Doppler Optomechanics of a Photonic Crystal

A laser beam directed at a mirror attached onto a flexible mount adds friction to its mechanical motion by the Doppler effect. For a normal mirror the efficiency of this radiative Doppler friction is very weak and practically masked by laser shot noise. We find that it can become very efficient using a photonic crystal mirror near its photonic band gaps. As an example, a Bragg mirror used at the long wavelength edge of its band stop can be efficiently optically cooled using the Doppler friction. The opposite effect opens new routes for optical pumping of mechanical systems: a laser pointing at a Bragg mirror and tuned at its short wavelength edge induces amplification of the vibrational excitation of the mirror leading eventually to its self-oscillation. These new effects rely on the strong dependency of a photonic crystal reflectivity on the wavelength.

Figure 1

(a) Schematics of a mirror of reflectivity $R(\lambda )$ and mass $m$ mechanically attached and thermally anchored to a spring of rigidity $K$. The friction mechanisms internal to the spring are responsible for losses of mechanical energy at a rate $\Gamma$. A laser of power $P$ is directed at the mirror from the left. (b) Schematics of the reflectivity wavelength dependency of a Bragg mirror. The gradients of $R$ are maximized at the edges ${\lambda }_B$ and ${\lambda }_R$ of the mirror band stop.