Mode Coupling and Vertical Radiation Loss for Whispering-Gallery Modes in 3-D Microcavities

The characteristics of whispering-gallery modes (WGMs) in 3-D cylindrical, square, and triangular microcavities with vertical optical confinement of semiconductors are numerically investigated by the finite-difference time-domain (FDTD) technique. For a microcylinder with a vertical refractive index 3.17/3.4/3.17 and a center layer thickness 0.2 mum, Q-factors of transverse electric (TE) WGMs around wavelength 1550 nm are smaller than 10³, as the radius R < 4 mum and reach the orders of 10⁴ and 10⁶ as R = 5 and 6 mum, respectively. However, the Q-factor of transverse magnetic (TM) WGMs at wavelength 1.659 mum reaches 7.5 times 10⁵ as R = 1 mum. The mode coupling between the WGMs and vertical radiation modes in the cladding layer results in vertical radiation loss for the WGMs. In the microcylinder, the mode wavelength of TM WGM is larger than the cutoff wavelength of the vertical radiation mode with the same mode numbers, so TM WGMs cannot couple with the vertical radiation mode and have high Q -factor. In contrast, TE WGMs can couple with the corresponding vertical radiation mode in the 3-D microcylinder as R < 5 mum. However, the mode wavelength of the TE WGM approaches (is larger than) the cutoff wavelength of the corresponding radiation modes at R = 5 mum (6 mum), so TE WGMs have high Q-factors in such microcylinders too. The results show that a critical lateral size is required for obtaining high Q-factor TE WGMs in the 3-D microcylinder. For 3-D square and triangular microcavities, we also find that the Q-factor of TM WGM is larger than that of TE WGM.     

Comparison of Mode Quality Factors for Equilateral Triangular,Square and Rhombus Optical Micro-Resonators

采用时域有限差分和Padé近似计算了等边三角形、正方形和平行四边形微谐振腔的模式频率和品质因子．数值结果表明等边三角形谐振腔中的谐振模式具有较高的品质因子,这主要是由于等边三角形谐振腔中的模式在横向上得到了完全的限制,而在其它两种谐振腔中,模式在横向上只是得到部分限制．对于边长为4μm,折射率为3.2的等边三角形谐振腔,发现在1.55μm波长处的模式品质因子可达5.5×103．     

Analysis of semiconductor microlasers with an equilateral triangleresonator by rate equations

Semiconductor microlasers with an equilateral triangle resonator (ETR) are analyzed by rate equations with the mode lifetimes calculated by the finite-difference time-domain technique and the Pade approximation. A gain spectrum based on the relation of the gain spectrum and the spontaneous emission spectrum is proposed for considering the mode selection in a wide wavelength span. For an ETR microlaser with a side length of about 5 μm, we find that single fundamental mode operation at about 1.55 μm can be obtained as the side length increases from 4.75 to 5.05 μm. The corresponding wavelength tuning range is 93 nm, and the threshold current is about 0.1 to 0.4 mA     

Equilateral-Triangle-Resonator Injection Lasers With Directional Emission

Equilateral-triangle-resonator (ETR) lasers with an output waveguide jointed at one vertex of the resonator are fabricated on (100) GaInAsP-InP wafers using photolithography and a two-step inductively coupled plasma (ICP) etching technique. Distinct peaks with the mode spacing of longitudinal mode intervals are observed in the luminescence spectra at room temperature. Furthermore, some minor peaks appear in the middle of the main peaks, which can be attributed to the first-order transverse modes as predicted in the theoretical results. CW directional lasing emissions are achieved for ETR lasers with side lengths ranging from 15 to 30 mum up to 200 K. The temperature dependences of the threshold current and lasing wavelength are measured for an ETR laser with the side length of 20 mum from 80 to 200 K. The observed threshold current rapidly increases as temperature increases over 170 K     

Analysis and numerical simulation of eigenmode characteristics forsemiconductor lasers with an equilateral triangle micro-resonator

The eigenmodes confined in the equilateral triangle resonator (ETR) are analyzed by deriving the eigenvalues and the mode field distributions and by the finite difference time domain (FDTD) technique. The analytical results show that the one-period-length for the mode light rays inside the ETR is the perimeter of the ETR, and the number of transverse modes is limited by the condition of total internal reflection. In addition, the sum of the longitudinal mode index and the transverse mode index should be an even number, which limits the number of confined modes again. Based on the FDTD technique and the Pade approximation, we calculate the mode resonant frequencies and the quality factors from the local maximum and the width of the spectral distribution of the intensity. The numerical results of mode frequencies agree very well with the analytical results, and the quality factor of the fundamental mode is usually higher than that of the higher order transverse modes. The results show that the ETR is suitable to realize single-mode operation as semiconductor microcavity lasers     

