Lagrangian approach for analysis of radiation pressure induced parametric instability in micro-resonators

We introduce a new scheme for determining radiation pressure coupling to microresonator devices. It is shown that for the input pump powers there exists a threshold value for instability behavior. Radiation pressure can couple mechanical modes of a cavity to it's optical modes, leading to parametric oscillation instability. Here we present an approximate analysis of such nonlinear effect with Hamilton's least action principle. Our Lagrangian includes no interaction term, but interaction between optical and mechanical modes has been taken into account through integration limit.     

Effective mass in quantum effects of radiation pressure

We study the quantum effects of radiation pressure in a high-finesse cavity with a mirror coated on a mechanical resonator. We show that the optomechanical coupling can be described by an effective susceptibility which takes into account every acoustic modes of the resonator and their coupling to the light. At low frequency this effective response is similar to a harmonic response with an effective mass smaller than the total mass of the mirror. For a plano-convex resonator the effective mass is related to the light spot size and becomes very small for small optical waists, thus enhancing the quantum effects of optomechanical coupling.     

Theory of space-charge waves in semiconductors with negative differential conductivity

Phenomena that accompany optical excitation of eigenmodes of electron gas oscillation in semiconductors with an N-shaped current-voltage (I-U) characteristic in a strong electric field are investigated theoretically. The dependence of the current flowing through a sample on the oscillation frequency of the interference pattern of light illuminating the sample is analyzed. Nonsteady-state and nonuniform illumination produces an internal electric field, which interacts resonantly with the eigenmodes when the oscillation frequency of the interference pattern coincides with an eigenfrequency of electronic gas oscillation. As the maximum of the I-U curve is approached, the interaction becomes nonlinear in character.     

The optical nonreciprocal response based on a four-mode optomechanical system

We propose a scheme for realizing the optical nonreciprocal response based a four-mode optomechanical system,consisting of two charged mechanical modes and two linearly coupled optical modes. Two charged mechanical modes are coupled by Coulomb interaction, and two optical modes are coupled to one of mechanical modes by radiation pressure. We numerically evaluate the transmission probability of the probe field to obtain the optimum optical nonreciprocal response parameters. Also, we show that the optical nonreciprocal response is caused by the quantum interference between the optomechanical couplings and the linearly coupled interaction that breaks the time-reversal symmetry.     

Wideband chaotic oscillation in a self-oscillatory system with a nonlinear transmission line on magnetostatic waves

Wideband chaotic microwave oscillation in a ring self-oscillatory system is studied. The system includes a solid-state power amplifier and a wideband nonlinear transmission line with a ferromagnetic film in which magnetostatic waves of different types are excited. It is found that the eigenmodes of the self-oscillatory system excited in the passband of the transmission line on magnetostatic waves become noisy because of spin wave parametric excitation due to the magnetostatic wave and nonlinearity of the power amplifier. A continuous spectrum of modes observed in the wideband chaotic signal is associated with the presence of a descending portion in the dynamic characteristic of the nonlinear transmission line, which arises when a magnetostatic surface wave is excited.     

非线性光学腔中的相位调制光机械动力学

研究了Fabry-Perot光学腔中包含一个光学参量放大器来增强腔场与机械振子之间的耦合的光机械动力学行为.在解析边带机制下用量子郎之万方程具体研究了振子的涨落光谱、光学多稳态行为、机械阻尼与修正共振频移和基态冷却,通过数值解讨论了辐射压力诱导机械振子和腔场的稳态振幅所展现的光学多稳态行为,同时也分析了辐射压力引起的修...     

三机械薄膜腔光力系统相互作用的研究

本文主要研究了利用传输矩阵理论和共振透射条件详细地推导光腔中均匀放置三个机械薄膜构成的腔光力系统中系统本征模式随机械运动的色散关系.计算结果发现系统的光学本征模式由一组四个的本征能级构成,且不同的能级随不同的机械运动模式的变化曲线各不相同,进而导致不同光学模式与不同机械运动模式之间的耦合也不相同.此外,利用微扰理论求解了当机械运动振幅远小于腔模波长、机械振子处于平衡位置附近时,各种光学模式与不同机械振动模式间相互作用耦合强度的解析表达式.研究结果能够为理论和实验上研究多模腔光力系统提供一定的参考.     

Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion

We show that eigenmodes of dielectric optical waveguides exert surface dilation forces on waveguide boundaries owing to radiation pressure, and we develop an exact scaling law relating modal dispersion of an arbitrary dielectric waveguide to the magnitude of optical forces generated by radiation pressure. This result points to highly dispersive waveguides as an optimal choice for the generation of large optical forces in nano-optomechanical systems. Exact agreement with ab initio calculations is demonstrated.     

Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode

We analyze experimentally and theoretically mechanical oscillation within an optical cavity stimulated by the pressure of circulating optical radiation. The resulting radio frequency cavity vibrations (phonon mode) cause modulation of the incident, continuous-wave (cw) input pump beam. Furthermore, with increasing cw pump power, an evolution from sinusoidal modulation to random oscillations is observed in the pump power coupled from the resonator. The temporal evolution with pump power is studied, and agreement was found with theory. In addition to applications in quantum optomechanics, the present work suggests that radiation-pressure-induced effects can establish a practical limit for the miniaturization of optical silica microcavities.     

Mechanical mode dependence of bolometric backaction in an atomic force microscopy microlever

Two backaction (BA) processes generated by an optical cavity-based detection device can deeply transform the dynamical behavior of an atomic force microscopy microlever: the photothermal force or the radiation pressure. Whereas noise damping or amplifying depends on the optical cavity response for radiation pressure BA, we present experimental results carried out under vacuum and at room temperature on the photothermal BA process which appears to be more complex. We show for the first time that it can simultaneously act on two vibration modes in opposite directions: Noise on one mode is amplified, whereas it is damped on another mode. Basic modeling of photothermal BA shows that the dynamical effect on the mechanical mode is laser spot position-dependent with respect to mode shape. This analysis accounts for opposite behaviors of different modes as observed.     

非线性光学腔中的相位调制光机械动力学

研究了Fabry-Perot光学腔中包含一个光学参量放大器来增强腔场与机械振子之间的耦合的光机械动力学行为.在解析边带机制下用量子郞之万方程具体研究了振子的涨落光谱、光学多稳态行为、机械阻尼与修正共振频移和基态冷却.通过数值解讨论了辐射压力诱导机械振子和腔场的稳态振幅所展现的光学多稳态行为,同时也分析了辐射压力引起的修正共振频移和机械阻尼与参量增益、输入激光功率和参量相位这三个因素的关系.此外,随着调节泵浦场的参量相位,振子的涨落光谱呈现简正模式分裂.通过精确求解最终有效声子数论证了基态冷却.结果表明,机械振子的冷却由初始浴温度、机械品质因数和参量相位这个三个因素控制.参量相提供一个新的方法来操控非线性光机械动力学.     

Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres

Quantitative measurements of the vibrational eigenmodes in ultrahigh-Q silica microspheres are reported. The modes are excited via radiation-pressure-induced dynamical backaction of light confined in the optical whispering-gallery modes of the microspheres (i.e., via the parametric oscillation instability). Two families of modes are studied and their frequency dependence on sphere size investigated. The measured frequencies are in good agreement both with Lamb's theory and numerical finite-element simulation and are found to be proportional to the sphere's inverse diameter. In addition, the quality factors of the vibrational modes are studied.     

Effect of the External Mirror Feedback Strength in the Dynamics and Spectrum of the Injected Semiconductor Lasers

We analytically investigate the effect of an external mirror on the stability of an injected semiconductor laser, the latter treated as injected damped oscillators. In the studied configuration, the injected semiconductor laser with an external mirror is under the influence of a chaotic oscillating optical signal that is generated by a similar semiconductor master laser. We derive our results in terms of the damping rate and resonance frequency. We show that the external mirror can eliminate the unstable modes of the injected laser at low frequencies. Furthermore, the mirror can enhance the damping of the oscillation modes of the injected semiconductor laser; consequently, the driven response of the injected laser may have a broad spectrum, even wider than that of the chaotic driving signal. We also show results for the bandwidths of the injection amplitude and phase increment as functions of the injection rate and feedback strength of the external mirror. In addition, we use bifurcation and time-series curves to describe the dynamical behavior of the injected laser. We identify the feedback strength of injected laser, relative to that of the master laser, which induces synchronization between the injected-laser oscillation modes and the master laser.     

Quantum nondemolition measurement by optomechanical coupling

 We show that a single-port optical cavity with a movable mirror can provide a quantum non-demolition measurement of the intensity of a light beam. Due to radiation pressure, the cavity length is sensitive to the light intensity and can be measured with a secondary light beam. Signal-meter correlations can be made very large even at non-zero temperature. We study these correlations when the moving mirror is a plane–convex crystal resonator and we show the importance of spatial matching between light and acoustic modes. Received: 12 June 1996/Revised version: 3 September 1996     

Characteristics of acoustic emissions during nucleation of superheated droplets

Superheated droplet nucleation and subsequent bubble oscillation produces an acoustic pressure pulse that contains valuable information about the nucleation process. Spectral analysis of the pressure pulse indicates excitation of different modes of bubble oscillations in the nucleation process. In the present study it is observed that gamma induced droplet nucleation excites higher modal oscillations and also emits higher intensity acoustic emission compared to that of spontaneous nucleations.     

