A general analysis of propagation along multiple-layersuperconducting stripline and microstrip transmission lines

A rigorous spectral-domain formulation for a superconducting stripline or microstrip transmission line with a multiple-layer dielectric substrate is presented. The formulation models the strip conductor as a surface current with an equivalent surface impedance, where the surface impedance is approximated in closed form when the strip is either much thinner or much thicker than a penetration depth. In either case the surface impedance is related to the complex conductivity of the material, which is calculated from a two-fluid model. Results are presented to show the slow-wave propagation and attenuation along both microstrip and stripline packages in a realistic multiple-layer configuration, which accounts for the field penetration into the superconducting ground planes     

Impact of a normally conducting surface layer on attenuation inhigh-Tc superconducting microstrip transmission lines

A two-dimensional (2-D) model is adopted to characterize high-T _c superconducting (HTS) microstrip transmission lines with a normally conducting surface layer. The model is verified by comparison with a full-wave analysis calculation for identical all-superconducting lines and by calculation of the current distribution and propagation properties for a normal conductor version of the microstrip. Estimates are obtained for the transmission line attenuation constant versus thickness and conductivity of the resistive surface layer. The results suggest that in situ deposition of a normal metal overlayer on the HTS film surface may be a viable technique to secure the long-term performance of microwave devices     

Transmission Modes in a Braided Coaxial Cable and Coupling to a Tunnel Environment

Radio frequency transmission in a semicircular tunnel containing a braided coaxial cable is considered. The general formulation accounts for both the ohmic losses in the tunnel wall and a thin lossy film layer on the outer surface of the dielectric jacket of the cable. Using a quasi-static approximation, it is found that the propagation constants of the low-frequency transmission line modes are obtained through the solution of a cubic equation. However, for the special case when the conductivity thickness product of the Iossy film layer vanishes, this cubic equation reduces to a quadratic. The spatially dispersive form of the braid transfer impedance is also accounted for. It is shown that the quasistatic theory is well justified for frequencies as high as 100 MHz for typical tunnel geometries. Finally, special characteristic impedances are derived for the various modes of the equivalent multiconductor transmission line.     

The effect of superconducting ground plane on microwavecharacteristics of unpatterned superconducting films in the mixed state

We microwave characteristics of a multilayer structure made of a type-II superconducting thin film and a dielectric substrate together with a superconducting ground plane is studied theoretically by using the model of the self-consistent treatment of vortex dynamics. The dependence of reflection coefficient on the temperature and static magnetic field is reduced owing to the existence of the superconducting ground plane, especially at temperatures near T_c and at higher fields. Comparison of the interesting oscillation phenomenon in the associated effective surface resistance between the Meissner state (b=0) and mixed state (b≠0) is made. We find that the superconducting ground plane not only strongly narrows down the resonant peak shape but also enhances the peak height. Finally, a similar layered structure made of a superconducting thin film on a dielectric substrate shielded by a buffer layer is also considered. We specifically demonstrate that the buffer layer has essentially no substantial influence on microwave reflectance, transmittance, and complex surface impedance. The role played by the buffer layer is in great contrast to that in a planar transmission line     

Frequency-dependent FDTD methods using Z transforms

The frequency-dependent finite-difference time-domain method (FD) ²TD method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent. However, as researchers search for more elaborate applications, the formulation of the (FD)²TD methods becomes more complex. In this work, the mathematics of the (FD) ²TD method is developed using Z transform theory. This has the advantages of presenting a clearer formulation, and allowing researchers to draw on the literature of systems analysis and signal processing disciplines     

Stacked superconductor structure for microwave transmission

Propagation characteristics of microwaves along a stacked superconductor microstrip structure are investigated. The suitability of such a structure for practical applications is discussed. A rigorous integral equation formulation has been used for the analysis of such structure. The effect of thickness of superconducting strip on propagation characteristics has been studied. Results presented show that the slow wave propagation and low dispersive coupling are possible in a realistic stacked multi-dielectric and superconducting layers microstrip line package.     