Radiation from Bends in Dielectric Rod Transmission Lines

The radiation from the fundamental mode propagating around curved dielectric rod transmission lines is investigated experimentally with microwave frequencies. Three methods are used to determine the attenuation by radiation: measuring the insertion loss of bends, measuring the Q-factor of ring resonators, and measuring the Q-factor of sections of curved dielectric rod transmission lines terminated by large reflecting plates. The attenuation is found to depend mainly on the combination R lambda/sub 0//sup 2/ / r/sub 0//sup 3/ where R is the radius of curvature, lambda/sub 0/ the free space wavelength and r/sub 0/ a measure of the transverse field extent of the HE/sub 11/ mode. The experimental results are compared with theoretical predictions of other authors. The measured values of the attenuation constant are found to be smaller than the theoretical values. The distribution of the electromagnetic field near bends is recorded using a semiautomatic field plotter. From the field pictures, it can be concluded that the curved dielectric waveguide radiates tangentially from the outer side. The results presented will also be useful for understanding the mechanism of radiation from bent optical waveguides.     

存在干扰模式时的微波谐振器Q值计算方法北大核心CSCD

谐振法测量介质介电常数时需要计算谐振器的无载Q值。当微波谐振器的工作模式受干扰模式影响时,会导致无载Q值的计算出现偏差。文章针对这种情况提出了一种存在干扰模式时计算微波谐振器无载Q值的迭代算法。该方法基于所提出的反向叠加和同相叠加两种等效电路模型,以传输系数模值平方之差在所有频点的平方之和作为目标函数,采用尺度变换最速下降法进行迭代。将圆柱形金属谐振腔的高Q值TE011模作为工作模式、简并的低Q值TM111模作为干扰模式,通过仿真和实测对该方法进行了验证。实测结果表明,当干扰模式较强时,3 dB法计算的工作模式Q值偏离真值14%,而所提出的迭代法的计算结果偏离真值不到1%。     

Mode Analysis and Q-Factor Enhancement Due to Mode Coupling in Rectangular Resonators

Modes in rectangular resonators are analyzed and classified according to symmetry properties, and quality factor (Q-factor) enhancement due to mode coupling is observed. In the analysis, mode numbers p and q are used to denote the number of wave nodes in the direction of two orthogonal sides. The even and odd mode numbers correspond to symmetric and antisymmetric field distribution relative to the midlines of sides, respectively. Thus, the modes in a rectangle resonator can be divided into four classes according to the parity of p and q. Mode coupling between modes of different classes is forbidden; however, anti-crossing mode coupling between the modes in the same class exists and results in new modes due to the combination of the coupled modes. One of the combined modes has very low power loss and high Q-factor based on far-field emission of the analytical field distribution, which agrees well with the numerical results of the finite-difference time-domain (FDTD) simulation. Both the analytical and FDTD results show that the Q-factors of the high Q-factor combined modes are over one order larger than those of the original modes. Furthermore, the general condition required to achieve high-Q modes in the rectangular resonator is given based on the analytical solution     

基于光子晶体渐变型双异构微腔的掺铒硅光致发光研究

实验验证了室温下二维氧化物下包层非对称平板三角晶格光子晶体渐变型双异构微腔对绝缘体上硅(SOI)基片上铒氧共掺硅材料的显著发光增强作用.在波长为488 nm、功率为15 mW激光激发下,微腔的光致发光(PL)谱呈现出一个位于1 557.93 nm通信波长处的尖锐狭窄的发光峰,相比于无光子晶体区域,发光增强了约13倍.谐振峰随光泵浦功率增加,发生明显的红移,Q值逐渐下降,在1.5mW光泵浦功率下,Q值达6 655.微腔谐振波长与光子晶体晶格周期之间呈线性正比关系,通过调整晶格周期,实现了掺铒硅发光增强峰波长的灵活可控.     

Quality factor measurement of micro gyroscope structure according to vacuum level and desired Q-factor range package method

A micro-machined gyro chip of gyroscope is normally packaged in specific vacuum level to get the specific quality factor(Q-factor). If the Q-factor is too high, frequency tuning and the approximate matching between driving and sensing comb structure become difficult, and if the Q-factor is too low, its sensitivity decreases. The optimum Q-factor of our gyro chip design is 4000 range. To get this range, we measured the drive mode Q-factor as vacuum level of our gyro chip and we found that the vacuum level of the desired Q-factor 4000 is in the range of 740 mTorr. Based on this data, we fabricate the wafer level package gyro chip of the desired Q-factor by controlled the basic pressure of package bonding chamber just prior to the bonding process. After wafer level package process, we measured Q-factor of whole samples. Among 804 samples, 502 packaged gyro chips are worked and the Q-factor of 67% samples is between 3500 and 4500 range.     

