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groups:mg:project_ptb-cavity:optical_contacting [2017/08/08 13:21] – ssauergroups:mg:project_ptb-cavity:optical_contacting [2017/10/24 09:38] (current) – ssauer
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   * Durchgeführt von T. Legero an der PTB.   * Durchgeführt von T. Legero an der PTB.
   * Dokumentation: {{ :groups:mg:project_ptb-cavity:labjournal_thomas_legero.pdf |labjournal_thomas_legero}}   * Dokumentation: {{ :groups:mg:project_ptb-cavity:labjournal_thomas_legero.pdf |labjournal_thomas_legero}}
- 
-===== Calculation between cavity spectrum and frequency distance ===== 
-Caculates the cavity spectrum and the frequency distance between TEM_00 and higher order modes m+n. Two curved mirrors possible. Programm made by T. Legero.  
-==Parameter== 
-    * Radius of curvature of mirror R1: R1= 1 m 
-    * Radius of curvature of mirror R2: R2= 1 m 
-    * Cavity Length: L= 0.48 m 
-    * Reflectivity of mirrors: R= 0.99998 
-    * Speed of light: c= 299792458 m/s 
-     
-**Step 1: Calculate the Free-Spectral-Rang and Gouy-Phase**\\ 
-  * Free-Spectral-Rang: FSR 
-  * Gouy-Phase: Gouy 
-$$FSR = \frac{c}{2\cdot L}$$   
-$$Gouy = \frac{FSR}{\pi} \cdot \arccos \left( \sqrt{(1-\frac{L}{R1})\cdot(1-\frac{L}{R2}} \right)$$ 
- 
-=> 
-  * FSR = 312.284 MHz 
-  * Gouy = 101.783 MHz 
- 
-**Step 2: Calculate the frequency difference between TEM_00 and TEM_mn**\\ 
-  * TEM mode number: mn 
-  * Frequency difference between TEM_00 and TEM_mn: Delta 
-$$ \Delta = FSR - mn\cdot Gouy  $$ 
- 
-  * Define maximum of mn and w: 
-    * mn_max = 100 
-    * w_max = 100 
-  * Define maximum of shown frequency difference to TEM_00: 
-    * abs(delta(mn,w)) < 10E6 
- 
-  * Frequency difference von (q-w)ter höherer Mode mn zu q-ter TEM_00-Mode (Matrix):  
-$$ \Delta(mn,w) = w\cdot FSR - mn\cdot Gouy $$ 
- 
-=> 
- 
-Freq. diff. of m+n = 3 higher order mode to 00-mode is 6.93401 MHz\\ 
-Freq. diff. of m+n = 43 higher order mode to 00-mode is -4.70713 MHz\\ 
-Freq. diff. of m+n = 46 higher order mode to 00-mode is 2.22688 MHz\\ 
-Freq. diff. of m+n = 49 higher order mode to 00-mode is 9.16089 MHz\\ 
-Freq. diff. of m+n = 86 higher order mode to 00-mode is -9.41427 MHz\\ 
-Freq. diff. of m+n = 89 higher order mode to 00-mode is -2.48026 MHz\\ 
-Freq. diff. of m+n = 92 higher order mode to 00-mode is 4.45375 MHz\\ 
- 
-**Step 3: Calculate the frequency difference depends on the mirror curvature **\\ 
- 
-  * Define the Modenumber of Higher-Order-Mode to plot (next Mode to 00): 
-    * mn = 3 
-  * Define the Vary Mirror-Curvature: 
-    * R = 0.95:0.01:1.05 
-  * Frequency difference between TEM_00 and TEM_mn 
-$$ \Delta = FSR - mn\cdot Gouy $$ 
- 
-  * plot(R,d)**[Important!]**: 
-{{:groups:mg:project_ptb-cavity:mode_diff.jpg?400|}} 
- 
-  * plot(R,Gouy): 
-{{:groups:mg:project_ptb-cavity:mode_diff_gouy.jpg?400|}} 
- 
-  * plot(Gouy,d): 
-{{:groups:mg:project_ptb-cavity:mode_diff_gouy_d.jpg?400|}} 
  
 ===== Photos ===== ===== Photos =====