Shot noise consists of random fluctuations of the electric current in an electrical conductor, which are caused by the fact that the current is carried by discrete charges (electrons). The strength of this noise increases for growing magnitude of the average current flowing through the conductor. Shot noise is to be distinguished from current fluctuations in equilibrium, which happen without any applied voltage and without any average current flowing. These equilibrium current fluctuations are known as Johnson-Nyquist noise.
The strength of the current fluctuations can be expressed by giving the variance
of the current I, where <I> is the average ("macroscopic") current. However, the value measured in this way depends on the frequency range of fluctuations which is measured ("bandwidth" of the measurement): The measured variance of the current grows linearly with bandwidth. Therefore, a more fundamental quantity is the noise power, which is essentially obtained by dividing through the bandwidth (and, therefore, has the dimension ampere squared divided by Hertz). It may be defined as the zero-frequency Fourier transform of the current-current correlation function:
Note: This is the total noise power, which includes the equilibrium fluctuations (Johnson-Nyquist noise). Some other commonly employed definitions may differ by a constant pre-factor.
Note: There is often a minor inconsistency in referring to shot noise in an optical system: many authors refer to shot noise loosely when speaking of the mean square shot noise current (amperes2) rather than noise power (watts).