The finite-Difference Time Domain method (FDTD) derives the discrete form of the Maxwell¡¦s equations with second-order central difference with the electromagnetic distribution of the Yee space lattice, and computes the value of the electric field and magnetic field in the simulation space using leapfrog for time derivatives. This method is different from the frequency domain method which needs to analyze its value individually (ex. Finite Element method). The frequency domain method needs to take a long time for analyzing the response on each spectrum point when the bandwidth is very wide. The advantage of time domain analysis is to obtain the complete frequency response from the simulation value through Fourier Transform method. It¡¦s difficult to combine the electromagnetic analysis with the lumped circuit simulation in current simulation CAD. Thereby the performance of the simulation result and the practical implementation always causes error. The FDTD method is the full-wave algorithm which can also simulate the lump element, nonlinear element or active element in simulation space by linking to SPICE or S-parameter. In this dissertation, an efficient scheme for processing arbitrary one-port devices in the finite-difference time-domain (FDTD) method is proposed. Generally speaking, methods invoking analytic pre-processing of the device¡¦s V-I relations (admittance or impedance) are computationally more efficient than methods employing numerical procedure to iteratively process the device at each time step. The accuracy of the proposed method is verified by comparison with results from the equivalent current-source method and is numerically stable.

A set of tools are proposed for the efficient modeling of several classes of problems related to periodic structures in microwave and optical regimes with Finite-Difference Time-Domain method. The first category of problems under study is the interaction of non-periodic sources and printed elements with infinitely periodic structures. Such problems would typically require a time-consuming simulation of a finite number of unit cells of the periodic structures, chosen to be large enough to achieve convergence. To alleviate computational cost, the sine-cosine method for the Finite-Difference Time-Domain based dispersion analysis of periodic structures is extended to incorporate the presence of non-periodic, wideband sources, enabling the fast modeling of driven periodic structures via a small number of low cost simulations. The proposed method is then modified for the accelerated simulation of microwave circuit geometries printed on periodic substrates. The scheme employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is also given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far-field transformation. It has been further demonstrated that from the mesh truncation point of view, the scheme, which has a unified form regardless dispersion and conductivity, serves as a much simpler but equally effective alternative to the Perfectly Matched Layer provided that the simulated domain is periodic in the direction of termination. The second category of problems focuses on the efficient characterization of nonlinear periodic structures. In Finite-Difference Time-Domain, the simulation of these problems is typically hindered by the fine spatial and time gridding. Originally proposed for linear structures, the Alternating-Direction Implicit Finite-Difference Time-Domain method, as well as a novel spatial filtering method, are extended to incorporate nonlinear media. Both methods are able to use time-step sizes beyond the conventional stability limit, offering significant savings in simulation time.

The unique frequency range and robustness of surface acoustic wave (SAW) devices has been a catalyst for their adoption as integral components in a range of consumer and military electronics. Furthermore, the strain and piezoelectric fields associated with SAWs are finding novel applications in nanostructured devices. In this thesis, the interaction of SAWs with periodic elastic structures, such as photonic or phononic crystals (PnCs), is studied both computationally and experimentally. To predict the behaviour of elastic waves in PnCs, a finite-difference time-domain simulator (PnCSim) was developed using C++. PnCSim was designed to calculate band structures and transmission spectra of elastic waves through two-dimensional PnCs. By developing appropriate boundary conditions, bulk waves, surface acoustic waves, and plate waves can be simulated. Results obtained using PnCSim demonstrate good agreement with theoretical data reported in the literature. To experimentally investigate the behaviour of SAWs in PnCs, fabrication procedures were developed to create interdigitated transducers (IDTs) and PnCs. Using lift-off photolithography, IDTs with finger widths as low as 1.8 um were fabricated on gallium arsenide (GaAs), corresponding to a SAW frequency of 397 MHz. A citric acid and hydrogen peroxide wet-etching solution was used to create shallow air hole PnCs in square and triangular lattice configurations, with lattice constants of 8 um and 12 um, respectively. The relative transmission of SAWs through these PnCs as a function of frequency was determined by comparing the insertion losses before and after etching the PnCs. In addition, using a scanning Sagnac interferometer, displacement maps were measured for SAWs incident on square lattice PnCs by Mathew (Creating and Imaging Surface Acoustic Waves on GaAs, Master’s Thesis). Reasonable agreement was found between simulations and measurements. Additional simulations indicate that SAW waveguiding should be possible with a PnC consiting of air holes in GaAs. The phononic properties of a commonly used photonic plate were also determined. Band structure simulations of the plate displayed no complete elastic band gaps. However, transmission simulations indicated that a pseudo-gap may form for elastic waves polarized in the sagittal plane. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-12-23 16:24:33.164