MDM光波导激发高阶SPP模的传输特性

研究了金属-介质-金属(MDM)型表面等离子体激元(SPP)光波导的电磁特性。理论计算结果表明,对于633nm的TM偏振入射光,当介质膜层厚度小于85nm时,波导中只能激发产生一阶SPP模(基模),其余高阶模全部截止。随着介质膜厚度增加,高阶SPP模逐渐被激发产生。当介质膜层厚度较小时,SPP模的有效折射率的实部随阶数的增加而减小,而虚部则随阶数的增加而增加,SPP基模具有最大传输距离。然而,当MDM波导中的介质层厚度超过0.555μm时,由于三阶SPP模的电磁场主要集中在离金属层相对较远的介质层中,其有效折射率的虚部具有最小值,具有最大的传输距离,而非基模。当入射光波长为633nm介质层厚度为0.9μm时,Ag/SiO2/Ag光波导中三阶SPP模的传输距离达到约150μm。     

基于SPP的1550纳米光波导的超长传输特性

采用严格电磁理论研究了介质-金属-介质型光波导激发表面等离子激元(SPPs)的电磁特性,对比分析了SPP波在SiO2/Ag/SiO2和Si/Ag/Si光波导的传输距离。研究表明,对于1550nm光通信波长入射光及10nm厚的金属银膜层,SiO2/Ag/SiO2光波导中非对称SPP的传输距离可达40cm,明显高于对称SPP波的传输距离,也显著高于非对称SPP波在Si/Ag/Si波导中的传输距离,具有超长传输距离;随着金属层厚度的增加SPP波的传输距离明显减小,当银层厚度超过50nm后,非对称的SPP在SiO2/Ag/SiO2及Si/Ag/Si波导中的传输距离趋于一致,约为200nm;此时银层厚度变化对SPP波传输距离的影响明显减弱。     

Simple and efficient finite-element analysis of microwave andoptical waveguides

A simple and efficient finite-element method for the analysis of microwave and optical waveguiding problems is formulated using three components of the electric or magnetic field. In order to eliminate spurious solutions, edge elements are introduced. In the edge element approach the nodal parameters are not limited to the magnetic field as in the conventional three-component formulation for the dielectric waveguiding problem. An eigenvalue equation that involves only the edge variables in the transversal plane and can provide a direct solution for the propagation constant is derived. To show the validity and usefulness of this approach, computed results are illustrated for microstrip transmission lines and dielectric waveguides     

Simulations of microwave characteristics of high-temperature superconducting microstrip lines by using an empirical two-fluid model

A numerical analysis of the microwave propagation characteristics of a high-temperature superconducting microstrip transmission line is presented. It is based on the transmission line theory and empirical two-fluid model which appropriately incorporates the quasiparticle scattering and residual loss of the superconductor. First, the calculated attenuation constant and phase velocity are compared with those predicted by the conventional two-fluid model for a YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// microstrip line with a linear substrate, lanthanum aluminate, LaAlO/sub 3/. Next, we have specifically investigated the effects of nonlinear substrate such as strontium titanate, SrTiO/sub 3/, on the attenuation constant and phase velocity. The tunable feature of such a microwave device owing to the nonlinear dielectric ferroelectric is illustrated and discussed.     

YBa2Cu3O7 superconductors forhigh-speed interconnects

The surface resistance of high-quality YBa₂Cu₃ O₇ superconducting films measured over a frequency range from 10 to 500 GHz using high-speed optoelectronic techniques is discussed. A direct comparison is made with the surface resistance of gold and superconducting niobium conductors. Using the measured surface resistance, the propagation characteristic of interconnects based on YBa ₂Cu₃O₇ superconductors at 77 K is simulated and compared to that of gold transmission lines at 77 K and superconducting niobium lines at 7.7 K     

Nonlinear analysis of microwave superconductor devices usingfull-wave electromagnetic model

This paper presents a full electromagnetic wave analysis for modeling the nonlinearity in high temperature superconductor (HTS) microwave and millimeter-wave devices. The HTS nonlinear model is based on the Ginzburg-Landau theory. The electromagnetic fields associated with the currents on the superconducting structure are obtained using a three-dimensional full wave solution of Maxwell's equations. A three-dimensional finite-difference time-domain algorithm simultaneously solves the resulting equations. The entire solution is performed in time domain, which is a must for this type of nonlinearity analysis. The macroscopic parameters of the HTS, the super fluid penetration depth and the normal fluid conductivity, are calculated as functions of the applied magnetic field. The nonlinear propagation characteristics for HTS transmission line, including the effective dielectric constant and the attenuation constant, are calculated, As the power on the transmission line increases, the phase velocity decreases and the line losses increase. The nonlinearity effects on the current distributions inside the HTS, the electromagnetic field distributions, and the frequency spectrum are also analyzed     

A new edge element analysis of dispersive waveguiding structures

A new functional is rigorously selected for the edge element method to solve the 2-D¹/₂ guided wave problems. The variational formulation is derived from the vector wave equation without any assumption or simplifications, and therefore the formulation is the full-wave analysis. Moderate to heavy ohmic loss and dielectric loss are taken into account in a natural and consistent manner. As a result, finite cross-section of arbitrary shape and finite conductivity can be handled without imposing the impedance boundary condition (IBC). The DEC may no longer be held for high-speed microelectronics applications, where the cross-section dimension may have been in the same order of the skin depths of some frequency components. The propagation modes are obtained by solving the large scale generalized eigenvalue and eigenvector equations employing the subspace iteration method. The spurious modes are totally suppressed in the whole frequency range of interest. Numerical examples of dielectric waveguides and microstrip transmission lines with finite conductivity are conducted     

