Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid

The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.

Effect of strain-gradients of surface micro-beams on frequency-shift of a quartz crystal resonator under thickness-shear vibrations

With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator（QCR） system,consisting of a QCR and surface micro-beam arrays.The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained,which have important significance in resonator design and applications.

Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

We study the dynamic behavior of a quartz crystal resonator （QCR） in thickness-shear vibrations with the upper surface covered by an array of micro-beams （MBs） under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right （left） translation for increasing elastic modulus （length/radius ratio） of MBs. Moreover, the frequency right （left） translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one,

Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams

The electric admittance of a compound system composed of a thickness-shear mode （TSM） quartz crystal resonator （QCR） and an array of surface viscoelastic micro-beams （MBs） is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin （SU-8） MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak（s） and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.

Thickness shear mode quartz crystal resonators with optimized elliptical electrodes

Quartz crystal resonators （QCRs） with circular electrodes have been widely used for various liquid and gas sensing applications. In this work, quartz crystal resonators with elliptical electrodes were studied and tested for liquid property measurement. Mindlin＇s theory was used to optimize the dimension and geometry of the electrodes and a 5-MHz QCR with minimum series resistance and without any spurious modes was obtained. A series of AT-cut QCRs with elliptical electrodes of different sizes were fabricated and their sensing performances were compared to devices with circular electrodes. The experimental result shows that the device with elliptical electrodes can obtain lower resonance impedance and a higher Q factor, which results in a better loading capability. Even though the sensitivities of devices with elliptical and circular electrodes are found to be similar, the sensor with elliptical electrodes has much higher resolution due to a better frequency stability. The study indicates that the performance of QCRs with elliptical electrodes is superior to that of traditional QCRs with circular electrodes.

The Multi-field Coupled Vibration Analysis of AT-Cut Quartz Crystal Resonators with Parallelism Error

During the fabrication of quartz crystal resonators(QCRs),parallelism error is inevitably generated,which is rarely investigated.In order to reveal the influence of parallelism error on the working performance of QCRs,the coupled vibration of a non-parallel AT-cut quartz crystal plate with electrodes is systematically studied from the views of theoretical analysis and numerical simulations.The two-dimensional thermal incremental field equations are solved for the free vibration analysis via the coefficient-formed partial differential equation module of the COMSOL Multiphysics software,from which the frequency spectra,frequency–temperature curves,and mode shapes are discussed in detail.Additionally,the piezoelectric module is utilized to obtain the admittance response under different conditions.It is demonstrated that the parallelism error reduces the resonant frequency.Additionally,symmetry broken by the non-parallelism increases the probability of activity dip and is harmful to QCR’s thermal stability.However,if the top and bottom surfaces incline synchronously in the same direction,the influence of parallelism error is tiny.The conclusions achieved are helpful for the QCR design,and the methodology presented can also be applied to other wave devices.

ON THE INTERACTION BETWEEN A QUARTZ CRYSTAL RESONATOR AND AN ARRAY OF MICRO-BEAMS IN THICKNESS-SHEAR VIBRATIONS

We studied the coupled dynamic behavior of a quartz-crystal-resonator （QCR）/micro- beams system in the thickness-shear motions. Through taking into account the couple stress in the dynamic equations of the quartz plate, both continuous conditions of shear force and bending moment at the resonator/micro-beams interface are realized. Frequency shift of the compound QCR system induced by micro-beams is studied in detail. The obtained results are useful in device design and frequency-stability analysis of quartz crystal resonators.

Design and analysis of multi-channel drop filter using dual L defected hexagonal photonic crystal ring resonator

In this paper,dual L defected hexagonal Photonic Crystal Ring Resonator(PCRR)using Channel Drop Filter(CDF)is designed for Coarse Wavelength Division Multiplexing(CWDM)systems.In this structure,the external rods of the ring resonator are arranged in a hexagon and the internal rods are removed in L arrangement for introducing defects.Scatter rods are used to prevent leakage.By using the L defected hexagonal resonator,a multi-channel CDF is designed,which exhibits multiple wavelengths of CWDM(1500 nm–1600 nm)region.In addition,the selection of rod size and the position of rods in the proposed multi-channel CDF are validated by varying the radius of coupling and scattering rods,as well as the position of resonators,respectively.By using plane wave expansion and opti Finite Difference Time Domain(FDTD)method,the electromagnetic wave propagation and the photonic band gap are obtained.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

