Figure 33 shows a plot of the analytical functions describing the power inside a cavity and its
differentiation by the cavity tuning. This example recreates the plot using a numerical model in
Finesse.
Finesse input file for ‘Cavity power and slope’
laser l1 1 0 n1 % laser with P=1W at the default frequency
space s1 1 1 n1 n2 % space of 1m length
mirror m1 0.9 0.1 0 n2 n3 % cavity input mirror
space L 1200 1 n3 n4 % cavity length of 1200m
mirror m2 1.0 0.0 0 n4 dump % cavity output mirror
pd P n3 % photo diode measuring the intra-cavity power
% for the plot we perform two sequenctial runs of Finesse using ‘mkat’
% 1) first trace: plot the power (switching to log plot)
run1: yaxis log abs
% 2) second trace: plot the differentiation
run2: diff m2 phi
xaxis m2 phi lin -50 250 300 % changing the microscopic tuning of mirror m2
Figure 39 shows the demodulated photodiode signal of a Michelson interferometer with Schnupp
modulation, as well as its differentiation, the latter being the optical gain of the system. Comparing this
figure to Figure 36
, it can be seen that with Schnupp modulation, the optical gain at the dark fringe
operating points is maximised and a suitable error signal for these points is obtained.
Finesse input file for ‘Michelson with Schnupp modulation’
laser l1 1 0 n1 % laser with P=1W at the default frequency
space s1 1 1 n1 n2 % space of 1m length
mod eom1 10M 0.3 1 pm n2 n3 % phase modulation at 10 MHz
space s2 1 1 n3 n4 % another space of 1m length
bs b1 0.5 0.5 0 0 n4 nN1 nE1 nS1 % 50:50 beam splitter
space LN 100 1 nN1 nN2 % north arm
space LE 110 1 nE1 nE2 % east arm
mirror mN 1 0 22 nN2 dump % north end mirror, lossless
mirror mE 1 0 -22 nE2 dump % east end mirror, lossless
space s3 1 1 nS1 nout
run1: pd1 South 10M -115 nout % demodulated output signal
run2: pd1 South 10M -115 nout % demodulated output signal
run2: diff mN phi % computing the slope of the signal
xaxis mN phi lin 0 300 100 % changing the microscopic position of mN
put mE phi $mx1 % moving mE as -mN to make a differential motion
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