Optical Networks, 3rd Edition

APPENDIX I

Receiver Noise Statistics

WE START OUT BY DERIVING an expression for the statistics of the photocurrent in the pin receiver, along the lines of [BL90, RH90]. It is useful to think of the photodetection process in the following way. Each time a photon hits the receiver, the receiver generates a small current pulse. Let t_k denote the arrival times of photons at the receiver. Then the photocurrent generated can be expressed as

(I.1)

where e is the electronic charge and eh(t – t_k) denotes the current impulse due to a photon arriving at time t_k. Note that since eh(t – t_k) is the current due to a single electron, we must have

The arrival ...