Optimization of directivity and signal-to-noise ratio of an arbitrary antenna array

In this paper, a unified formulation is made for the optimization of directivity and signal-to-noise ratio of an arbitrary array, with or without a constraint on the array Q-factor. When there is a constraint, the solution is reduced to that of a polynomial; when there is no constraint, the solution is given in a very simple form. First, it is shown that for a given array geometry there exists a finite permissible range of the Q-factor and this range reduces to zero for large spacings. Second, a detailed comparison between four well-known excitations (uniform, Hansen-Woodyard, optimum cophasal, and optimum) is made and the main results are as follows, 1) The Hansen-Woodyard excitation yields a directivity higher than that of the uniform only when the element spacing is somewhat smaller than a half wavelength (λ/2), but at the price of much higher Q. On the other hand, it is much lower than that of the optimum excitation. 2) For spacing less than λ/2, the optimum excitation is strongly tapered toward the ends of the array and approximately antiphasa (i.e., 0, 180° 0, 180°, ...); whereas for spacing greater than or equal to λ/2, it is nearly uniform and cophasal. 3) For large spacings, the directivity of uniform excitation is nearly optimum. For small spacings, the optimum directivity becomes much higher than all others, but is always associated with an enormously large Q-factor. Therefore in this case a constraint of the Q-factor is important. 4) Hansen-Woodyard and uniform arrays have the interesting property that their sensitivity factors are independent of spacing. The optimization of signal-to-noise ratio is also demonstrated. In particular, the result shows that although an improvement in gain over the uniform excitation is very difficult to realize in practice, a substantial improvement in signal-to-noise ratio is entirely practical. Other numerical results and some extensions of the theory to aperture antennas are also included.     

Mode characteristics of semiconductor equilateral triangle microcavities with side length of 5-20 /spl mu/m

Semiconductor equilateral triangle microresonators (ETRs) with side length of 5, 10, and 20 /spl mu/m are fabricated by the two-step inductively coupled plasma (ICP) etching technique. The mode properties of fabricated InGaAsP ETRs are investigated experimentally by photoluminescence (PL) with the pumping source of a 980-nm semiconductor laser and distinct peaks are observed in the measured PL spectra. The wavelength spacings of the distinct peaks agree very well with the theoretical longitudinal mode intervals of the fundamental transverse modes in the ETRs, which verifies that the distinct peaks are corresponding to the enhancement of resonant modes. The mode quality factors are calculated from the width of the resonant peaks of the PL spectra, which are about 100 for the ETR with side length of 20 /spl mu/m.     

双模方形谐振腔增益均衡器的设计与实现

针对均衡器小型化、高Q值的应用需求,提出并设计了一个工作在Ku波段的双模方形基片集成波导谐振腔均衡器.设计了两个正交的耦合缝隙,在谐振腔中激励起简并模TE₂₀₁和TE₁₀₂;使用金属柱微扰其中一个模式,实现独立调节该模式的谐振频率,并且频率调节自由度高;研究了薄膜电阻的加载位置,实现独立调节两个模式的衰减量和Q值;分析了双模谐振腔级联后谐振频率偏移量及可调性,给出了双模谐振腔均衡器的分析和设计方法.相比于传统单模谐振腔均衡器,该结构均衡器保持了原有的工作性能,并减少了一半数量的谐振腔,使得结构更加紧凑.测试结果与仿真结果吻合,最大误差0.4dB.     

Precise measurements of the Q factor of dielectric resonators inthe transmission mode-accounting for noise, crosstalk, delay ofuncalibrated lines, coupling loss, and coupling reactance

Accurate measurements of the unloaded Q₀ factor of microwave resonators are necessary in many microwave applications. The most accurate values of Q₀ can be obtained by Q-circle fits from multifrequency S-parameter data. Practical measurement systems cause S-parameters of the resonators to be distorted from the circular ideal shape, rotated, and shifted from the origin resulting in errors in the Q-factor values. A novel Q-factor measurement method has been developed based on equations derived for resonators working in the transmission mode and fractional linear circle-fitting techniques. The transmission-mode Q-factor (TMQF) technique removes measurement effects of noise, noncalibrated measurement cables, connectors, coupling structures, crosstalk between the coupling loops, and impedance mismatch from the measurement data. The TMQF is especially useful in cryogenic measurements of high-temperature superconducting thin films and dielectrics since these measurements are typically done in the transmission mode and contain cables and connectors that are difficult to calibrate. The accuracy of the TMQF is better than 1% for practical measurement ranges and the method is applicable to a wide range of coupling. The range of Q factors measurable is from 10³ up to 10⁷     

