Analysis of two stacked cylindrical dielectric resonators in a TE₁₀₂ microwave cavity for magnetic resonance spectroscopy

The frequency, field distributions and filling factors of a DR/TE??? probe, consisting of two cylindrical dielectric resonators (DR1 and DR2) in a rectangular TE??? cavity, are simulated and analyzed by finite element methods. The TE(+++) mode formed by the in-phase coupling of the TE??(δ)(DR1), TE??(δ)(DR2) and TE??? basic modes, is the most appropriate mode for X-band EPR experiments. The corresponding simulated B(+++) fields of the TE(+++) mode have significant amplitudes at DR1, DR2 and the cavity's iris resulting in efficient coupling between the DR/TE??? probe and the microwave bridge. At the experimental configuration, B(+++) in the vicinity of DR2 is much larger than that around DR1 indicating that DR1 mainly acts as a frequency tuner. In contrast to a simple microwave shield, the resonant cavity is an essential component of the probe that affects its frequency. The two dielectric resonators are always coupled and this is enhanced by the cavity. When DR1 and DR2 are close to the cavity walls, the TE(+++) frequency and B(+++) distribution are very similar to that of the empty TE??? cavity. When all the experimental details are taken into account, the agreement between the experimental and simulated TE(+++) frequencies is excellent. This confirms that the resonating mode of the spectrometer's DR/TE??? probe is the TE(+++) mode. Additional proof is obtained from B?(x), which is the calculated maximum x component of B(+++). It is predominantly due to DR2 and is approximately 4.4 G. The B?(x) maximum value of the DR/TE??? probe is found to be slightly larger than that for a single resonator in a cavity because DR1 further concentrates the cavity's magnetic field along its x axis. Even though DR1 slightly enhances the performance of the DR/TE??? probe its main benefit is to act as a frequency tuner. A waveguide iris can be used to over-couple the DR/TE??? probe and lower its Q to ≈150. Under these conditions, the probe has a short dead time and a large bandwidth. The DR/TE??? probe's calculated conversion factor is approximately three times that of a regular cavity making it a good candidate for pulsed EPR experiments.     

Enhanced EPR sensitivity from a ferroelectric cavity insert.

We report the development of a simple ferroelectric cavity insert that increases the electron paramagnetic resonance (EPR) sensitivity by an order of magnitude when a sample is placed within it. The insert is a hollow cylinder (length 4.8 mm, outside diameter 1.7 mm, inside diameter 0.6 mm) made from a single crystal of KTaO(3), which has a dielectric constant of 230 at X-band (9.5 GHz). Its outside dimensions were chosen to produce a resonant frequency in the X-band range, based on electromagnetic field modeling calculations. The insert increases the microwave magnetic field (H(1)) at the center of the insert by a factor of 7.4 when placed in an X-band TM(110) cavity. This increases the EPR signal for a small (volume 0.13 microL) unsaturated nitroxide spin label sample by a factor of 64 at constant microwave power, and by a factor of 9.8 at constant H(1). The insert does not significantly affect the cavity quality factor Q, indicating that this device simply redistributes the microwave fields within the cavity, focusing H(1) onto the sample inside the insert, thus increasing the filling factor. A similar signal enhancement is obtained in the TM(110) and TE(102) cavities, and when the insert is oriented either vertically (parallel to the microwave field) or horizontally (parallel to the DC magnetic field) in the TM(110) cavity. This order-of-magnitude sensitivity enhancement allows EPR spectroscopy to be performed in conventional high-Q cavities on small EPR samples previously only measurable in loop-gap or dielectric resonators. This is of particular importance for small samples of spin-labeled biomolecules.     

Dielectric resonator-based side-access probe for muscle fiber EPR study

We present a novel dielectric resonator (DR)-based resonant structure that accommodates aqueous sample capillaries in orientations that are either parallel (i.e., side-access) or perpendicular to the direction of an external (Zeeman) magnetic field, B(0). The resonant structure consists of two commercially available X-band DRs that are separated by a Rexolite spacer and resonate in the fundamental TE(01delta) mode. The separator between the DRs is used to tune the resonator to the desired frequency and, by appropriately drilled sample holes, to provide access for longitudinal samples, notably capillaries containing oriented, spin-labeled muscle fibers. In contrast to the topologically similar cylindrical TE(011) cavity, the DR-based structure has distinct microwave properties that favor its use for parallel orientation of lossy aqueous samples. For perpendicular orientation of a dilute (6.25 microM) aqueous solution of IASL spin label, the S/N ratio was at least one order of magnitude better for the side-access DR-based structure than for a standard TE(102) cavity. EPR spectra acquired for maleimide spin-labeled myosin filaments also revealed ca. 10 times better S/N ratio than those obtained with a standard TE(102) cavity. For the side-access DR with sample capillaries oriented either parallel or perpendicular to the external magnetic field, the Q- and filling factors are in good agreement with the theoretical estimates derived from the distribution of magnetic (H(1)) and electric (E(1)) components.     

