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Where are the resonator modes?

Where are the resonator modes?

Where are the resonator modes?

Well, I´m trying to calculate the modevolume of a resonator with etalons. For this I´m using a matrices model. I´m quite sure that this model is right, but I have some ploblems to understand the results.

Usually if you don´t have etalons between the mirrors you can say the wavelength has to fit exactly in the double optical way of the resonator. -> 2*l_opt/lambda=m, m=real number

My model works fine with it. But if I take a resonator with 2 different media with the same optical way as before the results differs a bit. It is logical that the altitude of the transmissionspeaks are modulated because now you have two weak resonators in a strong one. Maybe it is logical that the wavelength at the centerposition of the transmission peaks differs a bit, because the weak modulated etaloncurve cuts the transmissioncurve of the resonator in an angle and this weighting the exact position of the peak.

Now imagine you have a resonator with nealy perfect mirrors -> your transitionpeaks of the resonator are very steep. Is it now possible, that a weak etalon can move the position of the peak? Example: m=16000 without and m=165999,998 with etalon?

To my understanding it is possible that the center of the peak with etalon moves a bit, but only in the range where the resonator mode without etalon has a transmissionpeak
Its a bit complicated to explain, but more difficult to do a graph..  `.`: without etalon
           '+`: with etalon

1)                 2)             3)
     .              .              .
     .              .              .      
     .              .              .     
    . .            . .            . .    
    . .            . .            . .      
    . .            . .            . .   
    .+.           . .        +   . .    
   . + .        .+  .       +  .   .    
   . + .        .+  .       +  .   .   
   . + .        .+  .       +  .   .
   .+ +.       .+  .       +  .   .
  . + + .     .+ +  .    + +.     .   

1) I expected
2) I can imagine that it could be possible
3) I got with the calculation..

The peaks with etalons are allways at the same area of wavelength as it is without etalon, no matter at wich wavelength you are looking at, but it allways differs a bit, sometimes it is a bit more left, sometimes right and sometimes it hits the position of the resonatormode.

Did anyone understand my problem and has an explanation for this phenomena?

The point is, can a transmission peak be at a wavelength where the resonator without etalon has nearly no transmission at all??? Remember I kept the optical way in both cases at the same, the only different is a interface between medium one and two. As I know there can only be a jump of the phase of pi.

Cheers Rob

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