|MadSci Network: Physics|
Hi there, I have some experience in light detection so I'll explain from the point of view of a photomultiplier tube but this goes for all light detectors. A photon of a given energy hits the front plate of the light detector, this knocks off an electron of an energy corresponding to hf - W (the energy of the photon - the work function of the material). Due to an electric field between the front and back plate of the detector, the electron is accelerated through the material. This causes further electron emissions as the initial electron hits electrons orbiting atoms in the material. 1 becomes 2, 2 to 4, 4 to 8 and so on. At the end plate the number of electrons which have been knocked off is proportional to the initial number of photons which hit the front plate of the detector in the first place. The number of photons hitting the front of the detector is called the intensity and from Maxwells equations this is directly proportional to the square of the electric field of the photon. So the reason the detectors take the square of the electric field is because their output signal is proportional to the intensity of the light inputted. With regard to the integration of the detector, the minimum amount of integrated (or summed = same thing) signal is a function of how quickly the material it is made of can transmit the charge carriers through the lattice. This is known as electron mobility and is tabulated for many useful materials used for detection. The more time the charge is left to build up in the detector tells you the integration time of the signal. Using electronics after the detector it is possible to increase this integration time so you can have as long a time as you want, but no shorter than the electron mobility. For the electric energy, it is not defined as the square of the electric field, but this falls out as the relationship when you solve Gauss's law for the electric field and then integrating the electric field gives the electric potential. Its a straight forward proof and is in any university level electromagnetism text book such as Electromagnetism by Grant and Philips. I hope this answers most of your question.
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