Frequency dependence of the coupling coefficients and resonant frequency detuning in a nanophotonic waveguide-cavity system

Waveguide-cavity interactions may find important applications in future nanophotonic devices. This paper provides a detailed derivation of the evolution equation of the amplitude of a cavity mode coupled to a waveguide, starting from Maxwell's equations and using the reciprocity relations. The analysis applies to both constant cross-section and periodic waveguides as well. Unlike previous studies, the analysis enables the estimation of the frequency dependence of the coupling coefficients. It is also confirmed that the waveguide-cavity coupling causes a detuning of the resonant frequency of the cavity mode. The detuning is estimated in the case of a photonic crystal waveguide-cavity system and it is shown that it can be significant especially if the structure is intended for filtering applications. The analysis is generalized to the case of a multimode or multiple cavities and provides a useful tool in the analysis of devices based on coupled cavities.     

Dual mode coupling by square corner cut in resonators and filters

A method for realization of dual-mode coupling in rectangular waveguide cavities is described and analyzed. The method completely replaces the coupling screw, and therefore can be used to eliminate the need for tuning in dual-mode waveguide cavity filters. It also offers a wide range of coupling values and can achieve higher power-handling capability than coupling screws. Mode matching is used to calculate the mode chart of the infinitely long square corner cut rectangular waveguide (SCCRW), the field distributions of each mode, and the resonant frequencies of the cavity. An evanescent mode rectangular waveguide is used to provide dual-mode couplings between adjacent cavities. The junction discontinuity between the SCCRW and the rectangular waveguide is modeled by a double mode-matching method, yielding modal scattering parameters of the junction. A four-pole dual-mode elliptic-function rectangular waveguide cavity filter using the coupling method was constructed. The experimental filter results showed excellent agreement with theory     

Coupling coefficients of coupled laser cavities

We discuss certain properties of the coupling coefficients for a specific model consisting of two coupled resonant cavities separated by a lossy coupling gap. The coupling coefficients are here defined in the framework of time-dependent coupled-cavity theory-not as end-fire power coupling between traveling waves of two adjacent waveguides. In particular, we explore the validity of a heuristic formula for the coupling coefficients proposed in an earlier publication. It turns out that, in this example, the heuristic formula is directly applicable only if the coupling gap is lossless and off-resonance, but it becomes inapplicable if the lossless gap approaches resonance. The heuristic formula remains useful, but requires a correction if the coupling gap is lossy. The phase angle of the complex coupling coefficient is found to be linearly dependent on the width of the coupling gap, assuming the value 0 (to within multiples of 2π) for an off-resonant gap and the value ofpi/2for a resonant gap. It is not the purpose of this letter to explore properties of c³lasers or to specify their optimum operating conditions. Only the validity of the approximate coupling function is to be investigated.     

基于不同边界条件的SIW谐振腔导模场分析及应用

总结了完备的六种不同边界条件的基片集成波导(SIW)谐振腔结构体系.基于镜像原理和亥姆霍兹方程,给出而不同边界条件下SIW谐振腔的导模场的闭式解.分析了所有边界条件下的谐振腔的场分布,与全波仿真分析、传输线模型法和空腔模型理论给出的结果一致.给出了各种边界条件下SIW谐振腔的谐振频率计算公式.基于提出的传输线附加额外的两个边界条件与谐振腔等效的原理,分析了在SIW谐振腔内,TE模、TM模与TEM模的共存机理.阐述了不同边界条件下的SIW谐振腔的演变关系.最后设计了基于不同边界条件的SIW谐振腔结构的双模带通滤波器和均衡器,该滤波器的两个模式,TE100(TEM模式)和TE102独立可调.器件的实测结果与仿真结果一致,验证了理论分析的正确性,为微波器件的小型化设计提供了思路.     