Bistability of self-modulation of the GaAs intrinsic stimulated picosecond radiation spectrum

The bistability of self-modulation of the spectrum of the stimulated picosecond radiation that appears during picosecond optical pumping of GaAs is detected. The radiation is measured before it reaches the end faces of a sample. One set of equidistant modes occurs in the radiation spectrum at the radiation pulse front. A set of modes located at the center between the initial modes replaces the first set in the descending radiation branch. The intermode interval inside each set coincides with the calculated interval between the eigenmodes of the GaAs layer, which is an active cavity. The radiation rise time turns out to be an oscillating function of the photon energy. The spectrum evolution is self-consistent so that the time-integrated spectrum and the spectrum-integrated radiation pulse envelope have a smooth (without local singularities) shape. The revealed bistability explains the physical nature of the two radiation-induced states of population depletion between which subterahertz self-oscillations in the radiation field were detected earlier. The radiation spectrum self-modulation is assumed to be a variant of stimulated Raman scattering.     

Waveguide modulated non-local optical interaction of semiconductor microdisks

The non-local optical interaction of two semiconductor microdisks with a waveguide bridged at radial direction is proposed and studied by three dimensional finite-difference time-domain （FDTD） electromagnetic simulations. The strong and weak optical interactions between two microdisks are observed and ascribed to the internal coupled modes with different coupling ratios. The vertical radiation losses and the related mode quality factors are modulated by waveguide length and present oscillation characteristics for the resonant modes. In addition, the optical leakage of coupling system is affected by the etching depth of disks due to tile emission of minor components of electric field.     

Optical actuation of a macroscopic mechanical oscillator

An intensity-modulated HeNe-laser beam was utilized to optically actuate the mechanical resonance of a macroscopic torsional silicon oscillator (f₀ = 67 700 Hz, Q = 42 100 at p = 1 mbar and T = 300 K). Both radiation pressure and photothermal effects may cause optical actuation of a mechanical device. Both excitation effects were studied. In actuation through radiation pressure, the actuating laser beam was focused on the high-reflectivity-coated oscillator surface. In the case where the intensity-modulated laser beam was incident on the uncoated silicon surface the photothermal effect was shown to be the dominating excitation factor. Oscillation amplitudes due to the actuation through radiation pressure and photothermal effects were Δ x_rad = 1.4 pm and Δ x_ph = 4.3 pm with the same optical power of 1.5 mW. The measured resonance frequency and quality value were not changed when purely mechanical and radiation pressure actuation mechanisms were compared. With photothermal actuation the absorbed optical power heats the oscillator, introducing a slight decrease in the resonance frequency. Our experiments demonstrate that optical actuation combined with sensitive optical interferometric measurements can be utilized to perform dynamic vibration analysis of micromechanical components. Prospects of using micromechanical devices for observing extremely weak external forces are discussed.     

Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK

We report on the use of a radiation pressure induced restoring force, the optical spring effect, to optically dilute the mechanical damping of a 1 g suspended mirror, which is then cooled by active feedback (cold damping). Optical dilution relaxes the limit on cooling imposed by mechanical losses, allowing the oscillator mode to reach a minimum temperature of 6.9 mK, a factor of approximately 40 000 below the environmental temperature. A further advantage of the optical spring effect is that it can increase the number of oscillations before decoherence by several orders of magnitude. In the present experiment we infer an increase in the dynamical lifetime of the state by a factor of approximately 200.     

An all-optical trap for a gram-scale mirror

We report on a stable optical trap suitable for a macroscopic mirror, wherein the dynamics of the mirror are fully dominated by radiation pressure. The technique employs two frequency-offset laser fields to simultaneously create a stiff optical restoring force and a viscous optical damping force. We show how these forces may be used to optically trap a free mass without introducing thermal noise, and we demonstrate the technique experimentally with a 1 g mirror. The observed optical spring has an inferred Young's modulus of 1.2 TPa, 20% stiffer than diamond. The trap is intrinsically cold and reaches an effective temperature of 0.8 K, limited by technical noise in our apparatus.