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Message ID: 14057     Entry time: Thu Jul 12 14:06:39 2018
 Author: keerthana Type: Update Category: elog Subject: Finesse and Analytical solution - Comparison

I tried to compare the cavity scan data we get from the Finesse simulation and that we expect from the Analytical solution. The diagram of the cavity I defined in Finesse is given below along with the values of different quantities I used. For the analytical solution I have used two different equations and they are listed below.

Analytical 1 - Blue Graph

$\phi = \frac {2.L.\Omega_1}{c}$

$t_{cav} = \frac{t_e. t_f \exp^{-i\frac{\phi}{2}}}{1- r_f. r_e \exp^{-i\phi} }$

$T_{cav} = \left|{t_{cav}} \right|^2$

Analytical 2 - Red Graph

$F = \frac {4. r_f.r_e}{(1-r_f.r_e )^2}$

$\phi = \frac {2.L.\Omega_1}{c}$

$T_{cav} = \left|{t_{cav}} \right|^2 = \frac {(t_e.t_f)^2}{(1 - r_f . r_e)^2} \frac{1}{1+F(\sin\frac {\phi}{2})^2}$

The graph obtained from both these solutions completely matches with each other.

Finesse Solution

The cavity which I defined in Finesse is shown below. The solution from Finesse and the Analytical solution also matches with each other. Another plot is made by taking the difference between Finesse solution and Analytical solution. The difference seems to be of the order of $\approx 10^{-19}$.

The Difference plot is also attached below.

 Attachment 1: finesse_cavity.png  29 kB  Uploaded Thu Jul 12 15:09:11 2018
 Attachment 2: Analytical1.pdf  18 kB  Uploaded Thu Jul 12 16:52:44 2018
 Attachment 3: Finesse_Analytical.pdf  18 kB  Uploaded Thu Jul 12 16:57:16 2018
 Attachment 4: Difference.pdf  60 kB  Uploaded Thu Jul 12 17:10:15 2018
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