Compensation for thermal effects in mirrors of gravitational wave interferometers

In this paper we study several means of compensating for thermal lensing wh ich, otherwise, should be a source of concern for future upgrades of interf erometric detectors of gravitational waves. The methods we develop are base d on the principle of heating the cold parts of the mirrors. Ve find that t hermal compensation can help a lot but can not do miracles. It seems finall y that the best strategy for future upgrades ("advanced configurations") is may be to use thermal compensation together with another substrate materia ls than silica, for example sapphire.