Analysis of frequency noise in ultra-stable optical oscillators with active control of residual amplitude modulation

Two 1,064-nm Nd:YAG lasers frequency stabilized by high-finesse optical cavities are developed to investigate various noise mechanisms in ultra-stable optical oscillators. Active control of residual amplitude modulation using a separate sensing path is implemented and its effectiveness in the presence of a resonant optical cavity is theoretically analyzed and experimentally verified by measuring the rejection ratios in optical heterodyne beat between a perturbed laser and a stable reference. Laser frequency noises originated from vibration, residual amplitude modulation, quantum-limited shot noise, and electronic noise are experimentally analyzed. With active control, residual amplitude modulation is suppressed to below 1 x 10(-6) at 0.02-1,000 s, reaching a minimum of 2 x 10(-7) at similar to 2 s. A frequency stability of 2 x 10(-15) is obtained from 0.1 to 10 s, and the optical heterodyne beat of the two Nd: YAG lasers shows 1-Hz linewidth with a measurement time of 4.096 s. In addition, the experimentally determined linewidths agree well with the calculation according to a simplified relationship between the linewidth and the underlying flicker noise that modulates the laser frequency.