1. Where is the change in refractive index of the glass, and is the change in temperature due to heating. The relative phase change due to asymetric heating is given as Thermal Lensing Non uniform heat distribution of a high power laser on the beam splitter can cause the spatially dependent refractive indices to appear. This results in lens like effect also known as thermal lensing effect. Different refractive indices would cause different path lengths, consequently, shifting the phase. The phase of the beam near the axis shifts more than the phase at the end. The phase difference of beams returning from the end test masses would not cancel each other. Thus some of the waves would be detected in the detector. This can lead to the confusion with the gravitational wave. In case when gravitational wave is passing by, it would distort the data, and provide erroneous result. The change in refractive index due to heating is given by Thermal Lensing Effect on a Beam Splitter of a Michelson Interferometer Ramesh Shrestha, Dr. Sanichiro Yoshida Department of Chemistry and Physics, Southeastern Louisiana University Abstract With ground-based, laser interferometric gravitational wave detectors in mind, laser-induced thermal effects in the beam splitter of a Michelson type interferometer are discussed. Thermal lensing effect on beam splitter arising from the non spatial heat distribution has been discussed. A finite element model has been built to compute the temperature profile in the beam splitter. The optical phase shift resulting from the temperature dependence of the refractive index has been analyzed. One dimensional Temperature profile Acknowledgements -STAR Grant Southeastern Louisiana University Introduction LIGO(Laser Interferometric Gravitational wave Observatory) detectors are ground based Michelson Interferometers designed to detect the gravitational wave. The passage of gravitational wave through Earth causes the distortion in space time, theoretically, as low as in strain of the space. Such an extremely small strain is detected as a relative phase change between the beams reflecting back from the test end masses, behind the beam splitter. In passage of Gravitational wave, the beams reflecting back from test masses do not interfere destructively, and some light is observed at the detector. Y-arm Cavity Extra Path length X-arm Cavity Beam Splitter Schematic Illustration for extra optical path for X beam in beam splitter FEM Model of Spatial Heat Distribution in Beam Splitter Above is the 3 dimensional model of the beam splitter modeled in COMSOL. It was assumed that the radius of curvature of the Gaussian beam did not change as it passed through the beam splitter. The sub domain Setting for the Gaussian(TEM00) are 5cm spot size, radius of curvature are 2200m, laser power 100w, peak laser intensity 25/π W/cm^2 and absorption coefficient is 2ppm/cm. In boundary condition, Radiation coefficient was chosen to be. Conclusion Temperature variation in the beam splitter was observed, which caused the refractive indices to change non- uniformly. Phase difference due to asymmetric heating was also observed. Heat Source Differential Phase Change due to Thermal Effect Phase Fluctuation due to Temperature Change by beam’s Oscillation