In this example two laser beams are superimposed at a 50:50 beam splitter. The beams have a slightly different frequency: the second beam has a 10 kHz offset with respect to the first (and to the default laser frequency). The plot illustrates the output of four different detectors in one of the beam splitter output ports, while the phase of the second beam is tuned from 0° to 180°. The photodiode ‘pd1’ shows the total power remaining constant at 1. The amplitude detectors ‘ad1’ and ‘ad10k’ detect the laser light at 0 Hz (default frequency) and 10 kHz respectively. Both show a constant absolute of and the detector ‘ad10k’ tracks the tuning of the phase of the second laser beam. Finally, the detector ‘pd10k’ resembles a photodiode with demodulation at 10 kHz. In fact, this represents a photodiode and two mixers used to reconstruct a complex number as shown in Equation (82). One can see that the phase of the resulting electronic signal also directly follows the phase difference between the two laser beams.
Finesse input file for ‘Optical beat’
const freq 10k % creating a constant for the frequency offset
laser l1 1 0 n1 % laser with P=1W at the default frequency
space s1 1n 1 n1 n2 % space of 1nm length
laser l2 1 $freq n3 % a second laser with f=10kHz frequency offset
space s2 1n 1 n3 n4 % another space of 1nm length
bs b1 0.5 0.5 0 0 n2 n5 dump n4 % 50:50 beam splitter
space s3 1n 1 n5 n6 % another space of 1nm length
ad ad0 0 n6 % amplitude detector at f=0Hz
ad ad10k $freq n6 % amplitude detector at f=10kHz
pd pd1 n6 % simple photo detector
pd1 pd10k $freq n6 % photo detector with demodulation at 10kHz
xaxis l2 phi lin 0 180 100 % changing the phase of the l2-beam
yaxis abs:deg % plotting amplitude and phase
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