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.

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.

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.

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.

2D-material-integrated whispering-gallery-mode microcavity

Optical microcavities, which support whispering gallery modes, have attracted tremendous attention in both fundamental research and potential applications. The emerging of two-dimensional materials offers a feasible solution to improve the performance of traditional microcavity-based optical devices. Besides, the integration of two-dimensional materials with microcavities will benefit the research of heterogeneous materials on novel devices in photonics and optoelectronics, which is dominated by the strongly enhanced light–matter interaction.This review focuses on the research of heterogeneous two-dimensional-material whispering-gallery-mode microcavities, opening a myriad of lab-on-chip applications, such as optomechanics, quantum photonics, comb generation, and low-threshold microlasing.

Linearly polarised three-colour lasing emission from an evanescent wave pumped and gain coupled fibre laser

A novel Whispering-Gallery-Mode （WGM） fibre laser, emitting linearly polarised three-colour light, is demonstrated by pumping and gain coupling with evanescent waves. The pump light is longitudinally coupled into a bare optical fibre immersed in a dye solution of lower refractive index. The dye molecules around the bare fibre are excited by the evanescent waves of pump light when they propagate along the fibre in a total internal reflection. When the pump beam within the fibre is a meridian beam, the WGM lasing emission from the fibre laser is a linearly polarised transverse electric wave, while it is a mixed wave of the linearly polarised transverse electric and magnetic waves if the pump beam is a skew beam within the fibre. Because the excited molecules are located within the evanescent field of WGM, a good spatial overlap between the dye gain and the evanescent field leads to a high pumping efficiency and a longer gain distance along the fibre. Once the bare fibre is inserted into three glass capillaries filled with Rhodamine 6G, 610 and 640 dye solutions, respectively, WGM laser oscillations at the wavelengths of 567-575, 605-614 and 656-666 nm occur simultaneously, and a linearly polarised three-colour lasing emission is achieved in a single optical fibre.

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.

Experimental observation of Fano-like resonance in a whispering-gallery-mode microresonator in aqueous environment

We report on the transmission spectra of a sausage-like microresonator(SLM)in aqueous environment,where a fiber taper is used as a light coupler.The transmission spectra show an interesting dependence on the coupling position between the SLM and the fiber taper.When the SLM is moved along the fiber taper,the line shape can evolve periodically among symmetric dips,asymmetric Fano-like resonance line shapes,and symmetric peaks.A coupled-mode theory with feedback is developed to explain the observation.The observation of Fano-like resonance in aqueous environment holds great potential in biochemical sensing.

Frequency comb in a parametrically modulated micro-resonator

In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is observed.The finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation signals.By adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different applications.Theoretical analysis based on the dynamic model well explains the corresponding observations.

STUDY OF CROSSED FIELD GYROTRON OPERATING ON WHISPERING-GALLERY MODE

A linear and nonlinear analysis of crossed-field gyrotron operating on whispering-gallery mode TEm11 is presented. The detailed discussions are given for the starting oscillationcondition, the effect of the internal conductor in coaxial cavity on the cut-off frequency of modeand the spacing between adjacent modes as well as the effect of the applied voltage on thecyclotron frequency of electron, the starting oscillation beam power and the electron efficiency.It is shown that the efficiency of 41% can be attained for m=2. A comparison of these resultswith those in cylindrical cavity is made. The analyses are helpful for the engineering design.

Dual-stimuli responsive photonic barcodes based on perovskite quantum dots encapsulated in whispering-gallery-mode microspheres

Micro/nanoscale photonic barcodes hold great potential for broad applications in items tracking,mul-tiplexed bioassays and anti-counterfeiting.The ever-increasing demand in advanced anti-counterfeiting applications calls for micro/nanoscale barcodes with accurate recognition,large encoding capacity and high security level.Here,we proposed a strategy to construct the dual-stimuli responsive photonic barcodes based on the perovskite quantum dots(PQDs)doped polymer whispering-gallery-mode(WGM)microcavities via swelling-deswelling method.Benefiting from the well-defined spherical microcavities,the photoluminescence(PL)spectra of as-prepared composites exhibit a series of sharp peaks characteristics resulting from the effective WGM modulation,which constitutes the fingerprint of a specific resonator and thus allows a definition of photonic barcodes.On this basis,we achieved responsive photonic barcodes based on the volatile polar-solvent-controlled luminescence in the mi-crospheres benefitting from the space-confined microcavities and the ionic feature of the PQDs.More-over,the light-controlled photonic barcodes have further been acquired through reversibly regulating the inactivation and activation of the energy transfer(ET)process between the PQDs and photochromic dyes.The well-established protocols of PQDs@WGM enable the development of distinct responsive barcodes with multi-responsive features,which will pave an avenue to new types of flexible WGM-based components for optical data recording and security labels.

