High performance distributed Bragg reflector microwave resonator

A new resonator device structure is described that achieves Q-factors well above those currently realizable for conventional room temperature microwave structures. The new structure consists of a microwave cavity, for which the enclosure walls consist of distributed Bragg reflectors (DBR) made of low-loss sapphire. For this configuration, most of the resonant field resides in empty space, with small field strengths in the thin layers of sapphire which comprise the DBR structure. The physical structure takes the form of interpenetrating concentric rings and plates of low-loss sapphire contained in a cylindrical metal enclosure. The theoretical analysis of the DBR resonant structure allows the positions and dimensions of the component rings and plates to be precisely determined for a specified resonant frequency. The resonator Q can be accurately calculated, and plots of the resonant fields clearly show the physical mechanism leading to the observed efficiency of this resonator structure. Experimental results are given for resonators designed at 9.0 and 13.2 GHz. The measured unloaded Q's at room temperature are over 650000 and 450000, respectively.     

Distributed bragg reflector resonators with cylindrical symmetry and extremely high Q-factors

A simple non-Maxwellian method is presented that allows the approximate solution of all the dimensions of a multilayered dielectric TE0qp mode cylindrical resonant cavity that constitutes a distributed Bragg reflection (DBR) resonator. The analysis considers an arbitrary number of alternating dielectric and free-space layers of cylindrical geometry enclosed by a metal cylinder. The layers may be arranged along the axial direction, the radial direction, or both. Given only the aspect ratio of the cavity, the desired frequency and the dielectric constants of the material layers, the relevant dimensions are determined from only a set of simultaneous equations, and iterative techniques are not required. The formulas were verified using rigorous method of lines (MoL) calculations and previously published experimental work. We show that the simple approximation gives dimensions close to the values of the optimum Bragg reflection condition determined by the rigorous analysis. The resulting solution is more compact with a higher Q-factor when compared to other reported cylindrical DBR structures. This is because it properly takes into account the effect of the aspect ratio on the Bragg antiresonance condition along the z-axis of the resonator. Previous analyses assumed the propagation in the z-direction was independent of the aspect ratio, and the layers of the Bragg reflector were a quarter of a wavelength thick along the z-direction. When the aspect ratio is properly taken into account, we show that the thickness of the Bragg reflectors are equivalent to the thickness of plane wave Bragg reflectors (or quarter wavelength plates). Thus it turns out that the sizes of the reflectors are related to the free-space propagation constant rather than the propagation constant in the z-direction.     

Microwave oscillators incorporating high performance distributed Bragg reflector microwave resonators

We previously demonstrated a new resonator device structure that achieves Q-factors well above those currently realisable. The new structure consists of a microwave cavity, where the enclosure walls consist of distributed Bragg reflectors (DBRs) in three dimensions, made of low-loss sapphire. Theoretical analysis has demonstrated that the resonator's performance is critically dependent upon accurate alignment of the DBR components, thereby maintaining the desired symmetry of the resonant structure. Breaking of the symmetry causes mixing of the high performance Bragg reflected mode with low-Q hybrid cavity modes. The fabrication tolerances required to achieve the expected resonator performance are met with a precise but simple alignment tool. A pair of these resonators have been built at 9.0 GHz, and have demonstrated unloaded Qs in excess of 700,000 at room temperature. These resonators are incorporated into simple two-port feedback oscillator circuits. Phase noise measurements were performed on the two free-running oscillators.     

High Q-factor distributed bragg reflector resonators with reflectors of arbitrary thickness

The Bragg reflection technique improves the Q-factor of a resonator by reducing conductor and dielectric losses. This is achieved by designing a low-loss inner resonant region (usually free space) surrounded by an outer anti-resonant region made of distributed Bragg reflector layers. In this paper we develop a simple non-Maxwellian model and apply it to design three distinct cylindrical Bragg resonators based on the same set of single-crystal sapphire plates and rings by changing only the dimension of the cavity that supports the structure. To accomplish this, the simple model allows an arbitrary thickness for either the horizontal or the cylindrical dielectric reflectors by relaxing the condition that they must be lambda/4 thick. The model also allows for higher-order field variations in both the resonant and the anti-resonant regions. The resonators were constructed and experimental results were compared with the simple model and the rigorous method of lines analysis. For the fundamental mode, an unloaded Q-factor of 234,000 at 9.7 GHz was obtained. This is larger than that for a whispering gallery mode resonator. The resonator also exhibited a greatly reduced spurious mode density when compared to an overmoded whispering gallery mode resonator.     

