8.3 Finesse examples

8.3.1 Beam parameter

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Figure 55: Finesse example: Beam parameter

This example illustrates a possible use of the beam parameter detector ‘bp’: the beam radius of the laser beam is plotted as a function of distance to the laser. For this simulation, the interferometer matrix does not need to be solved. ‘bp’ merely returns the results from the beam tracing algorithm of Finesse.

Finesse input file for ‘Beam parameter’


laser i1 1 0 n1            % laser with P=1W
gauss g1 i1 n1 1m -2       % a dummy beam parameter
maxtem 0                   % we need only the ux00 mode 
s s1 1 n1 n2               % a space of 1m length
bp width x w n2            % detecting the beam width (horizontal)
xaxis s1 L lin 0.1 8 200   % tuning the length of s1

8.3.2 Mode cleaner

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Figure 56: Finesse example: Mode cleaner

This example uses the ‘tem’ command to create a laser beam which is a sum of equal parts in u00 and u10 modes. This beam is passed through a triangular cavity, which acts as a mode cleaner. Being resonant for the u00, the cavity transmits this mode and reflects the u10 mode as can be seen in the resulting plots.

Finesse input file for ‘Mode cleaner’


laser i1 1 0 n1            % laser with P=1W
maxtem 1                   % need Hermite-Gauss modes up to n+m=1
tem i1 0 0 1 0             % laser beam is a mix of u_00 and u_10 
tem i1 1 0 1 0
s s1 1 n1 n2               % a space of 1m length
% triangular mode cleaner cavity
bs bs1 .9 .1 0 0 n2 nrefl n3 n4     % input mirror
s sc1 2 n3 n5                       % distance between b1 and bs2
bs bs2 .9 .1 0 0 ntrans dump  n5 n6 % output mirror
s sc2 49 n4 n7                      % distance between b1 and bs3
s sc3 49 n6 n8                      % distance between b2 and bs3
bs bs3 1 0 0 0 n7 n8 dump dump      % end mirror
attr bs3 Rc 150                     % Rc=150m for bs3
cav cav1 bs1 n3 bs1 n4              % computing cavity parameters
run1: beam ccd ntrans       % beam shape in transmission
run2: beam ccd nrefl        % beam shape in reflection
xaxis ccd x lin -3 3 200    % tuning x,y axes of beam detector
x2axis ccd y lin -3 3 200
yaxis abs                   % plotting the absolute intensity 

8.3.3 LG33 mode

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Figure 57: Finesse example: LG33 mode. The ring structure in the phase plot is due to phase jumps, which could be removed by applying a phase ‘unwrap’.

Finesse uses the Hermite–Gauss modes as a base system for describing the spatial properties of laser beams. However, Laguerre–Gauss modes can be created using the coefficients given in Equation (149View Equation). This example demonstrates this and the use of a ‘beam’ detector to plot amplitude and phase of a beam cross section.

Finesse input file for ‘LG33 mode’


laser i1 1 0 n1           % laser with P=1W
gauss g1 i1 n1 1m 0       % a dummy beam parameter
maxtem 9                  % we need modes up to n+m=9
tem i1 0 0 0 0            % HG coefficients to create LG33 mode
tem i1 9 0 0.164063 0
tem i1 8 1 0.164063 -90
tem i1 7 2 0 0
tem i1 6 3 0.125 -90
tem i1 5 4 0.046875 180
tem i1 4 5 0.046875 -90
tem i1 3 6 0.125 180
tem i1 2 7 0 0
tem i1 1 8 0.164063 180
tem i1 0 9 0.164063 90
s s1 1 n1 n2              % space of 1m lentgh

beam ccd 0 n2  % beam detector for carrier light
xaxis ccd x lin -5 5 200  % tune x position of beam detector
x2axis ccd y lin -5 5 200 % tune y position of beam detector
yaxis abs:deg  % plot amplitude and phase
multi


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