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.

聚苯乙烯微粒光子晶体的反常透过特性

在实验上发现了 3μm聚苯乙烯 (PS)小球光子晶体在 35 0nm至 90 0nm波长上的透过率的周期扰动 .根据透过率曲线的周期扰动的峰谷值判断 ,这种周期性透过率特性是基于PS小球的whispering gallery mode(WGM)共振 ,而不是源于米氏散射或布拉格衍射 .实验表明 ,周期性排列小球在非带隙区域对光的传输同样有一定的影响 .

Whispering-gallery mode hexagonal micro-/nanocavity lasers [Invited]

Whispering-gallery-mode(WGM) hexagonal optical micro-/nanocavities can be utilized as high-quality(Q) resonators for realizing compact-size low-threshold lasers. In this paper, the progress in WGM hexagonal micro-/nanocavity lasers is reviewed comprehensively. High-Q WGMs in hexagonal cavities are divided into two kinds of resonances propagating along hexagonal and triangular periodic orbits, with distinct mode characteristics according to theoretical analyses and numerical simulations;however, WGMs in a wavelength-scale nanocavity cannot be well described by the ray model. Hexagonal micro-/nanocavity lasers can be constructed by both bottom-up and top-down processes, leading to a diversity of these lasers. The ZnO-or nitride-based semiconductor material generally has a wurtzite crystal structure and typically presents a natural hexagonal cross section. Bottom-up growth guarantees smooth surface faceting and hence reduces the scattering loss effectively.Laser emissions have been successfully demonstrated in hexagonal micro-/nanocavities synthesized with various materials and structures. Furthermore, slight deformation can be easily introduced and precisely controlled in top-down fabrication, which allows lasing-mode manipulation. WGM lasing with excellent singletransverse-mode property was realized in waveguide-coupled ideal and deformed hexagonal microcavity lasers.

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.

Plasmon enhancement for Vernier coupled single-mode lasing from ZnO/Pt hybrid microcavities

It is essential to develop a single mode operation and improve the performance of lasing in order to ensure practical applicability of microlasers and nanolasers. In this paper, two hexagonal microteeth with varied nanoscaled air-gaps of a ZnO microcomb are used to construct coupled whispering-gallery cavities. This is done to achieve a stable single mode lasing based on Vernier effect without requiring any complicated or sophisticated manipulation to achieve positioning with nanoscale precision. Optical gain and the corresponding ultraviolet lasing performance were improved greatly through coupling with localized surface plasmons of Pt nanoparticles. The ZnO/Pt hybrid microcavities achieved a seven-fold enhancement of intensity of single mode lasing with higher side- mode suppression ratio and lower threshold. The mechanism that led to this enhancement has been described in detail.

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.

Conformal optical black hole for cavity

Whispering-gallery-mode(WGM)cavity is important for exploring physics of strong light-matter interaction.Yet it suffers from the notorious radiation loss universally due to the light tunneling effect through the curved boundary.In this work,we propose and demonstrate an optical black hole(OBH)cavity based on transformation optics.The radiation loss of all WGMs in the ideal OBH cavity is completely inhibited by an infinite wide potential barrier.Besides,the WGM field in the OBH cladding is revealed to follow 1/r decay rule based on conformal mapping,which is fundamentally different from the conventional Hankel-function distributions in a homogeneous cavity.Experimentally,a truncated OBH cavity is achieved based on the effective medium theory,and both the Q-factor enhancement and tightly confined WGM fields are measured in the microwave spectra which agree well with the theoretical results.The circular OBH cavity is further applied to the arbitrary-shaped cavities including single-core and multi-core structures with high-Q factor via the conformal mapping.The OBH cavity design strategy can be generalized to resonant modes of various wave systems,such as acoustic and elastic waves,and finds applications in energy harvesting and optoelectronics.

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.