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Feedback control of thermal lensing in a high optical power cavity
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View: Figures


Image of FIG. 1.
FIG. 1.

Layout of the Advanced LIGO interferometric detector. BS represents the beam splitter, and ITM represents input test mass; ETM, end test mass; PRM, power recycling mirror; and SRM, signal recycling mirror. The incident laser power is 125 W, leading to about 2.1 kW in the power recycling cavity and 830 kW in the arm cavities.

Image of FIG. 2.
FIG. 2.

A schematic of the experimental setup at the HOPF at Gingin. A FP cavity consists of two suspended sapphire mirrors, separated by . A Nd:YAG laser is injected and phase locked into the FP cavity. The CP is inserted inside the cavity close to the ITM. The CCD located behind the ETM is used to measure the transmitted beam profile. The controller produces an error signal from the measured beam diameter change and this is used to control the heating power applied to the heating wire of the CP.

Image of FIG. 3.
FIG. 3.

A schematic based on a finite element model for correcting strong thermal lensing in the test mass by circumferential heating of a CP. The color scale indicates temperature in the sapphire test mass, the temperature in the CP is much higher. The CP is placed near the sapphire test mass and generates an opposite thermal gradient to the thermal lens in the test mass.

Image of FIG. 4.
FIG. 4.

(a) Temperature distribution inside the CP substrate, the simulation result of applying 5 W of heating power for 2 h. (b) Time evolution of the inverse of the focal length of the CP. The blue dotted curve is the simulated data. The solid curve is the exponential fitting result. The negative value represents a concave lens. The graph shows that this is a slow process due to the small thermal conductivity of the CP.

Image of FIG. 5.
FIG. 5.

The time evolution of the transmitted beam diameter due to heating power applied to the CP. The blue dots are the experimental data measured by the CCD camera. The dips and peaks in the data occur when the cavity lost lock and was relocked. The red solid line is the simulation result.

Image of FIG. 6.
FIG. 6.

Schematic of a FP cavity system modeled in SIMULINK of MATLAB. The system contains the transfer function model and a beam size calculation block used to compute the beam spot size corresponding to the change of the focal length change of the CP.

Image of FIG. 7.
FIG. 7.

(a) The time evolution of the transmitted beam size as the feedback control system was applied. The blue dots are experimental data while the solid curve is the analytical result evaluated in SIMULINK. (b) A dash plot of measured time dependence of the heating power applied onto the CP. The solid curve is the simulation result, which shows the heating power is about half of the practical power, agreement with previous analysis.

Image of FIG. 8.
FIG. 8.

Schematic of the feedback control system. The system includes the FP cavity system and a controller to tune the heating power to maintain the beam size at a desired value.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Feedback control of thermal lensing in a high optical power cavity