A set of tools are proposed for the efficient modeling of several classes of problems related to periodic structures in microwave and optical regimes with Finite-Difference Time-Domain method. The first category of problems under study is the interaction of non-periodic sources and printed elements with infinitely periodic structures. Such problems would typically require a time-consuming simulation of a finite number of unit cells of the periodic structures, chosen to be large enough to achieve convergence. To alleviate computational cost, the sine-cosine method for the Finite-Difference Time-Domain based dispersion analysis of periodic structures is extended to incorporate the presence of non-periodic, wideband sources, enabling the fast modeling of driven periodic structures via a small number of low cost simulations. The proposed method is then modified for the accelerated simulation of microwave circuit geometries printed on periodic substrates. The scheme employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is also given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far-field transformation. It has been further demonstrated that from the mesh truncation point of view, the scheme, which has a unified form regardless dispersion and conductivity, serves as a much simpler but equally effective alternative to the Perfectly Matched Layer provided that the simulated domain is periodic in the direction of termination. The second category of problems focuses on the efficient characterization of nonlinear periodic structures. In Finite-Difference Time-Domain, the simulation of these problems is typically hindered by the fine spatial and time gridding. Originally proposed for linear structures, the Alternating-Direction Implicit Finite-Difference Time-Domain method, as well as a novel spatial filtering method, are extended to incorporate nonlinear media. Both methods are able to use time-step sizes beyond the conventional stability limit, offering significant savings in simulation time.

Yes / When modeling objects that are small compared with the wavelength, e.g., biological cells at radio frequencies, the standard finite-difference time-domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating a generic lumped-element membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900,1800, and 2450 MHz. This method will facilitate deeper investigation of the phenomena in the interaction between electromagnetic fields and biological systems.

The aim of this thesis was to make a practical tool for low frequency analysis in room acoustics.The need arises from Acad’s experience that their results from simulations using raytracing software deviate in the lower frequencies when compared to field measurements inrooms. The tool was programmed in Matlab and utilizes the Finite Difference Time Domain (FDTD) method, which is a form of rapid finite element analysis in the time domain.A number of tests have been made to investigate the practical limitations of the FDTD method, such as numerical errors caused by sound sources, discretization and simulation time. Boundary conditions, with and without frequency dependence, have been analysed bycomparing results from simulations of a virtual impedance tube and reverberation room to analytical solutions. These tests show that the use of the FDTD method appears well suited for the purpose of the tool.A field test was made to verify that the tool enables easy and relatively quick simulations of real rooms, with results well in line with measured acoustic parameters. Comparisons of the results from using the FDTD method, ray-tracing and finite elements (FEM) showed goodcorrelation. This indicates that the deviations Acad experience between simulated results and field measurements are most likely caused by uncertainties in the sound absorption data used for low frequencies rather than by limitations in the ray-tracing software. The FDTDtool might still come in handy for more complex models, where edge diffraction is a more important factor, or simply as a means for a “second opinion” to ray-tracing - in general FEM is too time consuming a method to be used on a daily basis.Auxiliary tools made for importing models, providing output data in the of room acoustic parameters, graphs and audio files are not covered in detail here, as these lay outside the scope of this thesis. / Målet för detta examensarbete var att undersöka möjligheten att programmera ett praktisktanvändbart verktyg för lågfrekvensanalys inom rumsakustik. Behovet uppstår från Acadserfarenhet att resultat från simuleringar med hjälp av strålgångsmjukvara avviker i lågfrekvensområdeti jämförelse med fältmätningar i färdigställda rum. Verktyget är programmerati Matlab och använder Finite Difference Time Domain (FDTD) metoden, vilket är en typav snabb finita elementanalys i tidsdomänen.En rad tester har genomförts för att se metodens praktiska begräsningar orsakade av numeriskafel vid val av ljudkälla, diskretisering och simuleringstid. Randvillkor, med och utanfrekvensberoende, har analyserats genom jämförelser av simulerade resultat i virtuella impedansröroch efterklangsrum mot analytiska beräkningar. Testerna visar att FDTD-metodentycks fungerar väl för verktygets tilltänkta användningsområde.Ett fälttest genomfördes för att verifiera att det med verktyget är möjligt att enkelt och relativtsnabbt simulera resultat som väl matcher uppmätta rumsakustiska parametrar. Jämförelsermellan FDTD-metoden och resultat beräknade med strålgångsanalys och finita elementmetoden(FEM) visade även på god korrelation. Detta indikerar att de avvikelser Acaderfar mellan simulerade resultat och fältmätningar troligen orsakas av osäkerheter i den ingåendeljudabsorptionsdata som används för låga frekvenser, snarare än av begränsningar istrålgångsmjukvaran. Verktyget kan fortfarande komma till användning för mer komplexamodeller, där kantdiffraktion är en viktigare faktor, eller helt enkelt som ett sätt att få ett”andra utlåtande” till resultaten från strålgångsmjukvaran då FEM-analys generellt är en förtidskrävande metod för att användas på daglig basis.Kringverktyg skapade för t.ex. import av modeller, utdata i form av rumsakustiska parametrar,grafer och ljudfiler redovisas inte i detalj i denna rapport eftersom dessa ligger utanförexamensarbetet.