Modes and Fields of Two Stacked Dielectric Resonators in a Cavity of an Electron Paramagnetic Resonance Probe

An electron paramagnetic resonance (EPR) probe consisting of two dielectric resonators (DRs) and a cavity (CV) is ideal for EPR experiments where both signal enhancement and tuning capabilities are required. The coupling of two DRs, resonating in their \({\text{TE}}_{01\delta }\) mode and a CV resonating in its \({\text{TE}}_{011}\) mode, is studied using energy-coupled mode theory (ECMT). The frequencies and eigenvectors of the three coupled modes are analytically derived. As predicted numerically, ECMT confirms that the \({\text{TE}}^{ + + - }\) and \({\text{TE}}^{ + - - }\) modes are indeed found to be degenerate at a specific distance between the two DRs \(d_{12}\). Additionally, the condition at which degeneracy occurs is specified. For a considerable range, the calculated frequency of the \({\text{TE}}^{ + + + }\) mode changes linearly with respect to \(d_{12}\). The \({\text{TE}}^{ + + + }\) mode showed a 500 MHz frequency change over a distance of 2 cm, when the resonance frequency is around 9.7 GHz. This enables the experimentalist to linearly tune the probe over this large frequency range. Finally the asymmetric configuration, where one of the resonators (DR2) is kept at the cavity center and the other one is allowed to move along the cavity axis, is studied. It is estimated that the frequency changes by 600 MHz over a distance of 1.5 cm. A formula for the magnitude of the magnetic field along the cavity axis, where the EPR samples are usually placed, is developed. This is crucial in determining the magnetic field in the vicinity of the sample and the probe’s filling factor.     

X波段脉冲电子顺磁共振谱仪的矩形腔与微型平面腔的设计

为了满足脉冲式电子顺磁共振谱仪的需要,设计并制作了连续波谐振腔和脉冲谐振腔. 连续波谐振腔采用矩形谐振腔的设计,而脉冲谐振腔采用了微型平面腔的设计. 在设计阶段,使用Ansoft-HFSS三维电磁仿真软件对2种谐振腔进行模拟计算. 微型平面腔的加工采用了微纳加工技术. 制作完成的谐振腔的参数指标由网络分析仪测定. 实验测得2种谐振腔的参数指标符合理论模拟值,并满足脉冲式电子顺磁共振谱仪的要求.     

用于高温射频超导量子干涉器的介质谐振器的性质研究

介质谐振器是目前高温射频超导量子干涉器较常采用的一种高品质因数微波谐振器.它是由10 mm×10 mm×1 mm的SrTiO₃(STO)标准衬底及覆盖在其上的YBa₂Cu₃O_7-δ(YBCO)薄膜磁通聚焦器共同构成的.为探明磁通聚焦器构形对介质谐振器谐振频率的影响,本文采用Ansoft公司出品的HFSS高频结构仿真软件对磁通聚焦器构形不同的若干介质谐振器的谐振特性进行了仿真.结果表明:增大磁通聚焦器开     

左手介质对谐振腔谐振频率的影响

在谐振腔设计过程中, 谐振腔的品质因数以及谐振频率都是需要考虑的关键因素. 传统的方法是通过减小谐振腔的尺寸或者利用高次模来提高谐振腔的谐振频率, 但是由于两种方法都有其局限性, 导致设计结果并不理想. 通过理论计算与模拟仿真相结合的方法, 对影响谐振腔谐振频率的因素进行分析, 得出了填充介质的材料属性与谐振腔谐振频率的关系. 理论计算显示: 当用“左手介质”作为谐振腔的填充物质时, 可以在不改变谐振腔尺寸的基础上提高谐振频率. 高频结构仿真器(high frequency structure simulator)的仿真数据也证明了以上结果, 从而得出谐振腔的谐振频率可以不受谐振腔尺寸的限制. 相较于传统理论而言, 研究结论有进一步的发展, 为探索和设计新颖的谐振腔提供了理论依据.     