The AlN based solidly mounted resonators consisted of the all-metal conductive acoustic Bragg reflectors

The AlN based solidly mounted resonators utilizing the all-metal conductive Bragg reflectors have been demonstrated. The devices with different reflectors of Mo/Ti, W/Ti and AlN/Mo pairs have been fabricated and the frequency responses have been compared. The bottom electrode is incorporated into the conductive Bragg reflector, thereby reducing the parasitic resistance and the damping of the acoustic energy. The experimental results reveal that Mo/Ti and W/Ti reflectors exhibit excellent properties of frequency selection and clamping the acoustic wave. The devices show the distinct resonant phenomenon near 2.4 GHz with the excellent suppression of the shear mode and the sidelobe mode. Compared to the conventional device consisted of AlN/Mo reflector, the devices consisted of the conductive reflectors demonstrate the higher resonance frequency and obviously improved performance.     

Influence of surface roughness of Bragg reflectors on resonance characteristics of solidly-mounted resonators

The solidly mounted resonator (SMR) is fabricated using planar processes from a piezoelectric layer sandwiched between two electrodes upon Bragg reflectors, which then are attached to a substrate. To transform the effective acoustic impedance of the substrate to a near zero value, the Bragg reflectors are composed of alternating high and low acoustic impedance layers of quarter-wavelength thickness. This paper presents the influence of Bragg reflector surface roughness on the resonance characteristics of an SMR. Originally, an A1N/A1 multilayer is used as the Bragg reflector. The poor surface roughness of this Bragg reflector results in a poor SMR frequency response. To improve the surface roughness of Bragg reflectors, a molybdenum (Mo)/titanium (Ti) multilayer with a similar coefficient of thermal expansion is adopted. By controlling deposition parameters, the surface roughness of the Bragg reflector is improved, and better resonance characteristics of SMR are obtained.     

Theory of quarter-wave-stack dielectric mirrors used in a thin fabry-perot filter

I present a new derivation of the analytic form for the phase shift near resonance and the optical penetration length upon reflection from a distributed dielectric mirror consisting of a quarter-wave stack. The requirement of proper termination to achieve high reflectivity is suspended to investigate large optical penetration depths. Separate equations, derived for N and N + 1/2 layer pairs, are convenient for the design of tunable Fabry-Perot filters with a specified tuning range. The analysis is also applicable to distributed Bragg reflectors, vertical-cavity surface-emitting lasers, and resonant photodiodes. I show that the penetration length can sharply reduce the overly broad free spectral range of an ultrathin Fabry-Perot filter that might be useful in applications such as tunable wavelength filters for wavelength division multiplexing applications. The results also demonstrate regimes of zero dispersion and of superluminal reflection in the dielectric mirrors, which are of particular interest in photonic bandgap structures.     

Planar free-electron lasers with combined 1D/2D Bragg mirror resonators: A theoretical study

The operation of a free-electron laser with a combined Bragg mirror resonator is studied theoretically. The resonator comprises a pair of planar Bragg reflectors with a two-and a one-dimensional relief pattern, respectively, and is closed in the transverse direction so as to ensure unidirectional outcoupling. It is demonstrated that this design provides for a possibility of obtaining spatially coherent radiation from a sheet electron stream with the cross size exceeding the wavelength by several orders of magnitude.     

Generation of powerful narrow-band 75-GHz radiation in a free-electron maser with two-dimensional distributed feedback

A planar generator based on a free-electron maser (FEM generator) is developed employing a relativistic sheet electron beam (0.8 MeV/1 kA/4 μs) formed by an ELMI accelerator. A hybrid two-mirror resonator consisting of a two-dimensional upstream and a one-dimensional downstream Bragg reflectors is used as the electrodynamic system. The use of two-dimensional distributed feedback implemented in the upstream Bragg structure has made it possible to achieve stable well reproducible single mode generation regime with transverse dimensions of the system of ～25 × 2.5 wavelengths. Experiments carried out at a frequency of 75 GHz have yielded narrow-band radiation with spectrum width of ～20 MHz in pulses with a duration of ～100–200 ns and power of 30–50 MW.     