Finite-difference models have been used for nearly 40 years to solve electromagnetic problems of heterogeneous nature. Further, these techniques are well known for being computationally expensive, as well as subject to various numerical artifacts. However, little is yet understood about the errors arising in the simulation of wideband sources with the finitedifference time-domain (FDTD) method. Within this context, the focus of this thesis is on two different problems. On the one hand, the speed and accuracy of current FDTD implementations is analysed and increased. On the other hand, the distortion of numerical pulses is characterised and mitigation techniques proposed. In addition, recent developments in general-purpose computing on graphics processing units (GPGPU) have unveiled new methods for the efficient implementation of FDTD algorithms. Therefore, this thesis proposes specific GPU-based guidelines for the implementation of the standard FDTD. Then, metaheuristics are used for the calibration of a FDTD-based narrowband simulator. Regarding the simulation of wideband sources, this thesis uses first Lagrange multipliers to characterise the extrema of the numerical group velocity. Then, the spread of numerical Gaussian pulses is characterised analytically in terms of the FDTD grid parameters. The usefulness of the proposed solutions to the previously described problems is illustrated in this thesis using coverage and wideband predictions in large-scale scenarios. In particular, the indoor-to-outdoor radio channel in residential areas is studied. Furthermore, coverage and wideband measurements have also been used to validate the predictions. As a result of all the above, this thesis introduces first an efficient and accurate FDTD simulator. Then, it characterises analytically the propagation of numerical pulses. Finally, the narrowband and wideband indoorto-outdoor channels are modeled using the developed techniques.

New Quasi-optical sensor technology, based on the millimetre and submillimetre band of the electromagnetic spectrum, is actually being implemented for many commercial and scientific applications such as remote sensing, astronomy, collision avoidance radar, etc. These novel devices make use of integrated active and passive structures usually as planar arrays. The electromagnetic design and computer simulation of these new structures requires novel numerical techniques. The Finite Difference Time Domain method (FDTD) is well suited for the electromagnetic analysis of integrated devices using active non-linear elements, but is difficult to use for large and/or periodic structures. A rigorous revision of this popular numerical technique is performed in order to permit FDTD to model practical quasi-optical devices. The system impulse response or discrete Green's function (DGF) for FDTD is determined as a polynomial then the FDTD technique is reformulated as a convolution sum. This new alternative algorithm avoids Absorbing Boundary Conditions (ABC's) and can save large amounts of memory to model wire or slot structures. Many applications for the DGF can be foreseen, going beyond quasi-optical components. As an example, the exact ABC based on the DGF for FDTD is implemented for a single grid wall is presented. The problem of time domain analysis of planar periodic structures modelling only one periodic cell is also investigated. Simple Periodic Boundary Conditions (PBC) can be implemented for FDTD, but they can not handle periodic devices (such as phased shift arrays or dichroic screens) which produce fields periodic in a 4D basis (three spatial dimensions plus time). An extended FDTD scheme is presented which uses Lorentz type coordinate transformations to reduce the problem to 3D. The analysis of non-linear devices using FDTD is also considered in the thesis. In this case, the non linear devices are always model using an equivalent lumped element circuit. These circuits are introduced into the FDTD grid by means of the current density following an iterative implicit algorithm. As a demonstration of the technique a quasi-optically feed slot ring mixer with integral lens is designed for operation at 650 GHz.