基于宽度可调节的线缺陷平板型光子晶体的空气槽微腔

研究了一种空气槽光子晶体微腔,这种腔是由在平板型光子晶体上引入一条宽度可以调节的线缺陷空气槽形成的.腔模的电场被强烈局限在空气槽中,由于介电常量的不连续性,电场得到很大的提高,同时模体积被大大地降低.数值模拟与分析了微腔的能带结构和场分布,考虑到腔模的谐振频率和对称性,发现一阶偶膜同时具有较高的品质因子和较小的模体积;应用有限时域差分法,得到腔模的品质因子可以高达10⁶,模体积仅为0.02(λ/n)³.计算了一阶偶模谐振波长随空气槽宽度以及空气孔半径的变化,发现随着宽度的增加,波长越来越短.而随着空气孔半径的增加,波长近似线性地减小;当空气孔半径为170 nm时,可以获得最高的腔品质因子.     

基于宽度可调节的线缺陷平板型光子晶体的空气槽微腔

研究了一种空气槽光子晶体微腔,这种腔是由在平板型光子晶体上引入一条宽度可以调节的线缺陷空气槽形成的,腔模的电场被强烈局限在空气槽中,由于介电常量的不连续性,电场得到很大的提高,同时模体积被大大地降低.数值模拟与分析了微腔的能带结构和场分布,考虑到腔模的谐振频率和对称性,发现一阶偶膜同时具有较高的品质因子和较小的模体积;应用有限时域差分法,得到腔模的品质因子可以高达106,模体积仅为0.02(λ/n)3.计算了一阶偶模谐振波长随空气槽宽度以及空气孔半径的变化,发现随着宽度的增加,波长越来越短.而随着空气孔半径的增加,波长近似线性地减小;当空气孔半径为170 nm时,可以获得最高的腔品质因子.     

微波脉冲与带介质孔缝矩形腔体耦合的数值模拟研究

利用时域有限差分(FDTD)方法对微波脉冲与带介质孔缝矩形腔体的耦合过程进行了数值模拟研究. 如果孔缝填有介质, 则预期对微波耦合进入腔体的物理过程有重要影响, 研究了微波与带介质孔缝矩形腔体耦合的过程中影响介质孔缝耦合共振峰和共振频率点的因素, 包括孔缝长度、宽度和介质相对介电常数等物理量的影响. 通过大量不同孔缝尺寸的模拟研究, 发现孔缝的介质对孔缝耦合共振频率有明显影响, 我们对微波与带介质孔缝耦合发生共振的公式进行了拟合, 最后得出了微波脉冲与带介质孔缝矩形腔体耦合的共振条件.     

Design of MMICs employing whispering-gallery mode dielectric resonators at microwave and millimeter wave frequencies

A simple theoretical model for predicting the resonant frequencies of the modes of the whispering — gallery (WG) mode dielectric resonators MICs (Microwave Integrated Circuits) at microwave and millimetre wave frequencies is presented. The unsymmetric field distribution for WGE mode in the axial direction is taken into account. The theoretical results are found to be in good agreement with the practical results taken at microwaves C-X bands. In addition, the variation of resonant modes against dielectric resonator's dimensions and dielectric constant is modelled. The effect of the width of dielectric substrate on resonant modes is also illustrated.     

Broadband characteristics investigation of waves in a left-handed miniaturized waveguide loaded with ISRRs

In this paper, broadband transmission characteristics of waves in a left-handed miniaturised rectangular waveguide (LHMRW) loaded with improved split ring resonators (ISRRs), which shows that the bandwidth of negative permeability is up to 5.6 GHz by an optimization design, are investigated. Some unexpected phenomena such as the discontinuous left-handed passband below the cutoff frequency of the dominant TE mode, which cannot be transformed into a continuous one by any impedance matching approach, are observed. The EM field distributions in the LHMRW are calculated so as to explain these phenomena. Results show that the LHMRW can be considered as an open ended resonant cavity instead of a normal transmission structure. In addition, the backward wave inside the time domain in the LHMRW is directly observed. PACS 78.70.Gq; 81.05.Zx; 84.40.Ba     