Photonic crystal fiber polarization filter with two large apertures coated with gold layers

A novel photonic crystal fiber（PCF） polarization filter is designed and fabricated; it consists of two large apertures coated with gold. The asymmetric structure separates the resonance position in the vertical direction well. Due to the metal layer covering, loss is greatly improved. Finite element method is applied for numerical simulation. The influences of varying gold thickness and varying the diameters and the center positions of the larger apertures on filtering performance are evaluated. Theory of coupling between surface plasma and core mode is introduced. By modulating the parameters, we realize a single polarization filter at 1.31 μm and 1.55 μm. The basal mode loss in the y direction can reach 1408.80 dB/cm at 1.31 μm and 1911.22 dB/cm at 1.55 μm respectively, but basal mode loss in the x direction is relatively small, 0.82 dB/cm and 1.87 dB/cm. In addition, two kinds of broadband polarization filters are proposed. If the fiber length is set to 200 μm,the extinction ratio is greater than 20 dB with width of 570 nm and 490 nm. The filter has simple structure and excellent performance.

31P Nuclear Magnetic Resonance of Charge-Density-Wave Transition in a Single Crystal of RuP

We perform 31p nuclear magnetic resonance （NMR） measurements on a single crystal of RuP. The anomalies in resistivity at about TA = 270 K and TB = 330 K indicate that two phase transitions occur. The line shape of alp NMR spectra in different temperature ranges is attributed to the charge density distribution. The Knight shift and spin-lattice relaxation rate 1/T1T are measured from 1OK to 30OK. At about TA = 270K, they both decrease abruptly with the temperature reduction, which reveals the gap-opening behavior. Well below TA, they act like the case of normal metal. Charge-density-wave phase transition is proposed to interpret the transition occurring at about TA.

Highly efficient tunable optical filter based on liquid crystal micro-ring resonator with large free spectral range

A highly efficient tunable optical filter of liquid crystal （LC） optical micro-r/rig resonator （MRR） was proposed. The 4-pro-radius ring consists of a silicon-on- insulator （SOI） asymmetric bent slot waveguide with a LC cladding. The geometry of the slot waveguide resulted in the strong electro-optic effect of the LC, and therefore induced an increase in effective refractive index by 0.0720 for the quasi-TE mode light in the slot-waveguide. The ultra-wide tuning range （56.0 nm） and large free spectral range （FSR） （-28.0nm） of the optical filters enabled wavelength reconfigurable multiplexing devices with a drive voltage of only 5 V. The influences of parameters, such as the slot width, total width of Si rails and slot shift on the device＇s performance, were analyzed and the optimal design was given. Moreover, the influence of fabrication tolerances and the loss of device were both investigated. Compared with state-of-the-art tunable MRRs, the proposed electrically tunable micro-ring resonator owns the excellent features of wider tuning ranges, larger FSRs and ultralow voltages.

2-channel all optical demultiplexer based on photonic crystal ring resonator

In this paper, we proposed a 2-channel demultiplexer based on photonic crystal ring resonator （PCRR）. For performing wavelength selection, we used two ring resonators, two different wavelengths were obtained by using two resonant rings with different values for the radius of dielectric rods. All the simulations and calculations have been done using Rsoft Photonic CAD software, which employs finite difference time domain （FDTD） method. The output channels were respectively at 1590.8 and 1593.8nm, correspondingly had the quality factors of 7954 and 3984, the crosstalk values of -22 and -11 dB separately. The total footprint of our proposed structure is 681.36 μm2. Results suggest that 2-channels in the proposed structure are characterized with high transmission efficiency and low band width, resulting in a very sharp output spectrum and high quality factor values.

