# Measure detector response using shot-noise

2017-01-05

A photodetector combines a photodiode with a transimpedance amplifier. The amplifier conditions the photocurrent exiting the photodiode while being able to drive low impedance lines. For a wideband detector, the frequency response is determined by parasitic capacitances of many elements (photodiode, amplifier, feedback resistor, PCB tracks). Those parasitic values are not always well known and modeling often only gives estimates of the bandwidth.

A method to measure the detector frequency response would be to illuminate the detector with a light of known modulation amplitude and frequency. This requires to modulate a laser beam in a known way but this poses the problem of characterizing the laser modulation response.

## Using optical shot-noise

To perform a good calibration we need to excite the detector with an optical signal having the same power spectral density at all frequencies, that is a white noise. Having this condition guaranteed by physics and not by auxiliary calibrations would make the measurement easier and more trustworthy.

Such a noise is intrinsically present on the light: this is the shot-noise. It exists because the energy of the laser beam is not deposited continuously onto the detector but by packets associated with the absorption of single-photon by the semi-conductor.

Therefore, if the noise at the detector output is dominated by the shot-noise, the power spectral density of the voltage output provides the frequency response of the detector.

## Noise measurement

To perform this measurement, we need a low intensity noise laser. We use the Koheron LD100 laser which is shot-noise limited down to 100 kHz, thanks to the high power supply noise rejection of the driver. We characterize Koheron PD100 photodetector with the following setup:

Here are the measurements of the power spectral density for various optical powers on the detector:

We see that the noise power increases with the optical power. But are we sure we are observing shot-noise ? This is checked by looking at the way noise power scales with the optical power. In shot-noise limited operation, the noise variance should scale linearly with optical power. If a technical noise dominates, one should observe a quadratic behavior. In the following figure, we plot the noise power versus the optical power at 50 MHz:

The linear scaling shows that the LD100 laser is shot-noise limited.

## Frequency response

The voltage noise density at the detector output can be written as:

$$v^{2}_{n} = v^{2}_{0} + 2 e S P_{opt} R^{2}_{F}(f),$$

where v02 is the background noise, e is the elementary electric charge, S the photodiode sensitivity, Popt is the incident optical power and RF(f) is the transimpedance gain at frequency f. We obtain the detector gain response below by computing the difference between the power spectral densities with and without incident light.

The detector bandwidth at 3 dB is 164 MHz with less than 0.6 dB of peaking at 70 MHz.