Design of 57.5 MHz CW RFQ structure for the Rare Isotope Accelarator Facility

The Rare Isotope Accelerator (RIA) facility includes a driver LINAC for production of 400 kW CW heavy-ion beams. The initial acceleration of heavy ions delivered from an ECR ion source can be effectively performed by a 57.5 MHz 4 m long RFQ. The principal specifications of the RFQ are: (1) formation of extremely low longitudinal emittance: (2) stable operation over a wide range of voltage for acceleration of various ion species needed for RIA operation; (3) simultaneous acceleration of two-charge states of uranium ions. CW operation of an accelerating structure leads to a number of requirements for the resonators such as high shunt impedance, efficient water cooling of all parts of the resonant cavity, mechanical stability together with precise alignment, reliable rf contacts, a stable operating mode and fine tuning of the resonant frequency during operation. To satisfy these requirements a new resonant structure has been developed. This paper discusses beam dynamics and electrodynamics design of the RFQ cavity, as well as, some aspects of the mechanical design of this low-frequency CW RFQ.     

A tunable general purpose Q-band resonator for CW and pulse EPR/ENDOR experiments with large sample access and optical excitation

We describe a frequency tunable Q-band cavity (34 GHz) designed for CW and pulse Electron Paramagnetic Resonance (EPR) as well as Electron Nuclear Double Resonance (ENDOR) and Electron Electron Double Resonance (ELDOR) experiments. The TE(011) cylindrical resonator is machined either from brass or from graphite (which is subsequently gold plated), to improve the penetration of the 100 kHz field modulation signal. The (self-supporting) ENDOR coil consists of four 0.8mm silver posts at 2.67 mm distance from the cavity center axis, penetrating through the plunger heads. It is very robust and immune to mechanical vibrations. The coil is electrically shielded to enable CW ENDOR experiments with high RF power (500 W). The top plunger of the cavity is movable and allows a frequency tuning of ±2 GHz. In our setup the standard operation frequency is 34.0 GHz. The microwaves are coupled into the resonator through an iris in the cylinder wall and matching is accomplished by a sliding short in the coupling waveguide. Optical excitation of the sample is enabled through slits in the cavity wall (transmission ～60%). The resonator accepts 3mm o.d. sample tubes. This leads to a favorable sensitivity especially for pulse EPR experiments of low concentration biological samples. The probehead dimensions are compatible with that of Bruker flexline Q-band resonators and it fits perfectly into an Oxford CF935 Helium flow cryostat (4-300 K). It is demonstrated that, due to the relatively large active sample volume (20-30 μl), the described resonator has superior concentration sensitivity as compared to commercial pulse Q-band resonators. The quality factor (Q(L)) of the resonator can be varied between 2600 (critical coupling) and 1300 (over-coupling). The shortest achieved π/2-pulse durations are 20 ns using a 3 W microwave amplifier. ENDOR (RF) π-pulses of 20 μs ((1)H @ 51 MHz) were obtained for a 300 W amplifier and 7 μs using a 2500 W amplifier. Selected applications of the resonator are presented.     

Dielectric resonator-based resonant structure for sensitive ESR measurements at high-hydrostatic pressures

We present a newly developed microwave probe head that accommodates a gasketed sapphire anvil cell (SAC) for performing sensitive electron spin resonance (ESR) measurements under high-hydrostatic pressures. The system was designed around commercially available dielectric resonators (DRs) having the dielectric permittivity of approximately 30. The microwave resonant structure operates in a wide-stretched double-stacked geometry and resonates in the lowest cylindrical quasi TE(011) mode around 9.2 GHz. The most vital parts of the probe's microwave heart were made of plastic materials, thus making the resonant structure transparent to magnetic field modulation at 100 kHz. The overall ESR sensitivity of the probe was demonstrated for a small speck of 2,2-diphenyl-1-picrylhydrazyl radical (DPPH) positioned in the gasket of the SAC, using water as the pressure-transmitting medium. The system was also used for studying pressure-induced changes in spin-relaxation mechanisms of a quasi-1D-conducting polymer, K(1)C(60). For small samples located in the sample hole of the gasket the probe reveals sensitivity that is only approximately 3 times less than that yielded by regular ESR cavities.     

