domain, but it depends on the oscilloscope's bandwidth and calibration, and the pulse energy must stay low enough that the detector is not driven into saturation by the high peak power.

Conditions that change the answer

Bias. The depletion width, and with it the capacitance and the transit time, depend on reverse bias. A detector measured below its operating bias shows a lower bandwidth, and a response that improves with bias up to a plateau identifies a transit- or depletion-limited device.

Photocurrent. At high photocurrent, the space charge of the carriers in transit screens the field in the depletion region and the response slows. Measure the bandwidth at two or more photocurrents; the small-signal value is the one that no longer changes as the photocurrent is lowered. Uni-traveling-carrier photodiodes are designed to push this limit higher.

Load and packaging. The bandwidth quoted for a bare photodiode assumes a particular load, usually 50 Ω. Bond wires, the package and a transimpedance amplifier each change it, and a receiver's bandwidth is a property of the whole assembly.

Low-frequency behavior. Diffusion of carriers generated outside the depletion region adds a slow component that appears as a response falling off at low frequency before the main roll-off. Normalizing to the value at the lowest measured frequency then hides it; report where the normalization was taken.

Common failure modes

Uncalibrated reference. A modulator or detector response taken from a nominal datasheet curve transfers its error directly into the result.

Reference planes not matched. Cables, connectors or probes left outside the calibration appear as extra roll-off, typically a steady loss increasing with frequency.

Large-signal drive. A modulation depth or photocurrent too high for linear operation compresses the low-frequency response more than the high-frequency response and flattens the curve.

Polarization drift in the heterodyne method. The beat power falls as the two lasers' polarizations separate; unmonitored, the drift looks like roll-off.

Electrical and optical dB conventions. Detector bandwidth is quoted on the electrical scale above. Comparisons with modulator bandwidths, sometimes quoted on an optical scale, need the conversion described in Measuring Modulator Vπ and Bandwidth.

References: D. Derickson (ed.), Fiber Optic Test and Measurement (Prentice Hall, 1998), chapters on high-speed photodetector and lightwave component analysis; T. S. Tan, R. L. Jungerman and S. S. Elliott, "Optical receiver and modulator frequency response measurement with a Nd:YAG ring laser heterodyne technique," IEEE Transactions on Microwave Theory and Techniques 37, 1217 (1989); K. Kato, "Ultrawide-band/high-frequency photodetectors," IEEE Transactions on Microwave Theory and Techniques 47, 1265 (1999).