The Problem:

When laser light passes through an optic, a small amount of power is absorbed due to impurities, resonances, etc.(about 5 parts per million per cm in the bulk, and about 5 parts per million in the coating on the surface). Since the laser beam has a gaussian profile, more heat is deposited in the center than in the outer portions of the optic, thus inducing temperature gradients. The index of refraction is dependent on temperature (about 1*10^-5 per degree K), so temperature gradients translate directly into index gradients. This results in a net change in optical path which varies across the optic (called the "optical path distortion", or OPD, for short), which behaves like an additional lens added to the system (thus the term "thermal lensing"). Click here for an illustration.


Below is a schematic of LIGO II, along with the circulating power in the various optical cavities:

While the effect of thermal lensing in the first generation of LIGO detectors is manageable by grinding additional curvatures into various optical components, the problem for advanced detectors (with 20 times more ciruclating power) is serious enough that it must be actively compensated for (grinding the additional curvature fixes the problem in the heated steady state, although it makes the various optical cavities nearly impossible to bring into resonance in the unheated state). Click here to see the modeled thermal lens induced in the LIGO II input test mass (which has 4kW of power circulating in the bulk, with 200kW of power incident on Fabry-Perot cavity face).



The Solution(s):
Static Thermal Compensation
Dynamic Thermal Compensation


Last modified: Mon Nov 29 01:56:04 EST 1999