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Entry  Tue Feb 22 00:25:39 2011, Zach, Laser, GYRO, mode matching issue 
    Reply  Tue Feb 22 10:47:35 2011, Alastair?, Laser, GYRO, mode matching issue 
       Reply  Tue Feb 22 11:21:01 2011, Zach, Laser, GYRO, mode matching issue 
Message ID: 1319     Entry time: Tue Feb 22 11:21:01 2011     In reply to: 1318
Author: Zach 
Type: Laser 
Category: GYRO 
Subject: mode matching issue 

I agree, but that is what the calculation gives. I haven't plotted this yet, but it could be that in this case there are two coupling maxima (i.e. one where the X solution is closest to the cavity mode and one where the Y one is), and right in between---where the "average" solution is---there is a local minimum. Then, we could easily have adjusted the lenses slightly to get to one of the maxima and have something like 10-20% coupling like we saw, despite the fact that the other axis was way off.

I will do some crunching.


I think this 1% is a lot less than we have already seen coupling into the cavity - it doesn't seem quite right to me.

I think that you're correct that is the way we did the calculation, taking some average of the x and y parameters we measured for the beam.  I'd have to go back and check though.


 This afternoon I measured the distances required to calculate the mode matching, and then I came up with a solution using code that I wrote. In doing so, I realized that there is a problem with the way we have been calculating the overlap in the past.

Last summer, Jenna used the overlap function to show that an overlap of > 99% could be achieved with a non-astigmatic beam injected into a cavity with an elliptical eigenmode (like our gyro cavity, whose mode has a waist twice as big in one direction as in the other). This is fine, but there are two things to note:

  • The cavity is not astigmatic; the waists of the X and Y projections occur at the same places (i.e. the input and output coupling mirrors). It simply has an elliptical cross section.
  • Our beam is astigmatic! The output beam of the NPRO has X and Y waists that occur at different points on the Z axis.

Jenna calculated such a nice overlap because she assumed that our input beam was not astigmatic. The coupling is far more sensitive to curvature match at the input (i.e. making the beam flat at the flat mirror) than it is to the area of the beam cross section, and a non-astigmatic beam allows you to do that arbitrarily well.

If I take the solution I calculated for the average of the X and Y components of our input beams and apply it to both components individually, the overlap I get with the cavity eigenmode is < 1%, despite the fact that it is >99% if we assume that the average is a real, physical, circular beam.

I think we may need to do the cylindrical mode matching after all.



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