Tuning Fabry-Perot cavity modal frequencies using controlled thermoelastic deformations on mirror surface

Goal

To correct for the modal frequency shifts in the FP arm cavity that arise from the spatial inhomogeneities on the mirror surface (We are not looking to change the overall RoC of the mirror to suppress the higher order modes). This will be done by imaging heat patterns on the ETM surface. The thermoelastic deformations created on the mirror surface introduces phase shifts to the cavity modes. The green ALS system will be used to mode scan the cavity continuously. A feedback control system will actively correct for the frequency shifts based on the cavity mode scan information.

The lessons learned from this exercise will help in designing/implementing a similar kind of system for the folding mirrors in the signal recycling cavity.

System Overview

Description

The PSL laser is locked to the arm cavity using the PDH error signal. The green laser is injected from the ETM side of the arm. The relative phase between the two lasers is kept constant using a phase-locked-loop (PLL) servo. The transmitted end-green from the arm interferes with the frequency-doubled PSL and produces a beatnote.

Taking into account the following:

1. The amplitude of the beatnote depends on the intensity of the transmitted green.
2. Changing the frequency of the end-green laser (using the PLL local oscillator) will affect it's resonance conditions in the arm cavity and excite the various transverse modes.
3. The frequencies at which the various transverse mode resonances occur depend on the spatial inhomogeneities on the mirror surface.

we can conclude that the amplitude of the beatnote as a function of the end-green laser frequency (or the local oscillator frequency) will hold the information about the cavity resonance frequencies and hence the effect of the mirror distortions created by various heat patterns can be mapped.

We expect to correct for deformations of the order of a few nm (corresponding to frequency shifts of the order of a few KHz).

Simulation/Modelling

• SIS modelling of the arm cavity using the phase map measurements made for the ITM and ETM.

This will give an estimate of the modal content of the arm cavity. This should give an idea about the range of frequency shifts we are looking at, the highest order mode correction we are going to limit ourselves to,...

• COMSOL model:

Model various heat patterns and thermal deformations on the ETM: core heating, ring heating, core+ring heating. Estimate deformation patterns created on the ETM various heating pixel sizes and various deformation depths (heating power). Generate phase maps and analyze the effect of thermal deformed mirror on the modal content of the arm cavity using SIS.

• PLL servo design:

Look at the shortcomings of the earlier PLL design used for ALS. Model the PLL servo : Beat PD range that will give information about all the higher order mode resonances, LO frequency...

Design and construction

1. Heater array: Custom heater array. Array size decided based on the actuation area
2. Heater electronics:
3. Telescope components:
4. Apertures:
5. PLL for green laser:
6. Inversion matrix:
7. Front ends:

Tasks/Timeline

1. Initial modelling to decide on our requirements: Steps 1 and 2 under simulation/modelling. This will help us decide on what are our requirements of the system and if our requisites are plausible.