## 4 Optical Readout

In previous sections we have dealt with the amplitude of light fields directly and also used the amplitude
detector in the Finesse examples. This is the advantage of a mathematical analysis versus experimental
tests, in which only light intensity or light power can be measured directly. This section gives the
mathematical details for modelling photo detectors.

The intensity of a field impinging on a photo detector is given as the magnitude of the Poynting vector,
with the Poynting vector given as [58]

Inserting the electric and magnetic components of a plane wave, we obtain
with the electric permeability of vacuum and the speed of light.
The response of a photo detector is given by the total flux of effective
radiation
during the response time of the detector. For example, in a photo diode a photon will release a charge
in the n-p junction. The response time is given by the time it takes for the charge to travel
through the detector (and further time may be taken up in the electronic processing of the
signal). The size of the photodiode and the applied bias voltage determine the travel time of the
charges with typical values of approximately 10 ns. Thus, frequency components faster than
perhaps 100 MHz are not resolved by a standard photodiode. For example, a laser beam with a
wavelength of = 1064 nm has a frequency of . Thus, the
component is much too fast for the photo detector; instead, it returns the average power

In complex notation we can write
However, for more intuitive results the light fields can be given in converted units, so that the light power
can be computed as the square of the light field amplitudes. Unless otherwise noted, throughout this work
the unit of light field amplitudes is . Thus, the notation used in this document to describe the
computation of the light power of a laser beam is