Multiple limit cycles in laser interference transduced resonators

Blocher, David; Rand, Richard H.; Zehnder, Alan T.

doi:10.1016/j.ijnonlinmec.2013.02.008

Cited by 9 publications

(9 citation statements)

References 35 publications

(24 reference statements)

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“…Substituting (22) into (3), neglecting terms proportional toq(t)/c,q(t)/(cω 0 ), and higher powers of them (ω 0 the characteristic frequency of the field), and using the orthonormalization relation in (19) one obtains harmonic oscillator equations for each of the modes Q k [t,q(t)],…”

Section: -3mentioning

confidence: 99%

“…It was found that self-sustained oscillations of the movable mirror are present, that their amplitude settles into one of several attractors (see also [19] for this phenomenon), and that there is a regime where two mechanical modes of oscillation can be excited. Moreover, it was suggested that the multistability can be used as a device to measure small displacements.…”

Section: Introductionmentioning

confidence: 96%

“…Optomechanical systems not only have the potential to become a powerful probe with which to explore the quantum world [2,[4][5][6][7][8][9][10], but are also of great interest in the area of optical microelectromechanical systems [3] and constitute a setting in which classical nonlinear dynamics have to be analyzed [11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…The movable mirror is a mechanical oscillator and it is coupled to the electromagnetic field by radiation pressure and by thermal or bolometric effects (absorption of photons distorting and displacing the mirror). The classical dynamics of this type of systems has been studied in [11][12][13][14][15][16][17][18][19]. For the quantum dynamics, we refer the reader to [1,2,[4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Classical dynamics of a thin moving mirror interacting with a laser

Castaños

Weder

2014

Phys. Rev. A

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We analyze the classical dynamics of a system composed of a one-dimensional cavity with a perfect, fixed mirror and a movable mirror with nonzero transparency interacting with a monochromatic laser. The movable mirror can deviate far from an equilibrium position, it is assumed to be thin so that it is modeled by a δ function, and we use the exact modes of the complete system. The transparency and the mirror-position-dependent cavity resonance frequencies are built into the modes and this allows us to deduce that the radiation pressure force comes from a periodic potential with period half the wavelength of the field. The exact modes and the radiation pressure potential allow us to give intuitive physical interpretations of the dynamics of the system and to obtain approximate analytic solutions for the motion of the mirror. Three regimes are identified depending on the intensity of the field and it is found that the dynamics can be qualitatively very different in each of them with some regimes being very sensitive to the values of the parameters. Moreover, we determine conditions when the Maxwell-Newton equations used to describe the system constitute accurate approximations of the exact equations governing the dynamics.

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Section: -3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Classical dynamics of a thin moving mirror interacting with a laser

Castaños

Weder

2014

Phys. Rev. A

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“…Photothermal feedback places less stringent requirements on the optical system (as we show in this work), and has been explored in a broad range of mechanical device geometries through experiment, 9,10,12,[21][22][23][24] simulation, 25,26 and theoretical studies. 10,21,27 While these works provide many insights into the underlying physics, some neglect the thermally-induced change in resonator equilibrium position z 0 , while others neglect the change in resonant frequency ω 0 .…”

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confidence: 99%

Low-Power Photothermal Self-Oscillation of Bimetallic Nanowires

et al. 2017

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We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standing wave of optical intensity and subject to photothermal forces, the nanowire undergoes self-induced oscillations at low incident light thresholds of < 1 µW due to engineered strong temperature-position (T -z) coupling. Along with inducing self-oscillation, laser light causes large changes to the mechanical resonant frequency ω0 and equilibrium position z0 that cannot be neglected. We present experimental results and a theoretical model for the motion under laser illumination. In the model, we solve the governing nonlinear differential equations by perturbative means to show that self-oscillation amplitude is set by the competing effects of direct T -z coupling and 2ω0 parametric excitation due to T -ω0 coupling. We then study the linearized equations of motion to show that the optimal thermal time constant τ for photothermal feedback is τ → ∞ rather than the widely reported ω0τ = 1. Lastly, we demonstrate photothermal quality factor (Q) enhancement of driven motion as a means to counteract air damping. Understanding photothermal effects on micromechanical devices, as well as nonlinear aspects of optics-based motion detection, can enable new device applications as oscillators or other electronic elements with smaller device footprints and less stringent ambient vacuum requirements.Micro-and nano-mechanical resonators are widely studied for applications including electro-mechanical circuit elements and sensing of ultra-weak forces, 1 masses, 2 and displacements.3 An integral part of these systems is the detection method employed to readout motion, which must itself be extremely sensitive and inevitably imparts its own force on the resonator, influencing the dynamics. The phase relation between mechanical motion and the resulting detector back-action determines whether this interaction will serve to dampen vibrations or amplify them, potentially leading to self-oscillation if the detector supplies enough energy per cycle to overcome mechanical damping.Feedback due to external amplifiers has been used to generate self-oscillation of micro-mechanical resonators;4-8 in such systems the oscillation amplitude R is set either by nonlinearity of the amplifier or of the resonator. Systems in which mechanical motion influences the amount of laser light circulating in an optical cavity 9-12 or magnetic flux through a Superconducting QUantum Interference Device 13,14 (SQUID) have also been shown to self-oscillate under the right experimental conditions. In these systems R is set largely by the periodicity of the detection scheme -either R ≈ λ/4 where λ is the laser wavelength or R ≈ Φ 0 /2 where Φ 0 is the displacement needed to change the SQUID flux by one flux quantum. In the case of a mechanical resonator coupled to an optical cavity, back-action can arise either from radiation pressure or photothermal force -that is, thermally-induced deflectio...

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Vibration of the Axially Purely Nonlinear Rod

Cvetićanin

2017

Strong Nonlinear Oscillators

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Multiple limit cycles in laser interference transduced resonators

Cited by 9 publications

References 35 publications

Classical dynamics of a thin moving mirror interacting with a laser

Classical dynamics of a thin moving mirror interacting with a laser

Low-Power Photothermal Self-Oscillation of Bimetallic Nanowires

Vibration of the Axially Purely Nonlinear Rod

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