We study mode competition in a multimode "phonon laser" comprised of an optical cavity employing a highly reflective membrane as the output coupler. Mechanical gain is provided by the intracavity radiation pressure, to which many mechanical modes are coupled. We calculate the gain, and find that strong oscillation in one mode suppresses the gain in other modes. For sufficiently strong oscillation, the gain of the other modes actually switches sign and becomes damping, a process we call "anomalous cooling." We demonstrate that mode competition leads to single-mode operation and find excellent agreement with our theory, including anomalous cooling.Introduction. -While the laser was invented more than five decades ago, its acoustic analog has only recently been realized. Following the observation of phonon amplification in microwave-pumped ruby [1] in 1964, the possibility of "phonon lasing" was suggested. Subsequent work in ruby studied the emission spectrum of phonon generation[2] and multimode processes [3]. With the advent of optical pumping, detailed studies of the coherence of phonon emission were enabled[4], culminating in a ruby "saser" [5]. Shortly thereafter, phonon lasing was realized in a harmonically bound Mg + ion driven by optical forces [6]. Subsequently, it was recognized that a large class of optomechanical systems, in which optically furnished gain enables self-sustained mechanical oscillation, are properly called "phonon lasers" [7]. These include beams [7,8] and cantilevers [9] coupled to an optical cavity, microtoroids [10,11], and a cantilever deriving mechanical gain from optical bandgap excitation [12]. Analogous electromechanical [13,14] and purely mechanical [15] systems have also been discussed. Various phenomena associated with lasers, such as stimulated emission [6], oscillation threshold [6,7,11,12,15], gain narrowing [15], and injection locking [16], have been demonstrated.With few exceptions, these investigations have involved a single mechanical mode. Multimode emission was observed in ruby [2,3], and two-mode oscillation was observed in a photothermally coupled optomechanical system [9]. Intermodal coupling in an electromechanical system was exploited to realize a phonon laser without an optical pump [15]. In the domain of conventional lasers, an interesting and important feature arises when multimode operation is considered. As shown by Lamb in 1964[17], a saturation phenomenon occurs in which oscillation of one mode suppresses the gain of other modes. This has the dramatic consequence that, in the absence of inhomogeneous gain broadening, a laser oscillates in steady state on a single mode, even when the small-signal gain exceeds the losses for more than one mode [18].In view of the multimode oscillation observed in the photothermal system [9], it is natural to ask whether a phonon laser employing pure radiation pressure coupling

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We demonstrate micromechanical reflectors with a reflectivity as large as 99.4% and a mechanical quality factor Q as large as 7.8 × 10 5 for optomechanical applications. The reflectors are silicon nitride membranes patterned with sub-wavelength grating structures, obviating the need for the many dielectric layers used in conventional mirrors. We have employed the reflectors in the construction of a Fabry-Perot cavity with a finesse as high as F = 1200, and used the optical response to probe the mechanical properties of the membrane. By driving the cavity with light detuned to the high-frequency side of a cavity resonance, we create an optical antidamping force that causes the reflector to self-oscillate at 211 kHz.

We report on a promising approach to high-sensitivity anisotropy measurements using a high-finesse cavity locked by optical feedback to a diode laser. We provide a simple and effective way to decouple the weak anisotropy of interest from the inherent mirror's birefringence whose drift may be identified as the key limiting parameter in cavity-based techniques. We demonstrate a shot-noise-limited phase shift resolution previously inaccessible in an optical cavity, readily achieving the state-of-the-art level of 3 × 10 −13 rad.

We describe ongoing work in a Fabry-Perot interferometry system designed to measure displacements over a range of 50 mm with sub-pm uncertainty. The apparatus involves probing two nearby modes of the Fabry-Perot cavity with narrow-linewidth fiber telecom lasers and measuring both the mode spacing and the absolute mode frequencies relative to a third, frequency-stabilized, fiber laser. We explore the improvement in resolution obtained as the frequency separation between the two modes is increased and employ an internal consistency requirement to infer the magnitude of residual systematic errors. The measurement uncertainty is sufficiently small that we are easily able to see the Gouy phase shift as the cavity length is changed over several millimeters.

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We present measurements of the Gouy phase accumulation for the fundamental mode of an astigmatic Fabry-Perot cavity over 70 % of its stability range. The method is based on simultaneous measurement of the resonant frequencies of the fundamental mode and the TEM 11 Hermite-Gauss mode of the cavity. We achieve an uncertainty of 2:7 Â 10 À6 rad, which, in the context of displacement metrology, is sufficient to enable measurements over 50 mm with relative uncertainty below 10 À10 .

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