# Photocurrent shot noise correlation function

Hi

I have stumpled upon the following expression for the correlation function of the photocurrent shot noise for a photodiode
$$<\delta i(t)\delta i(t+\tau)> = \frac{e^2\eta}{h\nu}P\delta(\tau)$$
where η is the quantum efficiency and P the power in the signal. δ(τ) denotes the Dirac delta, which makes good sense as shot noise is white noise. However I am unsure of how the prefactor is derived. Can anyone point me in the right direction?

Best,
Niles.

Hi

I have stumpled upon the following expression for the correlation function of the photocurrent shot noise for a photodiode
$$<\delta i(t)\delta i(t+\tau)> = \frac{e^2\eta}{h\nu}P\delta(\tau)$$
where η is the quantum efficiency and P the power in the signal. δ(τ) denotes the Dirac delta, which makes good sense as shot noise is white noise. However I am unsure of how the prefactor is derived. Can anyone point me in the right direction?

Best,
Niles.
I can point in a direction. Sorry that I don't have a text editor, but I think you will see what I am getting at.
{h\nu} is the energy per photon. "P" is the power of the light illuminating the photodiode, which means energy per second. So {h\nu}P is the number of photons per second illuminating the photodiode.

Last edited:
marcusl