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Mode Matching of the Fabry-Perrot cavities

Julien Marque

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Contents

1. Mode matching with the old IBo Toolso Issueso Results

2. Mode matching with the new IBo New telescopeo New tool

3. Conclusion

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Mode matching principleo The mode matching consists in adjusting the input

telescope in order to match the mode parameters of the input beam (waist size, distance to waist) to the cavity eigenmodes (radius of curvature of the mirrors of the cavity, length of the cavity).

o This action can be performed by adjusting the position of the various optical elements of the telescope.

o The input bench telescope has been designed to match the input beam to the FP cavities and minimize the aberrations introduced by the telescope itself (astigmatism, spherical aberration).

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Mode matching discussionGoal : optimize power coupled into the FP cavities…

and not only?

Improvement of error signals for locking and alignment?

Does “Mode Matching noise” exist and is that a concern (phase shift, spurious cavities, …)?

Future issue: thermal lensing effect

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Tool 1 : Optocad

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Tool 1 : Optocad

Astigmatism is introduced by the Mode Matching Telescope : depends on the incidence angle of the beam on M5 and M6.

These angles depend obviously on the position of M4, M5 and M6 and on the centering of the beam on M5 and M6.

=> the angles have been estimated with Optocad taking into account rough estimation of the miscentering.

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Tool 2 : Finesse

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Tool 2 : Finesse

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Problems1. Diaphragm on the input bench too small => beam

shaper effect, impossible to measure the beam size respect to the telescope adjustment.Diaphragm replaced in March 2004.

2. Need to translate last mirror of the telescope by a few mm while keeping the beam aligned in the cavity.Created dedicated servo loop.

3. Dynamic range / picomotors behaviour

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Results

All the following results have been computed with a Finesse simulation and verified experimentally (relative DC measurement + amplitude of 01 mode resonant in the cavity)

Power coupled into the TEM00 mode:

- Before the matching activity = 76%

- First step = 92% (dynamic range limitated)

- Second step (M6 substituted) = 95% (astigmatism limitation)

A rearragement of the optics on the bench needed to remove astigmatism => we could reach 98% (limitation is the tuning of the distance between PR and the 2 mirrors)

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New IB / parabolic telescope

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New tool : Zemax

Interesting features:

o Tolerancing (by defining a function of merit = defining the target for beam size and waist location) => identify critical parameters with Monte-Carlo method

o Optimization (by defining compensators) => good help to now how to proceed!

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New tool : Zemax

No way to define a FP cavity with Zemax …How to compute the coupling?C = 4/( (w0/win+win/w0)2 + ((w0/win)*(Deltaz/b))2 )

with:w0 = cavity waist b = cavity Rayleigh lenght win = waist of the input beam Deltaz = distance between w and win

(Virgo physics book)

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New tool : Zemax

New telescope is compact=>

Very fine tuning requested

Need for many actuators (closed-loop picomotors for M6,

translation stages for M5, open-loop picomotors for M5, M3 and

M4)

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Conclusion

o Hope to get good results soon! Goal is a coupling better than 99% for FP cavities.

o Mode matching of the IMC to be done soon (coupling is currently 82%). Simulation already done with Finesse. Results show that astigmatism is not critical for such a short cavity. Goal is 98%.

o Mode matching of OMC was limitated by astigmatism (94%). Goal is > 99% now.

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Tuning of Finesse

All numbers, in the Finesse input file, are nominal except for (nominal numbers between parenthesis):

- DC power of the input beam = 1 W- Waist of the beam after the IMC = 4.8 mm (4.9)- Incident angle on M5 = -3.3 degrees (?)- Incident angle on M6 = 5.4 degrees (?)- M6 Rc = 3.162 m (3.16), 3.138 m for the old M6- NE Rc = 3530 m (3580)