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]

⃗ ⃗ ⃗ -1-⃗ ⃗ S = E × H = μ0 E × B. (68 )
Inserting the electric and magnetic components of a plane wave, we obtain
1 c𝜖 |⃗S| = ----E2 = c𝜖0E20 cos2(ωt) = -0-E20 (1 + cos(2ωt )) , (69 ) μ0c 2
with 𝜖0 the electric permeability of vacuum and c the speed of light.

The response of a photo detector is given by the total flux of effective radiation4 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 λ = 1064 nm has a frequency of f = c∕ λ ≈ 282 1012 Hz = 282 THz. Thus, the 2ω component is much too fast for the photo detector; instead, it returns the average power

-- |S⃗| = c𝜖0E2 . (70 ) 2 0
In complex notation we can write
-- c𝜖0 |⃗S| = ---EE ∗. (71 ) 2
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 ----- √ watt. Thus, the notation used in this document to describe the computation of the light power of a laser beam is
∗ P = EE . (72 )
View Image

Figure 22: A beam with two frequency components hits the photo diode. Shown in this plot are the field amplitude, the corresponding intensity and the electrical output of the photodiode.
 4.1 Detection of optical beats
 4.2 Signal demodulation
 4.3 Finesse examples
  4.3.1 Optical beat

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