A shorted waveguide-stub coupling mechanism for narrow-band multimode coupled resonator filters

A shorted waveguide-stub coupling mechanism is presented for implementing narrow-band multimode coupled cavity filters without coupling screws. The coupling element is a shorted rectangular waveguide stub placed in the end walls of cylindrical filter cavities, using perturbation of the magnetic fields to obtain coupling between degenerate modes. This structure is well suited to analysis and design with the efficient and accurate mode-matching method. Coupling coefficients and resonator frequencies can be controlled by varying cavity dimensions and the length, width, and depth of the rectangular coupling element. The accuracy with which the coupling can be realized and the elimination of coupling screws reduce the amount of tuning substantially. A third-order Chebyshev filter, realized in a triple-mode cavity with no coupling screws and only two tuning screws, is presented to verify the use of the coupling structure.     

Modeling of cylindrical dielectric resonators in rectangularwaveguides and cavities

The mode matching method is used to accurately model a generalized cylindrical dielectric resonator structure in a rectangular waveguide or cavity. The field distributions of different modes in cavities are given. The resonant frequencies of the cavities are calculated and compared to the measured data, showing very good agreement. The resonator structure can be a dielectric disk resonator, a ring resonator, a dielectric resonator with support, etc. This structure can be used in filter design as the basic element, providing very good mechanical stability. The slot coupling between cavities is also analyzed, showing some interesting results     

串行谐振滤波器调试中参数的提取理论

介绍一种提取串行耦合滤波器的各个谐振腔的谐振频率和相互谐振腔之间耦合系数的方法.利用终端短路网络的反射系数的相位来综合各个谐振腔的耦合谐振频率和相互谐振腔之间耦合系数.     

Closed form theory of multicavity reflectors and the output power of external cavity diode lasers

A closed form solution for the transmission and reflection coefficients of a double cavity Fabry-Perot resonator is given. The explicit expressions for these coefficients are used in a formula to give the output power of diode lasers coupled to multiple external cavities. Analysis of a cleaved or etched coupled-cavity laser shows that stable operation depends on proper choice of the phase length of both the gap and the control section. A study of a diode laser coupled to an external waveguide containing a Bragg reflector shows that for correct choice of grating reflectivity only modestly effective antireflection coatings (5 percent on laser facet and 2 percent on waveguide face) are required to allow the grating to dominate the operating wavelength of the laser diode. A single external cavity with loss coupled to a laser diode is also considered. In this case the theory indicates the necessity of proper control of loss or coupling fraction between diode and cavity for there to be effective control of wavelength.     

基于对称型齿波导和纳米盘的类EIT和慢光效应

设计了一种新型的基于金属表面等离子体激元（SPPs）的亚波长金属-绝缘体-金属（MIM）型类电磁诱导透明（EIT）系统,该系统由一个直波导及其两边对称的齿形腔和纳米盘耦合而成。利用耦合模式理论对结构进行分析,并通过时域有限差分方法（FDTD）进行数值模拟。当齿形腔和纳米盘的共振频率相近,可以获得类EIT效应,改变齿形腔的长度和纳米盘的半径可以调节透明窗的位置。该装置可以用作高性能的类EIT滤波器,透过率高达77.5%,半高宽低至35.5 nm,群指数高达65,为高度集成光网络提供了一种新的方法,可应用于波长选择器、超快开关、光存储等设备。     

Accurate determination of modes in dielectric-loaded cylindricalcavities using a one-dimensional finite element method

A unified approach is presented for calculating the resonant frequencies of all the modes in cylindrical cavities axisymmetrically loaded with dielectrics. In this method, the radial variations of the field components in the resonator are expressed in terms of first-degree finite-element polynomials, whereas the axial variations of the field components are approximated by trigonometric functions. To calculate the resonant frequencies, an H-vector variational formulation is employed and minimized with respect to the coefficients of the expanded field components. Spurious solutions which are inherent in the finite-element technique are effectively eliminated by means of a penalty term included in the variational expression, imposing a divergence-free magnetic field constraint. To show the capability of the method, resonant frequencies of several cylindrical cavities, including those loaded with dielectric rods and dielectric rings, were calculated. A mode chart is presented which can be used for designing certain multimode dielectric-loaded cavity filters. In contrast to other rigorous techniques reported in the literature, the present method is highly efficient when dielectrics are fully extended along the cavity length     

