Design and characterization of a 3D encapsulation with silicon vias for radio frequency micro-electromechanical system resonator

In this paper, we present a three-dimensional(3D) vacuum packaging technique at a wafer level for a radio frequency micro-electromechanical system(RF MEMS) resonator, in which low-loss silicon vias is used to transmit RF signals.Au–Sn solder bonding is adopted to provide a vacuum encapsulation as well as electrical conductions. A RF model of the encapsulation cap is established to evaluate the parasitic effect of the packaging, which provides an effective design solution of 3D RF MEMS encapsulation. With the proposed packaging structure, the signal-to-background ratio(SBR) of 24 dB is achieved, as well as the quality factor(Q-factor) of the resonator increases from 8000 to 10400 after packaging.The packaged resonator has a linear frequency–temperature( f –T) characteristic in a temperature range between 0℃ and 100℃. And the package shows favorable long-term stability of the Q-factor over 200 days, which indicates that the package has excellent hermeticity. Furthermore, the average shear strength is measured to be 43.58 MPa among 10 samples.     

Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators

The electrodynamic properties of coaxial two-dimensional Bragg resonators with two-dimensional distributed feedback are analyzed. These resonators are made of coaxial waveguide sections with doubly periodic corrugation, which provides coupling and mutual scattering of four partial waves. Two of them propagate along the waveguide, while the other two propagate in the transverse (azimuthal) direction. It is shown that the high azimuthal index selectivity of two-dimensional Bragg resonators may be related to a qualitative difference in topology of the dispersion characteristics of azimuth-symmetric and asymmetric normal waves propagating in infinite waveguides of such a geometry. For the finite-length systems used as two-dimensional Bragg resonators, the eigenmode spectrum is found for two types of boundary conditions that correspond to the limiting cases of perfectly matched (open) systems and, conversely, of systems closed for the extraction of transverse electromagnetic fluxes. Perimeter-to-length ratios of the resonator at which the Q factor of the fundamental azimuth-symmetric mode is greater than those of the other modes are determined. The applicability domain of the geometrical approach, which was earlier applied to two-dimensional Bragg resonators, is discussed.     

Generation of a spatially coherent field structure in free-electron masers with 2D distributed feedback

Nonlinear dynamics of free-electron masers (FEMs) is studied in the planar geometry with 2D distributed feedback (DFB). As is distinct from previous works, the field structure is not fixed with respect to the three spatial coordinates including the coordinate that is orthogonal to surfaces of the plates of the 2D Bragg resonator. Conditions on the allowed oversize parameter (ratio of the gap between the resonator plates to wavelength) under which the steady-state generation remains stable upon variation in electron-beam parameters are derived. It is demonstrated that, at a relatively large gap, variations in the mismatch lead to the jumps of oscillation frequency that correspond to the excitation of bunches of modes with different transverse indices of partial waves. The results of simulation using a particle-in-cell method are presented for a FEM prototype with 2D DFB that is created using an ELMI accelerator at the Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences. The simulated results show that narrow-band spatially coherent radiation can be generated at experimental parameters of the electron beam and electrodynamic system. The advantages of 2D Bragg structures in comparison with conventional 1D structures are demonstrated for FEMs.     

Powerful Cherenkov oscillators with 2D distributed feedback

The feasibility of using 2D distributed feedback based on 2D planar and coaxial Bragg structures for generating spatially coherent radiation from rectilinear ribbon and tubular electron beams is studied. One-section and sectional Cherenkov masers are analyzed. In the former design, a 2D Bragg structure acts as a resonator and a periodic slow-wave system simultaneously. In the latter (sectional) design, radiation is synchronized in a 2D Bragg structure that is placed at the cathode end of the interaction space and couples longitudinal and transverse (azimuthal) wave flows. The wave is amplified by the electron beam mainly in the fairly long middle section. The output (collector) part contains a standard 1D Bragg structure that partially reflects the amplified radiation toward the cathode and closes the feedback circuit. It is shown that dissipation introduced into the 2D Bragg structure of the sectional design makes it possible to increase one of the transverse sizes of the system to ∼10³ wavelengths with the energy exchange efficiency and one-frequency masing mode stability remaining the same. With such an overdimension, the millimeter-wave radiation integral power may reach a gigawatt level.     

Design considerations of the acousto-optic light deflector

Theoretical analysis of the performance of the acousto-optic light deflector is described. Detailed calculations for LiIO₃-SF₆ glass structure including the influence of the bonding layer and Q-factor on the frequency response of the deflector are presented. A method of increasing the bandwidth in the presence of the bonding layer is given.     