Exact formulas for wave impedance and propagation constants ofhomogeneous, lossy dielectric and/or magnetic materials

Calculations of propagation constants for lossy materials are performed under the approximations of low loss (or high conductivity). To improve the understanding and better predict the analysis of such materials, exact formulation for wave impedance and propagation constants of homogeneous, lossy, dielectric/magnetic materials are proposed. Formulation is based on dielectric and/or magnetic loss tangent of the material     

A simple technique for calculating the propagation dispersion ofmulticonductor transmission lines in multilayer dielectric media

A multiconductor transmission line in a multilayer dielectric medium is complicated and therefore is frequently analyzed by the simple quasi-TEM (transverse electromagnetic) approach. Unlike the full wave eigenvalue approach, the quasi-TEM approach does not give the propagation dispersion characteristics of the line. This work overcomes this problem by first obtaining the solution of each multiconductor mode from the quasi-TEM approach. Then these solutions are used as both basis and testing functions in a variational formulation of the full wave eigenvalue analysis. The result is high accuracy in the dispersive propagation constants of the multiconductor modes. By solving only for high frequency eigenvalues, not for the high frequency eigenvectors, the method is simpler and faster than the conventional full wave dispersion analyses     

Properties of an electromagnetically coupled small antenna with asuperconducting thin-film radiator

This paper describes the structure and properties of a 900-MHz-band small antenna with a superconducting thin-film radiator operated by electromagnetic coupling. The radiation efficiency of the antenna with a λ/38 radiator reached 74% at 79 K. The loss in this antenna comprised mismatching loss and radiator loss caused by the surface resistance of the superconducting thin film. A simulation model with a meander-line radiator and a parallel line is also proposed. This model makes it possible to design a superconducting thin-film radiator which can be fabricated on a dielectric substrate by using the moment method without taking account of the dielectric substrate     

Microwave characteristics of high Tcsuperconducting coplanar waveguide resonator

A theoretical formulation has been developed to calculate the coupling coefficient, London penetration depth, and surface resistance of a coplanar waveguide resonator fabricated from films of superconducting YBCO material. Experimental data of the reflection coefficient as a function of temperature and frequency agree reasonably well with calculations. The formulation is of sufficient generality to be applicable to other guided structures     

Microwave surface impedances of BCS superconducting thin films

The microwave propagation-dominated problem in the multilayer structure made of a BCS superconducting film and a dielectric substrate is investigated theoretically by using the modified two-fluid model and transmission line theory. The effective microwave surface impedances are studied as functions of temperature, frequency, and film thickness, as well as substrate thickness. Special attention is paid to the substrate resonance phenomenon in the resonant structure. The influence of BCS coherence effects on surface impedance and resonant behavior is clearly demonstrated. The resonant effect in the stack structure is well interpreted with the help of the transverse resonance technique in the microwave theory     

Polyimide/Ta2O5/polyimide antiresonantreflecting optical waveguides

A novel antiresonant reflecting optical waveguide (ARROW) fabricated using both the organic and dielectric thin film technologies is presented for the first time. The ARROW consisted of the fluorinated polyimide and tantalum pentoxide (Ta₂O₅) hybrid layers deposited on a Si substrate. For TE polarized light, the propagation loss of the waveguide as low as 0.8 dB/cm is obtained at 632.8 nm. The propagation loss for TM polarized light is 2.7 dB/cm. Some design considerations of the hybrid ARROW are also discussed in this work     

Dispersion characteristics of optically excited coplanarstriplines: pulse propagation

The propagation of optically excited picosecond electrical pulses on coplanar striplines is analyzed. A full-wave analysis method that includes dispersion and losses over terahertz bandwidths is outlined. Results of the full-wave analysis are interpreted in terms of the underlying physical phenomena. The full-wave analysis reveals the existence of peaks in the dispersion curve of the coplanar stripline. These are interpreted in terms of the onset and coupling of the substrate modes to the transmission line mode. Results of the full-wave analysis are in good agreement with those obtained by established theory. Pulse propagation is simulated using the dispersion and loss data obtained from the analysis and accounts for all the relevant mechanisms. Results of simulations are compared with previously published experimental data for normal as well as superconducting lines. It is demonstrated that the superconducting phenomena are not dominant, whereas modal dispersion and substrate losses dominate the evolution of the output pulse and must be included for accurate modeling of pulse propagation on coplanar striplines