NONLINEAR DYNAMICS OF LATERAL MICRO-RESONATOR INCLUDING VISCOUS AIR DAMPING

The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not be fixed as a constant. Therefore the linear dynamic analysis which used the constant air damping coefficient can not describe the actual dynamic characteristics of the mi-cro-resonator. The nonlinear dynamic model including the air damping force is established. On the base of Navier-Stokes equation and nonlinear dynamical equation, a coupled fluid-solid numerical simulation method is developed and demonstrates that damping force is a vital factor in micro-comb structures. Compared with existing experimental result, the nonlinear numerical value has quite good agreement with it. The differences of the amplitudes （peak） between the experimental data and the results by the linear model and the nonlinear model are 74.5% and 6% respectively. Nonlinear nu-merical value is more exact than linear value and the method can be applied in other mi-cro-electro-mechanical systeme （MEMS） structures to simulate the dynamic performance.

Integrated silicon-based suspended racetrack micro-resonator for biological solution sensing with high-order mode

A biological sensing structure with a high-order mode(E^(y)_(21))is designed,which is composed of a suspended racetrack micro-resonator(SRTMR)and a microfluidic channel.The mode characteristics,coupling properties,and sensing performances are simulated by using the finite element method(FEM).To analyze the mode confinement property,the confinement factors in the core and cladding of the suspended waveguide for the E^(x)_(11),E^(y)_(11),and E^(y)_(21) are calculated.The simulation results show that the refractive index(RI)sensitivity of the proposed sensing structure can be improved by using the high-order mode(Ey 21).The RI sensitivity for the E^(y)_(21) mode is~201 nm/RIU,which is twice to thrice higher than those for the E^(x)_(11) mode and the E^(y)_(11) mode.Considering a commercial spectrometer,the proposed sensing structure based on the SRTMR achieves a limit of detection(LOD)of -4.7×10^(-6) RIU.Combined with the microfluidic channel,the SRTMR can possess wide applications in the clinical diagnostic assays and biochemical detections.

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.

AFM Analysis on Polymer Optical Micro-Resonators: Investigation on Quality Factor Origin

This paper deals with the surface analysis of spherical polymeric optical micro-resonators in order to correlate surface defects with optical characteristics. Atomic force microscopy was used on structures to determine surface quality, which is the main origin of optical scattering losses. Surface morphologies were numerically treated to enable a relevant investigation on surface parameters such as root mean square (RMS) roughness (30.1 +/- 3.0 nm) or correlation length (few microns) necessary to express optical quality factors. A statistical analysis was conducted for calibration of these parameters as a function of cavities’ diameter. Results are in perfect agreement with spectral analyses performed in parallel on others structures. This comparison highlights the main role of scattering losses on quality factor origin.

Investigation of high-quality-factor aluminum nitride MEMS cantilever resonators

This paper presents the design,fabrication,and characterization of cantilever-type resonators with a novel stacked structure.Aluminum nitride is adopted as the material for both the structural layer and the piezoelectric layer;this simplifies the fabrication process and improves the quality factor of the resonator.Both in-plane and out-of-planeflexural modes were investigated.The effect of the structural dimensions and electrode patterns on the resonator’s performance were also studied.Finite-element simulations and experiments examining anchor loss and thermoelastic damping,which are the main loss mechanisms affecting the quality factor of these resonators,were carried out.The optimal structural dimensions and electrode patterns of the cantilever-type resonators are presented.A quality factor of 7922 with a motional impedance of 88.52 kΩand a quality factor of 8851 with a motional impedance of 67.03 kΩwere achieved for the in-plane and out-of-planeflexural-mode resonators,respectively.The proposed resonator design will contribute to the development of high-performance devices such as accelerometers,gyroscopes,and pressure sensors.

