Compensation of Strong Thermal Lensing in High-Optical-Power Cavities

In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors, we show for the first time that the time evolution of strong thermal lenses follows the predicted infinite sum of exponentials (approximated by a double exponential), and that such lenses can be compensated using an intracavity compensation plate heated on its cylindrical surface. We show that high finesse $\sim 1400$ can be achieved in cavities with internal compensation plates, and that mode matching can be maintained. The experiment achieves a wave front distortion similar to that expected for the input test mass substrate in the Advanced Laser Interferometer Gravitational Wave Observatory, and shows that thermal compensation schemes are viable. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.

Figure 1

Simplified schematic diagram of the optical layout of an advanced interferometer: ETM, ITM, power recycling mirror (PM), signal recycling mirror (SM), BS, photodiode (PD). Shading illustrates the thermal lensing in the various components; the beamwidth signifies light intensity.

Figure 2

A schematic diagram of the experiment setup. The beam from 10 W laser is mode matched into the Fabry-Perot cavity formed by the back-surface ITM and the ETM. The CP is placed near the ITM and heated by 6 turns of nichrome wire insulated by Teflon tape. The Fourier transform of the beam transmitted through the ETM is recorded by a CCD camera placed near the back focal plane of the 50 mm diameter, 500 mm focal length lens.

Figure 3

Simulation results of ITM thermal lensing time dependence when 0.5 W was absorbed; the dots are simulated results and the solid line is the fitted the curve using the sum of two exponentials with time constants of 0.76 and 5.91 s.

Figure 4

A plot of the measured time dependence of the beam radius at the ETM (dots) and the result of a simulation in which only the power absorbed by the ETM and CP were optimized (solid line). The cavity circulating power is shown on the top of the graph.

Figure 5

Time dependence of the measured (dots) and simulated (squares) ETM beam radius during thermal compensation. Optical power storage commenced at $t=0$; CP heating power was turned on at 450 s and turned off at time 4026 s. The power transmitted through the ETM, which is proportional to the stored cavity power, is also shown.