The thesis which is hereby presented describes a study of the numerical modelling of the coupled interaction of nanostructures with electromagnetic fields in the range of microwaves. This is a very ambitious task and requires a thorough and rigorous implementation of new algorithms designed to this purpose. The first issue to be encountered is the characterisation and the physical understanding of the behaviour of a nanostructure. The term itself, nanostructure, defines any device which has a nanometric size in at least one dimension, regardless of its material and geometry, hence it is a very wide definition. Carbon Nanotubes (CNT), quantum dots and quantum wells fall into this category, for example, and in electronics these structures are generally composed of semiconductor materials, like Silicon or Gallium Arsenide. The first step to take, in order to model such objects from an electronics point of view, is to solve the Schrodinger equation. The Schrodinger equation is a very general formula, widely used in quantum physics, which, when provided with a certain electrical potential in a material, determines the behaviour of the electrons in this material. Needless to say, the electrical potential is the DNA of a material or, in other words, it is the physical property which affects the propagation of electrons and therefore makes a material conducting or non-conducting. Nanostructures are often composed of several materials, hence the potential is not constant and, with opportune geometries, it is possible, in principle, to guide the electron currents through the device, as, for example, a channel in a MOSFET. This principle holds for very small structures where the electron transport can be considered ballistic, i.e. when the structures are smaller than the free mean path of the particle. The behaviour of the electrons is affected both by external factors, such as temperature or applied electric and magnetic fields, and internal factors, such as the electron mobility or the doping concentration, which are dependent on the used materials. This parameters play a very important role whilst modelling the behaviour of particles such as electrons and in this work the main focus is the study of the impact of external electromagnetic fields. The electromagnetic fields (EM fields) are composed of an electric field component and of a magnetic field component, which can be analysed separately in order to better understand the response of nanostructures to their application. A rigorous analysis is presented by showing numerical results, obtained with the modelling of the Schrodinger equation, compared with the expected theoretical results, exploiting simple structures, where it is possible to calculate the solutions analytically. The second part of thesis focuses on the impact of the EM fields on the nanostructure, hence the combined effect of both electric and magnetic fields affecting the electrons' propagation, and the mutual coupling of the fields with the quantum effects. Indeed the study of nanodevices for microwave applications requires to consider the contribution of a parameter called quantum current density, which accounts for the quantum effects generated by the structure. This is normally ignored in conventional devices because the quantum contributions are negligible but, by using opportune materials and opportune geometries, these currents become relevant and they may have an impact on the propagation of the EM fields. For this reason a consistent part of the thesis is dedicated to investigate the mutual coupling between EM fields and quantum effects, by implementing the Maxwell-Schrodinger coupled model. A chapter is dedicated to the novel approaches taken in order to tackle the issues and the limits of the numerical implementation; in particular two solutions are presented, nonuniform domains and the parallelisation of the algorithm. These approaches are vital whilst modelling numerically such physical problems since the required computational capacity increases with the accuracy requirements. Solving the presented algorithms conventionally would limit the potential of the method and thus a thorough study has been made in order to improve the efficiency of the simulations. In the last chapter, three different scenarios are presented, each one of them showing different features of the coupled model. The results are illustrated and discussed, including the limits due to the chosen approximations. References to the analytical solutions are provided in order to validate the obtained numerical results.

"Localization inside the human body using Radio Frequency (RF) transmission is gaining importance in a number of applications such as Wireless Capsule Endoscopy. The accuracy of RF localization depends on the technology adopted for this purpose. The two most common RF localization technologies use Received Signal Strength (RSS) and Time-Of-Arrival (TOA). This research first provides bounds for accuracy of localization of a Endoscopy capsule inside the human body as it moves through the gastro-Intestinal track with and without randomness in transmit power using RSS based localization with a triangulation algorithm. It is observed that in spite of presence of a large number of anchor nodes; the localization error is still in range of few cm, which is quite high; hence we resort to TOA based localization. Due to lack of a widely accepted model for TOA based localization inside human body we use a computational technique for simulation inside and around the human body, named Finite Difference Time Domain (FDTD). We first show that our proprietary FDTD simulation software shows acceptable results when compared with real empirical measurements using a vector network analyzer. We then show that, the FDTD method, which has been used extensively in all kinds of electromagnetic modeling due to its versatility and simplicity, suffers seriously because of its demanding requirement on memory storage and computation time, which is due to its inherently recursive nature and the need for absorbing boundary conditions. In this research we suggest a novel computationally efficient technique for simulation using FDTD by considering FDTD as a Linear Time Invariant (LTI) system. Then we use the software to simulate the TOA of the narrowband and wideband signals propagated inside the human body for RF localization to compare the accuracies of the two using this method. "