5.3 Finesse examples

5.3.1 Michelson power

View Image

Figure 30: Finesse example: Michelson power.

The power in the South port of a Michelson detector varies as the cosine squared of the microscopic arm length difference. The maximum output can be equal to the input power, but only if the Michelson interferometer is symmetric and lossless. The tuning for which the South port power is zero is referred to as the dark fringe.

Finesse input file for ‘Michelson power’


laser l1 1 0  n1      % laser with P=1W at the default frequency
space s1 1 1 n1 n2    % space of 1m length
run1: bs b1 0.5 0.5 0 0 n2 nN1 nE1 nS1 % 50:50 beam splitter 
run2: bs b1 0.4 0.6 0 0 n2 nN1 nE1 nS1 % 40:60 beam splitter 
run3: bs b1 0.45 0.45 0 0 n2 nN1 nE1 nS1 % 45:45 beam splitter 
space  LN 1 1 nN1 nN2    % north arm
space  LE 1 1 nE1 nE2    % east arm
mirror mN 1 0 0 nN2 dump % north end mirror, lossless
mirror mE 1 0 0 nE2 dump % east end mirror, lossless
space  s2 1 1 nS1 nout 
pd South nout            % photo detector in South port
xaxis mN phi lin 0 300 100 % changing the microscopic position of mN

5.3.2 Michelson modulation

View Image

Figure 31: Finesse example: Michelson modulation.

This example demonstrates how a macroscopic arm length difference can cause different ‘dark fringe’ tuning for injected fields with different frequencies. In this case, some of the 10 MHz modulation sidebands are transmitted when the interferometer is tuned to a dark fringe for the carrier light. This effect can be used to separate light fields of different frequencies. It is also the cause for transmission of laser noise (especially frequency noise) into the Michelson output port when the interferometer is not perfectly symmetric.

Finesse input file for ‘Michelson 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 0 nN2 dump % north end mirror, lossless
mirror mE 1 0 0 nE2 dump % east end mirror, lossless
space  s3 1 1 nS1 nout 
ad carrier 0 nout        % amplitude detector for carrier field
ad sideband 10M nout     % amplitude detector for +10 MHz sideband
xaxis mN phi lin 0 300 100 % changing the microscopic position of mN


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