An optical-fiber-based probe for photonic crystal microcavities

We review a novel method for characterizing both the spectral and spatial properties of resonant cavities within two- dimensional photonic crystals (PCs). An optical fiber taper serves as an external waveguide probe whose micron-scale field is used to source and couple light from the cavity modes, which appear as resonant features in the taper's wavelength-dependent transmission spectrum when it is placed within the cavity's near field. Studying the linewidth and depth of these resonances as a function of the taper's position with respect to the resonator produces quantitative measurements of the quality factor (Q) and modal volume (V/sub eff/) of the resonant cavity modes. Polarization information about the cavity modes can be obtained by studying their depths of coupling when the cavity is probed along different axes by the taper. This fiber-based technique has been used to measure Q/spl sim/40,000 and V/sub eff//spl sim/0.9 cubic wavelengths in a graded square lattice PC microcavity fabricated in silicon. The speed and versatility of this fiber-based probe is highlighted, and a discussion of its applicability to other wavelength-scale resonant elements is given.     

On the Theory of Strongly Coupled Cavity Chains

A chain of identical cavity resonators coupled together through slots in their common walls forms a band-pass microwave filter. The pass band characteristics of such a system are determined by a combination of field theory and circuit theory. The fields in the cavities are expressed in terms of the normal modes of the uncoupled cavities. The fields in the neighborhood of a slot are determined by representing the slot as a transmission line. Irrotational components of the field in the cavities account for direct slot-to-slot coupling. The method successfully predicts both the dispersion characteristics and field distributions over large frequency ranges for many practical systems, such as slow-wave circuits for high-power traveling-wave tubes.     

Dielectric slab-loaded resonant cavity for applications requiringenhanced field uniformity

This paper introduces and analyzes a rectangular resonant structure that provides an alternative to the multimode resonant cavity in applications requiring enhanced field uniformity. The resonant cavity contains four dielectric loading slabs placed along the cavity walls. Its first resonant mode is related to the uniform field distribution supported in a rectangular TEM waveguide. The electromagnetic fields within the cavity are described using a closed-form approach, with approximations taken to account for the presence of two of the loading slabs. Application of the boundary conditions leads to an eigenvalue formulation, which is used to determine resonant frequencies and electromagnetic field distributions within the cavity. Measurements of both resonant frequencies and electric field magnitudes confirm the analysis. This work provides the basis for future analyses and implementation of slab-loaded cavities in both scientific and industrial settings     

Electric and Magnetic Coupling through Small Apertures in Shield Walls of Any Thickness

A method is presented for evaluating the coupling between two identical resonant cavities coupled by a small aperture in a plane common wall of arbitrary thickness. The coupling is related to the frequencies of the symmetric and asymmetric modes of oscillation of the coupled cavity structure, and a variational technique is used to determine those frequencies. The method is applied to circular and rectangular apertures, and it is shown that the coupling is separable into electric and magnetic terms. The results enable theoretical solutions to be obtained for the electric and magnetic polarizabilities of circular and rectangular apertures in walls of zero thickness, and equivalent polarizabilities to be obtained when the wall thickness is nonzero. Curves of numerical values are given for circular and rectangular apertures. With zero wall thickness, the results obtained are the same as those of Bethe for a circular aperture and give good agreement with Cohn's experimental results for rectangular apertures.     

采用新型介质集成波导腔的小型双频滤波器

提出了一种新式的横电磁波-基片集成波导(TEM-SIW)谐振腔。这种TEM-SIW谐振腔由经典的基片集成波导(SIW)腔发展而来。通过在SIW腔的中心位置加入短路销钉,将SIW腔体的上金属平面与腔四周导体壁开路构成TEM-SIW腔。相同谐振频率下,单个TEM-SIW腔的面积可以减小到传统的SIW谐振腔面积的9.5%。分析了主模式工作情况下TEM-SIW谐振腔和传统的SIW谐振腔的结构以及腔内的磁场分布。由于其磁场分布与工作在TEM模式的电容加载同轴腔相似,因此,基于这种谐振腔的滤波器可以很方便的借鉴经典的电容加载同轴腔滤波器的耦合结构和综合设计技术。最后,设计了一个基于TEM-SIW腔的三级双频滤波器,其性能已经通过了数值仿真和实验验证。     

