# Photocurrent shot noise correlation function

• Niles
In summary, the expression for the correlation function of the photocurrent shot noise for a photodiode is <\delta i(t)\delta i(t+\tau)> = \frac{e^2\eta}{h\nu}P\delta(\tau), where η is the quantum efficiency and P is the power in the signal. The prefactor is derived from the energy per photon and the power of the light illuminating the photodiode, but it is unclear why it does not have units of {eP/hv}^2. Can anyone provide further insight on this?
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?Niles.

Niles said:
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?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:
No, P/(hv) is the photon flux, which equals the number of electrons/sec. The current is therefore eP/(hv). So I think the question from Niles is: why doesn't the expression above have units of {eP/hv}^2?

marcusl said:
No, P/(hv) is the photon flux, which equals the number of electrons/sec. The current is therefore eP/(hv). So I think the question from Niles is: why doesn't the expression above have units of {eP/hv}^2?

Hi

Thanks, that is exactly my question.

## 1. What is photocurrent shot noise correlation function?

The photocurrent shot noise correlation function is a measure of the correlation between the fluctuations in the photocurrent of a detector over time. It is used to analyze the noise in a photodetector and determine its sensitivity and performance.

## 2. How is photocurrent shot noise correlation function calculated?

The photocurrent shot noise correlation function is calculated by taking the autocorrelation of the photocurrent signal. This involves multiplying the photocurrent signal with a delayed version of itself and then averaging these values over time.

## 3. What factors affect the photocurrent shot noise correlation function?

The photocurrent shot noise correlation function is affected by various factors including the quantum efficiency of the detector, the dark current, the bandwidth of the detector, and the temperature of the detector. Any changes in these factors can impact the noise level and therefore the correlation function.

## 4. How is photocurrent shot noise correlation function used in research?

The photocurrent shot noise correlation function is used in research to study the performance of photodetectors, as well as to understand and minimize noise in optical systems. It is also used in the development of new detectors and in the optimization of detector parameters.

## 5. What are the practical applications of studying photocurrent shot noise correlation function?

Studying photocurrent shot noise correlation function has practical applications in various fields such as telecommunications, imaging, and spectroscopy. It is used to improve the sensitivity and accuracy of detectors in these applications, leading to better performance and results.

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