1 Advanced Virgo Workshop 14/06/2007 M Laval Fabry Perot cavity for LG and Flat modes Mikael Laval (OCA/ARTEMIS) Outlines: Tools: The optical simulation code DarkF (FFT) Authors: -Jean Yves Vinet (OCA/ARTEMIS) -Mikaël Laval (OCA/ARTEMIS)  Introduction  Configuration  Clipping.vs. Mirror size  Mismatching (waist shift & width modification)  Misalignment (tilt & miscentering)  Detuning of the cavity  Conclusion and outlooks Remark: Clipping by mirror in annex

2 Advanced Virgo Workshop 14/06/2007 M Laval Introduction Why using flat modes or Laguerre Gauss high order modes as incoming beam? To have a better distribution of the power on the mirror surfaces. The surface deformations are averaged and the thermal noise contribution to the sensitivity is reduced. The heating of the mirrors will be more uniform and thermal lensing should be less important. Problems:What mirror size is necessary to not have clipping losses? What are the effects of a mismatching? What are the specifications needed for the alignment (tilt and centering of the mirrors)?

3 Advanced Virgo Workshop 14/06/2007 M Laval E0 Eref Etr Ecav M1M2 L=3km T=11,8% Losses=0 Rc=3100m radius r E0=LG33 or LG55(matched with the cavity) Waist at the cavity center = 2,29cm Width on the mirror=3,19cm Cavity for LG modes (Finesse=25): Configuration (1/2) Scalar storage coefficient = 8.47

4 Advanced Virgo Workshop 14/06/2007 M Laval Configuration (2/2) E0 Eref Etr Ecav M1M2 L Cavity for flat modes (Finesse=25): T=11,8% Losses=0 radius r M1 = perfect flat mirror M2 = conjugate of twice a perfect flat mode argument in L=3km E0 = prefect flat mode = sum of tem00 of waist 3,188cm on a area of radius 11,3cm

5 Advanced Virgo Workshop 14/06/2007 M Laval Clipping.vs. Mirror size (1/2) Modification of the radius r of both cavity mirrors: LG cavity (w=3,19cm) Flat mode cavity (w=11,3cm)

6 Advanced Virgo Workshop 14/06/2007 M Laval Clipping.vs. Mirror size (2/2) Clipping losses < 1ppmLG33 : r/w>4,4 (=14,04cm here) LG55 : r/w>5,2 (=16,59cm here) FM : r/w>1,8 (=20,34cm here)

7 Advanced Virgo Workshop 14/06/2007 M Laval Mismatching Waist position (1/2) Resonance peak.vs. waist position: LG cavity (r/w=5,49 ; r=17,5cm) Flat mode cavity (r/w=1,81 ; r=20,5cm) Be careful to the y axis range!!

8 Advanced Virgo Workshop 14/06/2007 M Laval Mismatching Waist position (2/2) The Laguerre Gauss mode cavity is more dependant of the waist position of the incoming beam. The storage amplification decreases by 10% for a waist shift close to 130m for a LG55 and superior to 200m for a LG33.

9 Advanced Virgo Workshop 14/06/2007 M Laval Mismatching Width modification (1/2) Resonance peak.vs. incoming beam width: LG cavity (r/w=5,49 ; r=17,5cm) Flat mode cavity (r/w=1,81 ; r=20,5cm) Here the mismatching is: w(E0)/w(matched beam) -1

10 Advanced Virgo Workshop 14/06/2007 M Laval Mismatching Width modification (2/2) Conclusion: Results are similar to the previous case. The Laguerre Gauss modes are more dependant of the matching. The storage amplification decreases by 10% for a mismatching close to 5% for a LG55 and to 7% for a LG33.

11 Advanced Virgo Workshop 14/06/2007 M Laval Misalignment End mirror tilt (1/3) Resonance peak.vs. tilt angle: LG cavity (r/w=5,49 ; r=17,5cm) Flat mode cavity (r/w=1,81 ; r=20,5cm)

12 Advanced Virgo Workshop 14/06/2007 M Laval Misalignment End mirror tilt (2/3)

13 Advanced Virgo Workshop 14/06/2007 M Laval Misalignment End mirror tilt (3/3) Flat mode is more dependant of an end mirror tilt. The storage coefficient decreases by 10% for a tilt inferior to 0.15 microradians. Conclusion:

14 Advanced Virgo Workshop 14/06/2007 M Laval Misalignment End mirror vertical translation (1/2) Resonance peak.vs. end mirror translation: LG cavity (r/w=5,49 ; r=17,5cm) Flat mode cavity (r/w=1,81 ; r=20,5cm)

15 Advanced Virgo Workshop 14/06/2007 M Laval Misalignment End mirror vertical translation (2/3)

16 Advanced Virgo Workshop 14/06/2007 M Laval For the Laguerre Gauss high order modes a translation implies an increase of the clipping on the input mirror (see annex). The storage amplification decreases by 10% for a « miscentering » close to 3mm for the LG55 and to 4mm for a LG33. Conclusion: Misalignment End mirror vertical translation (3/3)

17 Advanced Virgo Workshop 14/06/2007 M Laval Detuning of the cavity LG modes We detune the cavity (end mirror tilted by 0.2μrad ; finesse = 500):

18 Advanced Virgo Workshop 14/06/2007 M Laval Detuning of the cavity Flat modes (1/2) We detune the cavity (end mirror tilted by 0.2μrad ; finesse = 500): ,

19 Advanced Virgo Workshop 14/06/2007 M Laval Detuning of the cavity Flat modes (2/2)

20 Advanced Virgo Workshop 14/06/2007 M Laval Outlooks and Conclusion LG mode (LG33)Flat mode Mirror sizeAs actual mirrorsSlightly larger Incoming beam matchingp(waist position)<200m p(beam width)<7% Weak effect Mirror centering<4mmWeak effect End mirror tiltWeak effect<0.15μrad Other modes2 modes close to ISL/210 modes To have less than 1ppm for the clipping losses or less than 10% decrease of the storage amplification: (p=precision) Outlooks:Add a surface map to the mirrors Simulate a Michelson interferometer

21 Advanced Virgo Workshop 14/06/2007 M Laval Clipping.vs. Mirror size

22 Advanced Virgo Workshop 14/06/2007 M Laval Clipping.vs. Mismatching Waist position

23 Advanced Virgo Workshop 14/06/2007 M Laval Clipping.vs. Mismatching Width modification

24 Advanced Virgo Workshop 14/06/2007 M Laval Clipping.vs. Misalignment End mirror tilt

25 Advanced Virgo Workshop 14/06/2007 M Laval Clipping.vs. Misalignment End mirror vertical translation

26 Advanced Virgo Workshop 14/06/2007 M Laval Detuning of the cavity LG modes We detune the cavity (end mirror tilted by 0.2μrad ; finesse = 500):

27 Advanced Virgo Workshop 14/06/2007 M Laval Detuning of the cavity Flat modes We detune the cavity (end mirror tilted by 0.2μrad ; finesse = 500):