FDTD-based full wave co-simulation model for hybrid electromagnetic systems

In high-frequency ranges, the present electronic design automation software has limited capabilities to model electromagnetic (EM) systems where there are strong field effects influencing their characteristics. In this situation, a full-wave simulation tool is desired for the analysis and design of high-speed and non-linear EM systems. It is necessary to explore the interaction between the field and electronic components during a transient process when field effects are more significant. The finite-difference time-domain (FDTD) technique receives growing attention in the area of EM system analysis and simulation due to its simplicity, flexibility and robustness. It is a full-wave simulation method that solves the Maxwell\u27s equations in time domain directly. Decades of research and development and rapid growth in computer capability have built up a firm foundation for FDTD techniques to be applied to many practical problems. Based on FDTD, this dissertation develops a stable CO-simulation method to perform a full-wave simulation of a hybrid EM system consisting of lumped elements and distributed structures. In this method, FDTD is used to solve the EM field problems associated with distributed structures, and a circuit simulator solves the response of lumped elements. A field-circuit model proposed in the dissertation serves as the interface between the two simulation tools. Compared with previous methods, the FDTD method based on this model is much more flexible and stable for linear and nonlinear lumped elements under both small and large signal conditions. Because of its flexibility and robustness, this model is a promising approach to integrate a field solver and a circuit simulator in the simulations of practical EM systems. In order to improve the simulation accuracy, some problems related to FDTD simulation are studied. Based on the numerical dispersion in homogeneous media uniform grids, the FDTD numerical reflection and transmission on the boundary of media, which are discritized by a non-uniform grid, are investigated. This investigation provides for the first time an estimation of FDTD numerical error in inhomogeneous media and non-uniform grids. Perfectly matched layer (PML) was previously utilized the homogeneous media or uniform grids. This dissertation extends the PML boundary conditions to handle the inhomogeneous media and non-uniform grid. Techniques extracting S parameters from FDTD simulation are also discussed. Two and three-dimensional CO-simulation software, written in C++, has be derived, developed and verified in this dissertation. The simulation results agree well with results from other simulation methods, like SPICE, for many test circuits. Taking data sampling and interpolation into account, simulation results generally fit well to measurement and other simulation results for complicated three-dimensional structures. With further improvements of the FDTD technique and circuit simulation, field-circuit CO-simulation model will widen its application to general EM systems

Modeling and Simulation of Photonic Crystal Fibers and Distributed Feedback Photonic Crystal Fiber Lasers

A photonic crystal fiber (PCF) is comprised of a solid or air core surrounded by periodically arranged air holes running along the length of the fiber, which guides light in a fundamentally new way compared to conventional optical fibers, affecting almost all areas of optics and photonics. To analyze the dispersion and loss properties of PCFs, a two-dimensional (2D) finite-difference frequency-domain (FDFD) method combined with the technique of perfectly matched layer (PML) is developed. The propagation constant and loss can be obtained with accuracies in the orders of ∼10-6 and ∼10 -3, respectively. The Bragg fiber is a kind of PCF with alternate layers surrounding a solid or air core. To improve the performance of the above algorithm, a 1D FDFD method in the cylindrical coordinates is proposed to fully utilize the rotational symmetry property of the Bragg fiber. In addition to improving the accuracy, this method reduces the computation region from 2D to a straight line, significantly relieving the computation burden. A second method, called Galerkin method, is also developed under cylindrical coordinates. The mode fields are expanded using orthogonal Laguerre-Gauss functions; and the method is accurate and stable. However, it cannot do the loss analysis. For photonic-band-gap-guiding PCFs, the properties of the confined modes are closely related to the band structures of the cladding photonic crystals. Therefore, a third FDFD method using periodic boundaries is developed in a generalized coordinate system. Various lattice geometries are analyzed in the same manner, and the results are comparable to those obtained by the plane wave expansion method which is commonly used in the literature. Finally, a theoretical model for analyzing distributed feedback (DFB) PCF lasers has been presented. Two structures are investigated: PCFs with triangular lattice (TPCF) and PCFs made of capillary tube (CPCF). The modeling and simulation of erbium-doped and erbium/ytterbium (Er/Yb) co-doped DFB lasers are aimed at finding suitable PCF geometry to achieve low threshold and high output power. Various steps involved in this model are: (1) the properties of PCFs are analyzed by the FDFD method; (2) the Bragg grating is investigated by coupled mode theory; (3) the coupled wave equations are solved by transfer matrix method; and (4) Er atom is modeled as a three-level medium while energy transfer between Yb and Er atoms is considered for Er/Yb co-doped fiber. It is found that a CPCF laser with a smaller mode area is useful for lower-threshold applications and both of CPCF and TPCF lasers with larger mode areas are suitable for high-power operation

Numerical Simulation of the Generation of Axisymmetric Mode Jet Screech Tones

An imperfectly expanded supersonic jet, invariably, radiates both broadband noise and discrete frequency sound called screech tones. Screech tones are known to be generated by a feedback loop driven by the large scale instability waves of the jet flow. Inside the jet plume is a quasi-periodic shock cell structure. The interaction of the instability waves and the shock cell structure, as the former propagates through the latter, is responsible for the generation of the tones. Presently, there are formulas that can predict the tone frequency fairly accurately. However, there is no known way to predict the screech tone intensity. In this work, the screech phenomenon of an axisymmetric jet at low supersonic Mach number is reproduced by numerical simulation. The computed mean velocity profiles and the shock cell pressure distribution of the jet are found to be in good agreement with experimental measurements. The same is true with the simulated screech frequency. Calculated screech tone intensity and directivity at selected jet Mach number are reported in this paper. The present results demonstrate that numerical simulation using computational aeroacoustics methods offers not only a reliable way to determine the screech tone intensity and directivity but also an opportunity to study the physics and detailed mechanisms of the phenomenon by an entirely new approach

Annual Review of Progress in Applied Computational Electromagnetics

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