回旋管光子带隙谐振腔冷腔电磁模式分析

利用二维三角格子金属光子带隙谐振腔代替回旋管的传统柱形谐振腔,并对腔体进行了TE波模式的计算与分析.综合考虑腔体内外的结构特征,给出了光子带隙谐振腔冷腔模式理论的研究方法,发现腔内存在单模工作的可能与条件以及非角对称情况下的电磁模式分布特征.研究结果表明,利用光子带隙谐振腔代替回旋管的传统腔体,可使回旋管在不受腔体横向尺度限制的条件下实现单模工作.这对于提高回旋管的功率容量、有效实现高次单模与高次回旋谐波耦合条件下的注-波互作用、降低工作磁场并从物理上根本改变回旋管的工作状态提供了理论依据. 关键词： 回旋管 金属光子带隙 谐振腔     

铁电薄膜可调带通滤波器

铁电薄膜的介电常数随外加电场强度的增加而减小.依据铁电薄膜的这一特性,提出了一种新颖的基于共面传输线结构的铁电薄膜可调带通滤波器.为了减小传输损耗,滤波器的导体部分由超导薄膜构成.滤波器的输入输出采用抽头线的方式分别与谐振器相接,外加电压通过输入输出端口直接施加到共面谐振器缝隙处的铁电薄膜上,用以改变铁电薄膜的介电常数,从而改变谐振器的谐振频率,实现带通滤波器通带频率的移动.这种新型可调带通滤波器具有结构紧凑、尺寸小及施加外加偏压容易等优点.仿真结果表明:铁电薄膜的介电常数在外加偏压下从250减小到150时,带通滤波器的传输特性曲线的形状基本保持不变,通带的中心频率从10.283GHz增加到10.518GHz,其3dB带宽保持在0.150GHz左右,反射损耗始终小于-17dB.     

Aqueous sample in an EPR cavity: sensitivity considerations

The radial mode matching (RMM) method has been used to calculate accurately the microwave field distribution of the TE(011) mode in a spherical EPR cavity containing a linear aqueous sample, in order to understand in detail the factors affecting sensitivity in EPR measurements at X band. Specific details of the experiment were included in the calculations, such as the cavity geometry, the presence of a quartz dewar, the size of the aqueous sample, and the sample's dielectric properties. From the field distribution, several key physical parameters were calculated, including cavity Q, filling factor, mean microwave magnetic field at the sample, and cavity efficiency parameter Lambda. The dependence of EPR signal intensity on sample diameter for a cylindrical aqueous sample was calculated and measured experimentally for non-saturated and half-saturated samples. The optimal aqueous sample diameter was determined for both cases. The impact of sample temperature, conductivity, and cavity Q on sensitivity of EPR is discussed.     

An advanced EPR stopped-flow apparatus based on a dielectric ring resonator

A novel EPR stopped-flow accessory is described which allows time-dependent cw-EPR measurements of rate constants of reactions involving paramagnetic species after rapid mixing of two liquid reagents. The EPR stopped-flow design represents a state-of-the-art, computer controlled fluid driving system, a miniresonant EPR structure with an integrated small ball mixer, and a stopping valve. The X-band EPR detection system is an improved version of that reported by Sienkiewicz et al. [Rev. Sci. Instr. 65 (1994) 68], and utilizes a resonator with two stacked ceramic dielectric rings separated by a variable spacer. The resonator with the mode TE(H)011 is tailored particularly for conditions of fast flowing and rapidly stopped aqueous solutions, and for a high time resolution. The short distance between the ball mixer and the small EPR active volume (1.8 microl) yields a measured dead time of 330 micros. A compact assembly of all parts results in minimization of disturbing microphonics. The computer controlled driving system from BioLogic with two independent stepping motors was optimized for EPR stopped-flow with a hard-stop valve. Performance tests on the EPR spectrometer ESP 300E from BRUKER using redox reactions of nitroxide radicals revealed the EPR stopped-flow accessory as an advanced, versatile, and reliable instrument with high reproducibility.     

腔壁弹性对水下小型圆柱形亥姆霍兹共振器共振频率的影响

理论和实验研究了腔壁弹性对水下小型圆柱形亥姆霍兹共振器共振频率的影响.基于电-声类比理论,建立了小型共振器的简化模型,利用电路分析方法得到了便于计算的共振频率一般表达式.分别仿真分析了共振器壁面厚度和材料对共振频率的影响,得到了不同尺寸的小型共振器的近似刚性条件.在充水驻波罐中对不同壁厚、不同材料的小型圆柱形亥姆霍兹共振器的共振频率进行了测量,实验结果较好地验证了理论分析和近似刚性条件的正确性.所得结果对小型圆柱形亥姆霍兹共振器的设计和水下应用具有较好的参考价值. 关键词： 亥姆霍兹共振器 共振频率 传递函数 辐射阻抗