====== Mode Matching - plan and curve mirrors ======

==== Mirror configuration ====
{{ :groups:mg:project_ptb-cavity:img_3440.jpg?400|}}
==Parameter==
    * Radius of curvature of mirror R1: R1= 1 m
    * Radius of curvature of mirror R2: R2= infinity (Incoupling side) 
    * Wavelength: λ= 1542.0 nm
    * Length between the resonator mirrors: L= 480 mm
    * Beam radius at cavity-waist: w0=w2
    * Beam radius at mirror R1 and R2: w1, w2
    * Distance between:
      * mirror R1 and mirror R2: L
      * mirror R2/lense 1 and lense 2: X
      * mirror R2/lense 1 and collimatorlense: 600mm - X
        * 615mm = optical way of the incoupling breadboard (450mm) + thickness breadboard (10mm) + distance between breadboard and vacuumchamber (30mm) + distance between vacuumchamber and cavity mirror R2 (130mm) 
      * collimatorlense and fiber: 2.75 mm

We used the programm //Strahl.exe// (@IQ) or //STRAHLFP.EXE// (@PTB) (same software, but different names).\\
**Step 0: Choose parameter**\\
  * Wellenlänge: 1542 nm
  * Brechungsindex: 1 (Air)

  * Welcher Resonatortyp: linearer Resonator

**Step 1: Beam waist calculation from resonator**\\
  * Nr. 1: Spiegel 1 with Brennweite  500 mm; Einfallwinkel: 0
  * Nr. 2: Abstand 480 mm
  * Nr. 3: Spiegel 2 with Brennweite  10000000000 (so viel es ging) mm; Einfallwinkel: 0

-> Waistradius: w0=w2=495.2 µm; Strahlradius on the mirrors: w1=686.7 µm; w2=495.2 µm\\  

**Step 2: **\\
  * Change Spiegel 2 to Linse 1
    * Brechungsindex: 1.5
    * Brennweite: -4000000000000000000 mm
<note important>The values of the Waistradius and Strahlradius must not change!!!</note>
**Step 3: **\\
  * Nr. 4: Abstand with Variable X
  * Nr. 5: Linse 2 with Variable Y
  * Nr. 6: Abstand 600 - X
  * Nr. 7: Linse 3 with Brennweite 2.75 mm
  * Nr. 8: Abstand 2.75 mm

  * Zielwaist: 5.2 µm
**Step 4: Playing with the parameters X and Y for the best Überlapp**\\

Case: //Mirror R2/lense 1 and collimatorlense: 615mm - X//
^ Lense focal length: Y [mm]                      |  400   |  300   |  **250**   |  200   |  175   |
^ Distance between mirror R2 and lense 2: X [mm]  |  258   |  314   |  **335**   |  375   |  400   |
^ Überlapp [%]                                   |  92.7  |  99.1  |  **99.8**  |  94.7  |  88.6  |

**Step 5: Check what is happend for the wavelength 1560 nm**\\

No effect!