Mode Competition and Anomalous Cooling in a Multimode Phonon Laser

Abstract

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

Nonlinear dynamics and chaos in an optomechanical beam

“…11) driven by F o , predicting that the chaotic dynamics are only present in Δ T and N , while the two mechanical modes oscillate coherently at incommensurate frequencies. It is worth noting that the only additional mode to be amplified is an out-of-plane flexural one having a large g o,OM value, while the other in-plane ones, although having large g o,OM values as well, are probably damped because of mechanical mode competition21.…”

Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

“…Among their chief virtues is the highly tunable coupling with electromagnetic radiation which can be enhanced with a resonator and which allows for flexible engineering of interactions and readout. Arrays of mechanical oscillators are particularly interesting as long-range interactions between the mechanics can be engineered [20,21] in a well-controlled fashion and collective phenomena, such as self-oscillations, phonon lasing or synchronization, can occur [15,62,[31][32][33][34][35][36].…”

Membrane-in-the-middle optomechanics with high-contrast gratings

“…3 The combination of low mass, high reflectivity, and high mechanical quality factor possible with subwavelength gratings fabricated from silicon nitride has made them an attractive platform for optomechanics. In recent work, 4 a mechanically compliant subwavelength grating served as one end mirror of an optical cavity, and radiation pressure associated with the circulating optical power was used to cool modes of the device to cryogenic temperatures 5 and study mode competition in a multimode phonon laser.…”

“…In recent work, 4 a mechanically compliant subwavelength grating served as one end mirror of an optical cavity, and radiation pressure associated with the circulating optical power was used to cool modes of the device to cryogenic temperatures 5 and study mode competition in a multimode phonon laser. 3 An interesting variant on such optomechanical platforms is the "membrane-in-the-middle" configuration, in which a mechanically compliant dielectric membrane is placed within a Fabry-Perot cavity, and modifies the spectral characteristics of the cavity without changing the overall cavity length. Such a configuration was first demonstrated experimentally in 2008, 6 where the authors noted that in addition to the standard linear optomechanical coupling, this configuration offered the possibility of quadratic and even quartic 7 couplings between the optical and mechanical degrees of freedom.…”