MadSci Network: Physics Query:

Re: Why do light detectors always square the electric field ?

Date: Fri Jun 17 07:07:37 2005
Posted By: Ben Tordoff, Grad student, Lasers in nuclear physics, University of Jyvaskyla
Area of science: Physics
ID: 1118743458.Ph
Message:
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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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