  Metrology experiments can be limited by the noise produced by the laser
involved via small fluctuations in the laser's power or frequency. Typically,
active power stabilization schemes consisting of an in-loop sensor and a
feedback control loop are employed. Those schemes are fundamentally limited by
shot noise coupling at the in-loop sensor. In this letter we propose to use the
optical spring effect to passively stabilize the classical power fluctuations
of a laser beam. In a proof of principle experiment, we show that the relative
power noise of the laser is stabilized from approximately $2 \times 10^{-5}$
Hz$^{-1/2}$ to a minimum value of $1.6 \times 10^{-7}$ Hz$^{-1/2}$,
corresponding to the power noise reduction by a factor of $125$. The bandwidth
at which stabilization occurs ranges from $400$ Hz to $100$ kHz. The work
reported in this letter further paves the way for high power laser stability
techniques which could be implemented in optomechanical experiments and in
gravitational wave detectors.