Purcell effect in one-dimensional photonic quasicrystals

The change in probability of spontaneous emission for emitter placed in one-dimensional photonic quasicrystal (optical Fibonacci lattice) was examined. When the dipole is placed in Fibonacci lattice two different scenarios can be expected: enhancing (if frequency and direction of the dipole emission correspond to optical eigenmode of structure, and position corresponds to maximum value of modes electric field profile) or suppression (in case of photonic band gap) of spontaneous emission rate. Fact that both effects are expressed in quasicrystals less than in the Bragg reflectors and in the microcavities was demonstrated.     

A note on the heating of the cold plasma blanket in a linear fusion reactor

On the basis of a simple model it is demonstrated that the Q-factor of present-day conceptual linear reactors is not enhanced by -particle heating of the cold plasma blanket surrounding the fusioning plasma column.     

A Simple Bi-directional Mode Expansion Propagation Algorithm Based on Modes of a Parallel-plate Waveguide

The bi-directional mode expansion propagation algorithm (BEP) is known to be an accurate and efficient method for modelling field distribution in high-index contrast waveguide structures with strong back-reflections like Bragg gratings and photonic crystals. The main difficulty of this method is that for lossy structures, the propagation constants of modes are to be searched in the complex plane. To speed-up this procedure, a two-step algorithm for eigenmode calculation based on the expansion into the modes of an empty metallic waveguide has recently been proposed. Proper truncation rules possessing good convergence of the expansion method for both TE and TM modes have also been recently published. In this contribution, both these approaches are combined in the development of an extremely simple version of the two-dimensional BEP method that makes use of the field expansion into the eigenmodes of a parallel-plate waveguide. The method is strictly reciprocal and appeared to be computationally reliable also for strongly lossy structures. High numerical stability is ensured using the scattering matrix formalism, and an efficient method of calculating Bloch modes for symmetric as well as asymmetric periodic waveguide structures is adopted. A wide range of applicability of the method is demonstrated by a few examples.     

Rare earth photoionization study by the resonant microwave cavity technique

Photoconductivity spectra of rare earth-doped insulating materials are measured using the resonant microwave cavity method. This technique is based on the detection of the cavity Q-factor changes induced by irradiation of the sample (inserted in the cavity) by a pulsed tunable laser. Results obtained with Lu₂(SiO₄)O:Ce³⁺ and BaF₂:Eu²⁺ are presented and discussed. Photoionization thresholds at 400 nm (3.1 eV) and 310 nm (4.0 eV) are measured for Lu₂(SiO₄)O:Ce³⁺ and BaF₂:Eu²⁺, respectively.     

Nonlinear theory of coaxial free-electron masers with 2D distributed feedback (quasi-optical approximation)

The nonlinear dynamics of coaxial free-electron masers with 2D distributed feedback, which is realizable in 2D Bragg structures, is analyzed in terms of a quasi-optical approximation. It is shown that feedback with the spatial synchronization of radiations from tubular electron beams with a perimeter exceeding 1000 wavelengths can be provided under such conditions. The objects of investigation are the one-section design of a free-electron maser with 2D distributed feedback and a design with a combined two-mirror resonator. In the latter, an entrance 2D Bragg mirror provides the spatial synchronization of radiation and weak reflections from a conventional exit Bragg mirror are sufficient for the self-excitation of the oscillator. The advantage of the two-mirror design is a decrease in ohmic losses. The adequacy of the geometric optics approximation used earlier to describe the dynamics of such self-excited oscillators is demonstrated under various boundary conditions for transverse (azimuthal) energy fluxes at the edges of a Bragg structure.     

一种新型光学微腔的理论分析

应用波动光学理论,分析了一种新型锥顶柱状光学微腔的本征模式,得到了谐振腔的谐振波长表达式.在谐振波长1550 nm附近进行了设计与仿真优化,优化结果显示新型谐振腔与传统平行腔相比,在腔长为4512.5 nm,直径为3134.4 nm时,其品质因数可以提高22.4%,达到了49928.5,同时谐振腔的有效模式体积减小了47.8%.     

Electrically pumped two-dimensional Bragg grating lasers

We demonstrate electrically pumped InGaAsP two-dimensional Bragg grating (2DBG) lasers with two line defects. The 2DBG structure uses a weak 2D index perturbation surface grating to control the optical modes in the plane of the wafer. Measurements of the 2DBG lasers show that modal control in both the longitudinal and transverse directions is due to the gratings and defects. The 2DBG lasers are promising candidates for single-mode, high power, and high efficiency large-area lasers.     

Specific features of mode spectrum of planar structures with two-dimensional Bragg corrugation (theory and “cold” experiment)

Electrodynamic properties of two-dimensional-periodic Bragg structures of planar geometry are theoretically analyzed within the framework of the geometrical-optics approximation. Specific features of two-dimensional structures with different profiles, such as two-dimensional sinusoidal and “chess-board” corrugation and corrugation in the form of rectangular grooves, are studied. “Cold” testing of the Bragg structures in frequency ranges of 60 and 75 GHz is performed. The measured frequency dependences of the coefficients of reflection, transmission, and scattering in the transverse direction are in good argeement with the calculations. Existence of high-quality modes near the frequency of exact Bragg resonance is experimentally confirmed.     

