====== Mode Matching - two 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= 1 m (Incoupling side) 
    * Wavelength: λ= 1542.0 nm
    * Length between the resonator mirrors: L= 480 mm
    * Beam radius at cavity-waist: w0
    * Beam radius at mirror: 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
        * 600mm (+15mm) = 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  500 mm; Einfallwinkel: 0

-> Waistradius: 457 µm; Strahlradius on the mirrors: 525.2 µm\\  

**Step 2: **\\
  * Change Spiegel 2 to Linse 1
    * Brechungsindex: 1.5
    * Brennweite: -2000 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: 600mm - X//
^ Lense focal length Y [mm]                      |  400   |  300   |  **250**   |  200   |  175   |
^ Distance between mirror R2 and lense 2 X [mm]  |  179    |  208   |  **243**   |  316   |  357   |
^ Überlapp [%]                                   |  83.1  |  97.6  |  **99.5**  |  87.9  |  77.4  |

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]  |  170   |  215   |  **265**   |  332   |  357   |
^ Überlapp [%]                                   |  83.2  |  97.9  |  **99.2**  |  87.0  |  76.3  |

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

No effect!