A photonic crystal L-shaped bend based on ring resonators

We propose a new type of two-dimensional （2D） photonic crystal L-shaped bent waveguides based on ring resonators with an acceptable bandwidth. The proposed structure mechanism is based on coupling between a waveguide and a ring resonator. This structure is designed and verified by finite-difference time-domain （FDTD） computation. Our simulation using this method gets over 90% output.

Novel Design of Ring Resonator Based Temperature Sensor Using Photonics Technology

In the present paper, we study the transmission of the two-dimensional photonic crystal （PC） superellipse ring resonator. The fast growing applications of optomechanical systems lead to strong demands in new sensing mechanism in order to design the sensing elements to nanometer scale. The photonic crystal based resonator has been investigated as promising solutions because the band gap structure and resonator characteristics are extremely sensitive to the deformation and position shift of rod/cavity in PC resonators. This structure opens a single channel filter. The study is extended for tuning of channel filter＇s wavelength with a temperature of this structure. The transmission of the channel filter shows a red shift with temperature linearly. This wavelength shift of the channel filter is used for the sensor application. The sensitivity for the proposed structure is found to be 65.3pm/℃. The outstanding sensing capability renders PC resonators as a promising optomechanical sensing element to be integrated into various transducers for temperature sensing applications.

Resonant Raman scattering in GaN single crystals and GaN-based heterostructures: feasibility for laser cooling

The recent progress on Raman scattering in GaN single crystals and GaN/A1N heterostructures is re- viewed. Anti-Stokes Raman scattering is used to determine electron-phonon scattering time and decay time constant for longitudinal-opticat phonons. In a typical high electron mobility transistor based on GaN/A1N heterostructures, strong resonances are reached for the first-order and second-order Raman scattering processes. Therefore, both Stokes and anti-Stokes Raman intensities are dramatically enhanced. The feasibility for laser cooling of a nitride structure is studied. A further optimization will enable us to reach the threshold for laser cooling. Raman scattering have potential applications in up-conversion lasers and laser cooling of nitride ultrafast electronic and optoelectronic devices.

Noise suppression for the detection laser of a nuclear magnetic resonance gyroscope based on a liquid crystal variable retarder

Nuclear magnetic resonance gyroscopes （NMRGs） are a kind of rotation-speed sensor that senses the angular velocity by measuring a frequency shift in the Larmor pre- cession of the nuclear spin in a constant magnetic field.

Ultra-wide tuning single channel filter based on one-dimensional photonic crystal with an air cavity

By inserting an air cavity into a one-dimensional photonic crystal of LiF/GaSb, a tunable filter covering the whole visible range is proposed. Following consideration of the dispersion of the materials, through modulating the thickness of the air cavity, we demonstrate that a single resonant peak can shift from 416.1 to 667.3 nm in the band gap at normal incidence by means of the transfer matrix method. The research also shows that the transmittance of the channel can be maximized when the number of periodic Li F/Ga Sb layers on one side of the air defect layer is equal to that of the other side. When adding a period to both sides respectively, the full width at half maximum of the defect mode is reduced by one order of magnitude. This structure will provide a promising approach to fabricate practical tunable filters in the visible region with ultra-wide tuning range.

Optimized guided mode resonant structure as thermooptic sensor and liquid crystal tunable filter

Applicability of guided mode resonant structures to tunable optical filtering and sensing is demonstrated using nematic liquid crystals. As a sensor, a minimum refractive index detectivity of 10^-5 is demonstrated while as a tunable filter, tunability range of few tens of nanometers with 2-nm bandwidth is presented. The optimum design is achieved by maximizing the evanescent field region in the analyte which maximizes the overlap integral. The device can be operated in reflection or transmission modes at normal incidence. It can also be operated at a single wavelength by measuring the angular profile of the light beam.

A compact single-polarization erbium-doped fiber laser by exploiting vernier effect

A compact single-polarization fiber laser with fiber Bragg gratings inscripted in a polarization-maintaining erbium-doped germanosilicate fiber is demonstrated experimentally. The single-wavelength and single- polarization regime of our studied laser is achieved by applying a radial stress upon one of two gratings and stretching the other one axially to adjust the reflection peak match. Two single-wavelength and single- polarization lasing lines are realized respectively with fine power stability.