Theory of a planar free-electron maser with transverse electromagnetic flux circulation in a 2D Bragg mirror

A planar free-electron maser with a resonator consisting of a 2D entrance Bragg mirror and a 1D exit Bragg mirror is theoretically studied in the framework of a nonstationary 2D model. In such a configuration, the 2D Bragg mirror provides synchronization of the radiation emitted by a wide (compared with the wavelength) ribbon-shaped electron beam. The transverse electromagnetic energy fluxes arising in this mirror are closed through an additional coupling waveguide, which provides a single-mode single-frequency masing regime insensitive to variation of the beam parameters over wide limits.     

长周期光纤光栅模式与耦合的研究

长周期光纤光栅是在光纤纤芯中沿轴向形成折射率周期性调制的带阻型光纤器件。与光纤布拉格光栅不同，它表现为前向传播的纤芯基模与同向传播的各阶次包层模式在特定波长的耦合。研究了纤芯基模、包层模式（HE1t/EH1t）及其有效折射率随波长的变化，研究了纤芯基模与包层模式（HE1t/EH1t）的耦合系数。研究表明，纤芯基模与一阶低次包层模式的有效折射率随波长增大而减小，纤芯基模与HE1t产生的耦合系数远大于与EH1t的耦合系数，并且包层模式次数较低时，耦合系数随次数的升高而增加。这与以前的研究结果有所不同。     

Semi-infinite structures resonant phenomena in filters design problems

Conclusions The investigations carried out show that discriminator device synthesis based on eigenmode diffraction problem by semi-infinite periodical and finite periodical diaphragm system decision may be perspective for different devices designing. These devices use the physical fact of total reflection regions in semi-infinite periodical structures. Similarly procedure (with any modifications) one can use for discriminators designing based on another transmitting line types, for example, for rejection filters based on insulated image guides.     

均匀光纤Bragg光栅局部横向受力特性研究

对均匀光纤Bragg光栅(FBG)局部横向受力特性进行了理论和实验研究.采用传输矩阵法分析了FBG其中一段横向受力时的反射光谱变化,并且建立了相应的数学模型.研究表明,当FBG局部横向受力时,受压长度对反射光谱无影响,反射光谱分裂点的波长与横向作用力呈线性正比关系并具有周期性,分裂点反射率与受力位置的关系为近似双曲正切关系. 关键词： 光纤Bragg光栅 传输矩阵法 局部横向受力 分裂点     

Properties of single and multiple defect modes in one-dimensional photonic crystals containing left-handed metamaterials

Wave propagation is studied in structures consisting of alternate left- and right-handed layers.Bragg gap and zero-n gap appear in different frequency regions of the structure.The periodicity of the structure is broken by simply reversing the order of the layers in one half of the structure,resulting in defect modes located inside the zero-n gap and Bragg gap.These modes can be made very narrow by adding more layers in the structure.The defect mode located inside the zero-n gap is sensitive to the symmetry of the structure and insensitive to the angle of incidence of the incoming radiation.Multiple modes are also generated inside the gaps by repeating the structural pattern.Thus,a simple structure can be used for single and multiple modes that are important for different applications.     

Polarization-Independent Guided-Mode Resonance Filters under Oblique Incidence

We present the dispersion relation of guided-mode resonances in planar periodic waveguides, both for s-polarized （TF, mode） and p-polarized （TM mode） incident waves. For a fixed homogeneous planar waveguide, dispersion curves of the TE eigenmode cannot cross that of the TM eigenmode at all. That is to say, at a certain wavelength, TE and TM modes cannot be excited with the same propagation constant. Due to Bragg reflection in the planar periodic waveguide, dispersion curves of the TE leaky mode may intersect with that of the TM leaky mode in the first Brillouin zone. We employ these intersections to achieve polarization-independent guided-mode resonance filters.     

Geometrical freedom for constructing variable size photonic bandgap structures

In order to study the design flexibility of photonic bandgap structures, we investigate different examples of 1D traditional Bragg layers and 2D photonic crystals. We have also considered a simple case of 3D woodpile structures. It turns out that in systems with large gaps, the evanescent waves penetrate into the bulk only distances comparable to one lattice constant. Therefore confinement of light can also be achieved without long range order, which leads to the introduction of novel photonic bandgap designs. Adhering to some constraints, the changes in the photonic bandgap in disordered structures are negligible. The important quantity to characterize the presence or absence of modes is the local photonic density of states, however bandgap phenomena in size and position disordered arrangements can also be verified with plane wave supercell calculations as well as finite difference time domain techniques.