Athermal third harmonic generation in micro‐ring resonators

Nonlinear high-harmonic generation in micro-resonators is a common technique used to extend the operating range of applications such as self-referencing systems and coherent communications in the visible region.However,the generated high-harmonic emissions are subject to a resonance shift with a change in temperature.We present a comprehensive study of the thermal behavior induced phase mismatch that shows this resonance shift can be compensated by a combination of the linear and nonlinear thermo-optics effects.Using this model,we predict and experimentally demonstrate visible third harmonic modes having temperature dependent wavelength shifts between−2.84 pm/ºC and 2.35 pm/ºC when pumped at the L-band.Besides providing a new way to achieve athermal operation,this also allows one to measure the thermal coefficients and Q-factor of the visible modes.Through steady state analysis,we have also identified the existence of stable athermal third harmonic generation and experimentally demonstrated orthogonally pumped visible third harmonic modes with a temperature dependent wavelength shift of 0.05 pm/ºC over a temperature range of 12ºC.Our findings promise a configurable and active temperature dependent wavelength shift compensation scheme for highly efficient and precise visible emission generation for potential 2f–3f self-referencing in metrology,biological and chemical sensing applications.

Analysis of Microdisk/Microring’s Surface Roughness Effect by Orthogonal Decomposition

Application of micro-resonator is limited by different types of surface inhomogeneity. The 1-th derivative of inhomogeneity (i.e. Δrˊ(φ)) affects the wave transport as well as the height of inhomogeneity (i.e. Δrˊ(φ)). A method based on orthogonal decomposition is proposed to analysis both scattering mechanism respectively. Then surface roughness effect on Q-factor of micro-disk waveguide gallery mode (WGM) resonator is investigated with our method and the analysis fits well with FDTD simulation results.

An encapsulated optical microsphere sensor for ultrasound detection and photoacoustic imaging

Optical whispering-gallery microresonators have attracted considerable interest for ultrasensitive ultrasound detection and photoacoustic imaging because of the combination of high quality factors and small cavity sizes.In the last decade,ultrasonic sensors with on-chip microcavities have been extensively developed;however,they are unsuitable for the near-field photoacoustic microscopy of micro/nanoscale objects in complex biological environments and endoscopic imaging.In this work,we developed ultrasonic sensors using two types of encapsulated microsphere resonators with different cavity materials.A noise equivalent pressure of as low as 160 Pa at 20 MHz was achieved with the acoustic response up to 70 MHz at-6 d B.Furthermore,the microsensor was used for photoacoustic microscopy in which we successfully performed 3 D imaging of hairs and leaf veins.The microsphere ultrasonic sensor has considerable potential as a probe-type ultrasonic detector for near-field photoacoustic microscopy of micro/nanoscale objects such as subcellular structures and high-resolution endoscopic photoacoustic imaging with its high sensitivity and wide bandwidth.

Optically controlled elastic microcavities

Whispering gallery mode(WGM)resonators made from dielectrics like glass or polymers have outstanding optical properties like huge cavity quality(Q)factors which can be achieved on scales compatible with on-chip integration.However,tunability of these resonances is typically difficult to achieve or not suitable for robust device applications.We report here on the fabrication of polymeric micro-goblet WGM resonators with an optically controlled and stable reversible tunability over a large spectral range.This tunability is achieved by integration of photo-responsive liquid crystalline elastomers(LCEs)into micro-goblet cavities.The optical response of the elastomer allows reshaping the goblet by employing low pump power,leading to a fully reversible tuning of the modes.The structure can be realistically implemented in on-chip devices,combining the ultra-high Q factors,typical of WGM resonators,with reliable,optical tunability.This result serves as an example of how light can control light,by invoking a physical reshaping of the structure.This way of optical tuning creates interesting possibilities for all-optical control in circuits,enabling interaction between signal and control beams and the realization of self-tuning cavities.

Multiscale Nanorod Metamaterials and Realizable Permittivity Tensors

Our aim is to evidence new 3D composite diffractive structures whose effective permittivity tensor can exhibit very large positive or negative real eigenvalues.We use a reiterated homogenization procedure in which the first step consists in considering a bounded obstacle made of periodically disposed parallel high conducting metallic fibers of finite length and very thin cross section.As shown in[2],the resulting constitutive law is non-local.Then by reproducing periodically the same kind of obstacle at small scale,we obtain a local effective law described by a permittivity tensor that we make explicit as a function of the frequency.Due to internal resonances,the eigenvalues of this tensor have real part that change of sign and are possibly very large within some range of frequencies.Numerical simulations are shown.