Photo-thermal Shot Noise in End Mirrors of LIGO due to Correlation of Power Fluctuation

The effect of input power fluctuation on photo-thermal shot noise in the end mirrors of a laser interferometer gravitational-wave observatory (LIGO) is analysed according to the statistical optics, which is a supplement of Braginsky's research. The laser light folding in LIGO increases a correlation of input power fluctuation in the photo-thermal shot noise. This part of noise has spectral density proportional to ω^-2 in low frequency bands, and ω^-4 in high frequency bands. It is not a white noise and may affect the processing about data of interferometers. To obtain an advanced LIGO, photo-thermal shot noise in end mirrors due to correlation of input power fluctuation is up to Braginsky's photo-thermal noise in the frequency range 1--100 Hz.