SAW impedance elements

In the past few years a new class of SAW devices has been under development based on the use of one port SAW resonators as lumped elements with their impedance strongly changing in a frequency range of effective SAW excitation. These `SAW impedance elements' can be connected in ladder type, balanced bridge type, or others types of networks to provide desired filter characteristics. In this paper the admittance characteristics of a single element are analyzed using coupling of mode (COM) model simulations. It is found that resonant type characteristics of a long transducer can be described by very simple formulas. The frequency gap between resonance and anti-resonance, important for filter design, is determined practically by the ΔV/V parameter of the piezoelectric substrate used, while the minimum magnitude of the impedance at the resonant frequency is determined by the SAW attenuation. The internal reflections only shift the resonance to the left edge of the stopband not changing other characteristics. A case of a synchronous resonator comprising a relatively short transducer and two reflectors placed on both sides of it is also analyzed. This type of impedance element has smaller frequency shift between resonance and anti-resonance points     

共振型进气消声器腔体尺寸对其共振频率影响研究

亥姆赫兹共振腔结构简单,且有良好的低频消声性能,近几年来广泛地应用于发动机进排气消声上.由于其消声有效带宽很窄,共振频率的精确确定直接关系到消声器能否有效消声,但是通常所采用的集中参数模型有时候会失效.建立了共振腔型消声器一维轴向声传播模型,揭示了圆形旁支型共振进气消声器的消声机理.同时对连接管长度的修正问题做了阐述,得出了共振腔一维轴向传播模型共振频率的计算公式.此外,设计了发动机进气消声器性能测试专用实验台,从实验角度研究了共振频率与腔体尺寸之间的关系.撰写为正确设计亥姆赫兹共振腔型进气消声器提供一个重要方法.     

以四面体非晶碳为布拉格反射栅高声阻抗材料的固贴式薄膜体声波谐振器性能仿真分析

为了提高固贴式薄膜体声波谐振器(SMR)的电学和声学品质,实现四面体非晶碳(ta-C)在体声波器件领域的新应用,建立了以ta-C为布拉格反射栅高声阻抗材料的SMR模型,利用MathCAD仿真研究布拉格反射栅层数对该SMR的谐振特性的影响以及ta-C中sp3杂化含量和高/低声阻抗层厚度偏差对SMR的品质因子(Q值)的影响。结果表明层数的增加提高了SMR的品质;ta-C薄膜sp3杂化含量越高,达到饱和Q值所需层数越少,当含量为80%时,至少需要6层(3对)布拉格反射层使SMR达到优异Q值;距离压电堆越近的高/低声阻抗层,其厚度偏差对Q值的影响越大,从而实现了高频率(8GHz)低损耗的SMR的设计。     

Narrowband electrooptic tunable notch filter

We describe the theory of a narrowband electrooptic tunable filter based on a Fabry-Perot etalon with distributed Bragg reflectors. The filter can be in either bulk or waveguide form. The input to the filter must be prefiltered to the stop-band of the Bragg mirrors. Once this is accomplished, the etalon possesses a very narrow notch in the Bragg filter stop-band. The notch width is extremely narrow when the Bragg reflectance is high. The location of the notch in the Bragg stop-band is determined by the etalon cavity length and can be tuned by application of an electric field to the electrooptic material comprising the etalon cavity. Absorption in the cavity and Bragg reflectors is included in the theoretical model of the filter. The filter can be constructed from any one of several existing electrooptic organic polymer crystals, if the gratings are made either by partial polymerization of the monomer in crossed-UV beams or by corrugating the surface of the polymer. We show a theoretical example of a notch filter operating at a center wavelength of 1 microm that is 62.75 microm thick, with a notch width of under 1 A and a transmission of 35%. This type of filter should have applications in high-speed optical modulation and Q-switches for lasers.     

矩形共振腔截面纵横比对其共振频率影响研究

亥姆赫兹共振腔具有良好的低频消声性能,被广泛地应用于低频消声方面.在实际应用中,共振腔的使用往往受到安装空间的限制,有时候只能安装矩形腔.利用定体积定长度时的矩形共振腔模型,从理论上探讨了腔体纵横比对共振腔共振频率的影响.同时设计了发动机进气消声器性能测试专用实验台,从实验角度研究了腔体截面纵横比与共振频率之间的关系.理论与实验初步结果表明,在算例条件下截面纵横比对共振频率影响不大,在应用时可以不考虑纵横比问题.所讨论内容对其它条件下的研究有借鉴作用.     

Designs of a microwave TE011 mode cavity for a space borne H-maser.

Method of Lines and Finite Element Analysis investigations have been performed to optimize parameters in a TE011 mode cavity resonator suitable for a spaceborne hydrogen maser. We report on designs that were explored to find a global maximum in the important design parameters for the microwave cavity used in a hydrogen maser. The criteria sought in this exercise were both the minimization of the total volume of the cavity and the maximization of the product of the z-component of the magnetic energy filling factor and the cavity TE011 mode Q-factor (Q.eta). Different configurations were studied. They were a sapphire tube in a copper cylinder, a sapphire tube in a copper cylinder with Bragg reflectors, and spherical copper cavities both empty and sapphire-lined on the inside cavity surface. At 320 K, the simulations resulted in an optimum product Q.eta = 4.9 x 10(4), with an inner cavity radius of 80 mm and unity aspect ratio. This represents a 54% improvement over an earlier design. The expected increase in the product Q . eta) with the inclusion of Bragg reflectors to the sapphire tube was not achieved. Moreover, the z-component of the magnetic energy filling factor was greatly reduced due to an increase in the radial magnetic field. The sapphire-lined spherical cavity showed no better performance than an equivalent-sized empty copper spherical cavity. For the empty cavity the simulations resulted in the product Q.eta = 4.4 x 10(4). The empty spherical cavity resonator is not suitable for the spaceborne hydrogen maser as the total volume in this case is 33% larger than that of the optimized sapphire tube resonator.     