基于FBG解复用的PON下行传输系统的仿真分析

为了探索提高无源光网络的传输质量的方法,采用将光纤布喇格光栅与密集波分复用结合的方法,提出了一个基于光纤布喇格光栅解复用的无源光网络下行系统,进行了理论分析并利用OptiSystem对该系统进行了仿真,从信道串扰、误比特特性等多方面测试了系统的传输特性,分析了影响传输性能的因素。在与现有的WDM-PON系统对比后发现,本方案有更高的边模抑制比和Q因子以及更低的误比特率。结果表明,该系统性能优异,较现有其它方案有一定的提升。     

Artificially integrated synthetic rectangular waveguide

A synthetic rectangular waveguide (SRW), which consists of two electrical sidewalls and two parallel periodical structures placed at the top and bottom surfaces of the waveguide, is presented. The SRW is made by multilayered integrated circuit processes, which typically have large ratios of SRW lateral dimensions to substrate thickness. Two theoretical methods, finite-element method and deembedding of composite structure consisting of SRW and mode converters, are applied to investigate the propagation characteristics of the SRW. Application of the dispersion characteristics of the two-dimensional periodical structures coupled with appropriate mode converter designs leads to results in SRW designs supporting TE/sub 10/, TM/sub 00/, and TM/sub 10/ modes. Measurements and the two theoretical approaches indicate that the slow-wave factor is 4.9 and Q-factor is 260 at 6.85 GHz for the TE/sub 10/ mode propagation with a cutoff frequency of 4.10 GHz (0.348 factor of cutoff frequency of conventional rectangular waveguide using the same material and dimensions). The theoretical data show the TM/sub 00/ mode to have a slow-wave factor of 1.8, Q-factor of 187.6 at 11.4 GHz, and cutoff frequency of 10.2 GHz. The TM/sub 10/ mode has a slow-wave factor of 1.98, Q-factor of 187.6 at 12.5 GHz, and cutoff frequency of 10.4 GHz.     

On the active compensation of noninverting integrators

A new active compensated balanced time constant (BTC) noninverting integrator is proposed. The compensation is achieved by using a voltage follower in the feedback path, and this result in an extremely high Q-factor, namely Q ≃ |A|³. It is also shown, that the use of a voltage follower with the Deboo noninverting integrator will only double its Q-factor. A novel method is proposed for active compensation of the Deboo integrator, which results in an extremely high Q-factor.     

Attenuation characteristics in confocal annular elliptic waveguidesand resonators

The perturbation method is used to obtain the attenuation constant and Q-factor of several TEM, TE, and TM modes in confocal annular elliptic waveguides (CAE-Ws) and confocal annular elliptic resonators (CAE-Rs). Normalized attenuation and Q-factor charts are given for a variety of possible combinations of the focal distance and the eccentricities. Comparisons between the first higher mode in a CAE-W and a coaxial waveguide with the same cutoff frequency and cross-sectional propagating area reveals a lower attenuation in elliptic geometry. Consequently, the Q-factor in a CAE-R is 20%-40% greater than a Q factor for a coaxial resonator with the same volume and resonant frequency     

高次模多注速调管同轴输出腔性能改进的研究

该文针对工作在TM310模的多注速调管同轴输出腔中工作模式的场分布均匀性、外观品质因数及其与邻近模式的频率间隔等问题进行了研究,提出了一种带有短路杆和金属环的多注速调管同轴输出腔结构。分析发现,适当设置短路杆和金属环不仅可以使外观品质因数降低,还可以改善工作模式的场分布;而且设置金属环还可以增大TM310模和邻近模式的频率间隔以实现抑制杂模。利用仿真软件对X波段的同轴输出腔进行了模拟计算,计算结果与理论分析一致。在此基础上加工了冷测模型,测试结果表明TM310模与邻近模式的频率间隔均达到了1.2 GHz以上,外观品质因数从507.4降至193.5,工作模式的场分布也变得均匀。     

Modelization of the whispering gallery mode in microgear resonators using the Floquet-Bloch formalism

In this paper, a two-dimensional (2-D) method describing the whispering gallery mode in a microgear resonator is presented. The microgear is a microdisk surrounded by a circular grating. The method, which is based on the Floquet-Bloch formalism, analytically describes the field within the disk and outside the grating. On the other hand, the field within the grating is calculated using a finite-difference scheme in polar coordinates. Matching the boundary conditions, it is possible to work in a forced oscillation regime or in a free oscillation regime (laser mode). The resonant wavelength and quality factor can then be deduced. Compared to the coupled mode theory and to 2-D finite-difference time-domain computations, the method is faster and more accurate. Moreover, a polarization effect of the microgear is demonstrated. The TE polarization experiences a Q-factor improvement contrary to TM polarization. Finally, microgear structures prove to be more efficient than micro flowers.