Proposal for a Compact Resonant-Coupling-Type Polarization Splitter Based on Photonic Crystal Waveguide With Absolute Photonic Bandgap

We propose a resonant-coupling-type polarization splitter based on a photonic crystal structure with absolute photonic bandgap. The scalar finite-element method was used to calculate resonant frequencies of the cavity and frequency dependences of the polarization splitter. This device supports single-mode operation for both transverse-electric and transverse-magnetic waves. We show that miniaturization of the proposed polarization splitter can be realized by utilizing resonant coupling.     

An original approach to the design of bandpass cavity filters withmultiple couplings

A novel approach to the design of general cavity filters with each cavity coupled to an arbitrary number of other cavities is presented. This approach is based on a suitable characterization of the filter structure which does not require one to model separately the cavities (resonators) and the coupling elements. Suitably defined equivalent admittances are associated with each cavity allowing one to design the filter structure once the parameters of a suitable low-pass prototype are given; an efficient procedure for the synthesis of such a prototype with equiripple passband response is also presented which allows one to arbitrarily prescribe transmission zeros placed in the complex plane (even asymmetrically). The described design approach is particularly convenient when the filter structure does not allow a simple modeling of the resonators and coupling elements separately. This is the case of slot-coupled cavity filters and of filter structures based on arrays of coupled transmission lines. It is also shown that the simplified design approach often adopted in the past, where only two coupled cavities at a time are considered, can produce large errors even in the case of filters with all attenuation poles at infinity (i.e., two couplings per cavity)     

Mode conversion losses in highly overmoded waveguide cavities

A technique to quantify the effects of mode conversion losses in highly overmoded waveguide cavity resonators using the WKB method is presented. The WKB theory is accurate for weakly irregular waveguide cavities with small amounts of mode conversion. This approach to the problem has the advantage that the mode conversion losses in waveguide cavities can be quantified quickly and cheaply. The objective is to compute the amplitude and phase of a resonant mode in the cavity to zeroth order (i.e. without regard to mode conversion effects), and then use amplitude and phase of the computed zeroth-order fields to compute the amplitude of the converted mode. This approach is valid to the extent that the converted modes are not a major perturbation to the resonant mode. The results of the theory are presented in the context of the trade-offs associated with the design of an 85 GHz TE_1.3 phase-locked gyroklystron oscillator experiment. Mode conversion losses in the input cavity are a particular problem, and place limits on the amount of usable beam current (and therefore the output power capabilities of the gyroklystron). The isolation of the input and output cavities due to mode conversion must be carefully considered in any design     

Observation of electromagnetic coupling to a closed superconductingthin-film cavity

We have studied Josephson junctions coupled to closed, superconducting, thin-film cavities. We briefly discuss the coupling mechanism in this system as well as the fabrication methods and expected resonant modes. Cavities consisting of both quartz and anodized niobium were studied. Small current steps have been observed in the current-voltage (I-V) measurements of junctions at voltages corresponding to the calculated modes of the closed cavity indicating Josephson coupling     

A coupled optoelectronic oscillator with three resonant cavities

A new single-mode optoelectronic oscillator (OEO) with three coupled cavities is proposed and demonstrated. A Fabry-Perot (F-P) cavity fiber laser and an optical-electrical feedback branch are coupled together to construct an optoelectronic oscillator, where the F-P cavity fiber laser serves as a light source, and a modulator is placed in the laser cavity to implement reciprocating modulation, which simultaneously splits the laser cavity into two parts and forms a dual-loop configuration. To complete an optoelectronic oscillator, part of optical signal is output from the F-P cavity to implement the feedback modulation, which constructs the third cavity. Since only the oscillation signal satisfies the requirements of all the three cavities, a single-mode oscillation can be finally achieved. Three resonant cavities are successfully designed without adding more optoelectronic devices, and the side-modes can be well suppressed with low cost. The oscillation condition is theoretically analyzed. In the experimental demonstration, a 20 GHz single longitudinal mode microwave signal is successfully obtained.