Compact, high-Q, zero temperature coefficient, TE011 sapphire-rutile microwave distributed Bragg reflector resonators

Some novel new resonator designs based on the distributed Bragg reflector are presented. The resonators implement a TE₀₁₁ resonance in a cylindrical sapphire dielectric, which is confined by the addition of rutile and sapphire dielectric reflectors at the end faces. Finite element calculations are utilized to optimize the dimensions to obtain the highest Q-factors and zero frequency-temperature coefficient for a resonator operating near 0°C. We show that a Q-factor of 70,000 and 65,000 can be achieved with and without the condition of zero frequency-temperature coefficients, respectively     

A SAW resonator with two-dimensional reflectors

It is known that a part of the loss of leaky SAW resonators is due to radiation of acoustic energy in the bus-bars. Many researchers are working on so-called phononic crystals. A 2-D grating of very strong reflectors allows these devices to fully reflect, for a given frequency band, any incoming wave. A new device based on the superposition of a regular SAW resonator and a 2-D periodic grating of reflectors is proposed. Several arrangements and geometries of the reflectors were studied and compared experimentally on 48° rotated Y-cut lithium tantalate. In particular, a very narrow aperture (7.5 ?) resonator was manufactured in the 900 MHz range. Because of its small size, this resonator has a resonance Q of only 575 when using the standard technology, whereas a resonance Q of 1100 was obtained for the new device without degradation of the other characteristics. Because of the narrow aperture, the admittance of the standard resonator showed a very strong parasitic above the resonance frequency, whereas this effect is drastically reduced for the new device. These results demonstrate the feasibility of the new approach.     

Design and properties of STW asynchronous resonators on quartz

In a surface transverse wave (STW) asynchronous resonator, grating phase shifters are placed between interdigital transducers and reflectors to obtain the incident and reflected waves in phase, and the resonance frequency is located near the center frequency of the reflectors. In this paper, the scattering matrix method is used for design of such resonators with one dominant longitudinal mode. At a frequency of about 509.5 MHz, insertion loss, and loaded and unloaded quality factors of about 6 dB, 5,300 and 11,000, respectively, were obtained. The measured and calculated parameters of this resonator are in good agreement. Design guidelines and comparison of synchronous and asynchronous resonators are presented. Compared to synchronous resonators, low spurious signals' level, location of the resonance frequency near the center frequency of the reflectors, and simple design method make the asynchronous resonators more attractive for manufacture and practical applications.     

Frequency-temperature compensation of piezoelectric resonators by electric DC bias field

Electromechanical resonators have been widely used in signal processing and frequency control applications. It has been found that the resonant frequency of most resonator devices is highly temperature dependent, as temperature variation leads to materials properties change as well as resonator dimension change, which result in the undesirable shift of the resonance frequency. In this paper, we present a new frequency tuning method in which direct current (DC) bias field is used to control the resonance frequency of the piezoelectric resonator that is subjected to ambient temperature variations. It has been found that, depending on the polarity, the application of a DC bias field can reduce or increase the resonance frequency of the resonator. The experimental results demonstrate that the DC bias field tuning can achieve fairly good temperature compensation within a certain temperature range, and that the mechanical Q factor of the resonator is quite stable under different DC bias fields.     

Ellipsometric determination of polarization-dependent transmission in resonant feedback systems

The polarization-dependent transmission of a basic anisotropic feedback system (Fabry-Perot resonator) is mathematically modeled by means of the Jones-matrix formalism. Detailed numerical simulations of the resonance case are performed. Small phase anisotropies as well as small polarization-dependent losses of the resonator components can be extremely amplified by resonant feedback. The amplification factors depend on the magnitudes of amplitude and phase anisotropy and their mutual interactions as well as on the polarization-independent system parameters (forward transmission, system feedback). However, for higher phase anisotropies, saturation effects occur and, therefore, the anisotropy amplification factors decrease. Our experimental investigations applying anisotropic Fabry-Perot resonators in different ellipsometer systems confirm the predicted amplification of phase and loss anisotropies in resonance operation.