Noise Equivalent Power (NEP) is a standard metric for quantifying the sensitivity of photodetectors. In this post we present a method to measure the NEP using optical shot-noise.
Noise Equivalent Power (NEP)
In a photonic system, the optical signal is converted into an electrical signal using a photodetector. Several sources are contributing to the photodetector noise:
- Schottky noise from the photodiode dark current
- Thermal noise
- Amplifier voltage and current noise
Noise can be equivalently given on both sides of the detector either as a voltage noise density vn at the output (in V/Hz1/2) or as a Noise Equivalent Power (NEP) at the input (in W/Hz1/2). Both quantities are related by:
where G is the detector gain in V / W.
The NEP defines the incident optical power required to obtain a signal-to-noise ratio (SNR) of 1. For example, when detecting a signal in a Δf = 10 kHz bandwidth with a detector of NEP = 1 pW/Hz1/2, the optical power required for a SNR of 1 is NEP x (Δf)1/2 = 100 pW.
Usually, the NEP is obtained by measuring G and vn. We show here how to obtain the NEP by relying on the statistical properties of optical shot-noise.
The following setup is used for the measurement:
A Koheron DRV200 driver controls a DFB laser. The current is set to deliver 2 mW at the laser output. A variable optical attenuator (VOA) is used to control the optical power incident on the Koheron PD01 photodetector. A power meter measures the power delivered to the photodetector. The photodetector output is connected to the input of a Koheron Alpha250 acquisition board.
On the Alpha250 acquisition board, we run the adc-dac-dma instrument. This instrument allows us to acquire data buffers up to 8 million samples, resulting in power spectrums spanning from 30 Hz to 125 MHz. A simple Python script acquires a full buffer and performs its Fourier Transform.
Here are the acquired raw power spectral densities:
As expected, the noise increases with the incident optical power. It exhibits 1/f noise followed by a white noise region and then a roll-off induced by the 400 kHz bandwidth of the Koheron PD01 photodetector. The 1/f noise corresponds to the relative intensity noise (RIN) of the DFB laser, whose relative contribution increases with optical power.
It seems that the laser is shot-noise limited at higher frequencies. This is confirmed by plotting the power spectral density at 200 kHz versus the incident optical power:
The blue dots are the measured data. The green line is a quadratic fit of the variance:
The offset is the photodetector noise floor (that is the one we want to convert into a Noise Equivalent Power). The linear term is the optical shot-noise and the quadratic term is the laser RIN. With 40.5 µW of incident power the RIN contributes to about 13 % of the noise at 200 kHz.
The equivalent power of the optical shot-noise is:
where e is the elementary charge and S is the photodiode sensitivity (A / W).
Assuming the photodetector response is linear, we have:
Coming back to the initial raw data where PSD0 is the blue curve and using the value of $A$ obtained from the fit and a sensitivity S = 0.9 A/W for the photodiode, we get the Noise Equivalent Power of our photodetector: