### 2.7 Finesse examples

#### 2.7.1 Mirror reflectivity and transmittance

We use Finesse to plot the amplitudes of the light fields transmitted and reflected by a mirror (given by a single surface). Initially, the mirror has a power reflectance and transmittance of and is, thus, lossless. For the plot in Figure 13 we tune the transmittance from 0.5 to 0. Since we do not explicitly change the reflectivity, remains at 0.5 and the mirror loss increases instead, which is shown by the trace labelled ‘total’ corresponding to the sum of the reflected and transmitted light power. The plot also shows the phase convention of a 90° phase shift for the transmitted light.

Finesse input file for ‘Mirror reflectivity and transmittance’

laser  l1 1 0 n1  % laser with P=1W at the default frequency
space  s1 1 n1 n2 % space of 1m length
mirror m1 0.5 0.5 0 n2 n3 % mirror with T=R=0.5 at zero tuning
func total = \$r^2 + \$t^2 % computing the sum of the reflected and transmitted power

xaxis m1 t lin 0.5 0 100 % changing the transmittance of the mirror ‘m1’
yaxis abs:deg     % plotting amplitude and phase of the results

#### 2.7.2 Length and tunings

This Finesse file demonstrates the conventions for lengths and microscopic positions introduced in Section 2.5. The top trace in Figure 14 depicts the phase change of a beam reflected by a beam splitter as the function of the beam splitter tuning. By changing the tuning from 0 to 180° the beam splitter is moved forward and shortens the path length by one wavelength, which by convention increases the light phase by 360°. On the other hand, if a length of a space is changed, the phase of the transmitted light is unchanged (for the default wavelength ), as shown the in the lower trace.

Finesse input file for ‘Length and tunings’

laser  l1 1 0 n1    % laser with P=1W at the default frequency
space  s1 1 1 n1 n2 % space of 1m length
bs     b1 1 0 0 0 n2 n3 dump dump % beam splitter as ‘turning mirror’,  normal incidence
space  s2 1 1 n3 n4 % another space of 1m length