Estimation of the Astigmatism of AdVIRGO NDRCs by benbenzhou

VIEWS: 26 PAGES: 15

More Info
									  Estimation of the Astigmatism of
          AdVIRGO NDRCs




Massimo Granata and Matteo Barsuglia – APC
26/02/09 OSD weekly meeting
                                             2


                Outlook

•  NDRCs astigmatism estimation method and
   related losses

•  NDRCs stability

•  Plots and numbers
                                                                                 3



Estimation of astigmatism

   •  Tangential & sagittal ABCD matrices for
      reflection/refraction on all the surfaces

   •  Estimation of the gaussian parameters after a
      roundtrip in the power/signal recycling cavity

   Massey&Siegman: Reflection and Refraction of Gaussian Light Beams at Tilted
     Ellipsoidal Surfaces , May 1969 / Vol. 8, No. 5 / APPLIED OPTICS 975
                                                                                              4


    Estimation of the losses
       mode overlap integral:

                                                             *
                                     E(w1,R1) E (w2,R2)
           losses = 1−                                           *
                                    E (w1,R1) E (w1,R1)
           E0(w1, R1) = FP arm cavity mode
           E0(w2, R2) = PRC astigmatic mode
                                        − jP(z)          21       k      2 1       k
    Fundamental mode:          E0 = e             exp{−x ( 2 + j     )− y ( 2 + j     )}
€                                                         wx     2Rx       wy     2Ry

     Arain: Analysis of Mode Mismatch due to Astigmatism at Recycling Cavity Mirrors, LIGO note
       T080315-00-Z
                 €
                                                      5


Stability

•  The current design of NDRCs is very sensitive to
   small variations of RM3/RM2 RoCs and
   telescope tilt angle

•  Even small fractions of percent can make RCs
   unstable on one or both of transverse directions
                                                                     6

Scenario n.1
 unstable cavities for lens tilt = 2°




Y arm, 3 astigmatic elements: PRM3 @ 2.5° & PRM2 @ 3.5°, lens @ 1°

X arm, 4 astigmatic elements: BS, PRM3, PRM2, lens
                                                  7

Scenario n.1 – X arm   total losses 0.5 % - 1 %
                                          8

Scenario n.1 – Y arm   total losses 1 %
                                                           9

Scenario n.2
 unstable cavities for telescope tilt = 3.3°
 stable cavities for telescope tilt < 2°




Y arm, NO lens ; 2 astigm. el. : PRM3 & PRM2 @ 1.7°

X arm, NO lens ; 3 astigm. el. : PRM3 & PRM2 @ 1.7° + BS
                                  10

Scenario 2 – X arm
          αPRM3 = αPRM2 = 2 deg
                                                                11

Scenario 2 – X arm               tangential/sagittal match does NOT
losses 6 % ; same on Y arm       change the magnitude of losses

                             PRM3 [m]




                                               PRM2 [m]
                                                           12

Scenario n.3




Y arm, NO lens ; 2 astigm. el. : PRM3 & PRM2 @ 1.9°

X arm, NO lens ; 3 astigm. el. : PRM3 & PRM2 @ 1.9° + BS
                                                           13

Scenario 3 – X arm           tangential/sagittal match does NOT
losses 3 % ; same on Y arm   change the magnitude of losses
                                                           14

Scenario n.4




Y arm, NO lens ; 2 astigm. el. : PRM3 & PRM2 @ 1.9°

X arm, NO lens ; 3 astigm. el. : PRM3 & PRM2 @ 1.9° + BS
                                                             15

Scenario n.4 – X arm           tangential/sagittal match does NOT
losses 2.5 % ; same on Y arm   change the magnitude of losses

								
To top