Full-wave Finite Element Research Articles

Scattering Cancellation-Based Cloaking for the Maxwell-Cattaneo Heat Waves

In this work we theoretically propose scattering cancellation-based cloaks for heat waves that obey the Maxwell-Cattaneo equation. The proposed cloaks possess carefully tailored diffusivity to cancel the dipole scattering from the object that they surround, and thus can render a small object invisible in the near and far fields, as demonstrated by full-wave finite-element simulations. Mantle heat cloaking is further analyzed and proposed to simplify the design and bring this cloaking technology one step closer to its practical implementation, with promising applications in nanoelectronics and defense related applications.

Low-index-contrast waveguide bend based on truncated Eaton lens implemented by graded photonic crystals

Low-index contrast waveguides such as silica waveguides are indispensable part of passive integrated optical components. Reducing the bending radius of silica waveguides with low bend loss is vital in miniaturizing silica planar lightwave circuits. The Eaton lens is a gradient index lens that can bend parallel light rays by 90{\deg}, 180{\deg}, or 360{\deg}. We present a low-loss and compact 90{\deg} waveguide bend with a radius of 9 $\mu$m designed by truncating the Eaton lens. The performance of the designed bend, implemented by graded photonic crystal, was evaluated by full-wave two-dimensional finite element method. The average bend loss in the C-band is 0.9dB while the average bend loss for the wavelength range of 1260-1675nm is 1.05dB. The proposed design strategy can be applied to other low-index contrast waveguides.

Exceptional singular resonance in gain mediated metamaterials.

We study the scattering of optical field by a hybridized metamaterial with properly imprinted gain. We predict that an occasionally real-eigen valued singularity in the interaction matrix of the coupled dark-bright meta-molecule would produce a high-Q resonance. This effect is demonstrated in full-wave three-dimensional finite element optical simulation. Field is efficiently amplified at this resonance. Further investigation shows that the resonance is associated with an exceptional point. The difference of this exceptional singularity from other high-Q resonances such as the spectral singularities in the scattering or transfer matrixes of parity-time symmetric systems and the bound states in the continuum is discussed. The non-Hermitian nature of the exceptional singularity promises some nonlinear applications.

Degenerate four-wave mixing in nonlinear resonators comprising two-dimensional materials: A coupled-mode theory approach

Two-dimensional (2D) or sheet materials have been recently recognized as fascinating materials for nonlinear photonics. Here, we develop a rigorous mathematical framework based on perturbation theory and temporal coupled-mode theory capable of analyzing third-order, ${\ensuremath{\chi}}^{(3)}$, multichannel nonlinear processes in resonant systems comprising 2D materials. The framework is applied to model degenerate four-wave mixing in a guided-wave graphene plasmon-polariton resonant structure, consisting of a standing-wave resonator directly coupled to access waveguides. The results obtained with the proposed framework are compared with full-wave finite-element simulations revealing excellent agreement. Aside from being accurate and efficient, our framework allows for selectively incorporating different nonlinear phenomena, identifying their unique impact on the nonlinear response and providing valuable physical insight. We are, thus, able to specify the optimal operating point leading to maximum conversion efficiency for the generated wave in a multiparameter space. In addition, we identify unstable operating regimes exhibiting optical bistability or limit cycles, thoroughly characterizing the component performance. Our framework enables the study of diverse multichannel phenomena (frequency generation, frequency mixing, and parametric amplification) in the thriving field of 2D material photonics, thus allowing for assessing the potential of these exciting materials for practical nonlinear applications.

First-Order Grating TM Coupling Coefficients for Distributed Feedback Quantum Cascade Lasers

A ray optics (RO) technique utilizing diffraction grating theory and a transfer matrix method is used to derive a closed form expression for the 1st-order distributed feedback coupling coefficient in practical quantum cascade laser structures. Values of the coupling coefficient obtained using a full-wave finite element numerical method (COMSOL Multiphysics) are in good agreement with those obtained using the RO-derived expression.

Patient-specific large-volume hyperthermia in the liver for ultrasound-enhanced drug delivery from thermosensitive carriers

Ultrasound-mediated mild hyperthermia in the range of 39C to 42C is a promising technique for noninvasive targeted release of thermally sensitive carriers in cancer therapy. The need to sustain a temperature rise of a few degrees evenly throughout a large volume currently limits this therapy to regions with a large accessible acoustic window. Furthermore, the need to continuously scan clinically available highly focused therapeutic ultrasound transducers typically used for ablation limits the volume that can be maintained at this temperature for tens of minutes, and greatly extends treatment time per unit volume. In addition, bone structures, such as the ribs, significantly restrict accessible target locations in areas such as the liver and play a significant role in preventing this therapy from entering into clinical practice. In order to overcome these limitations, we present a combined 3D full wave finite element modelling and experimental approach to design a sectored lens that can be placed on focused transducers to enable direct mild heating of a larger volume in the liver while accounting for patient-specific aberration in the prefocal path. [Work supported by the RCUK Digital Economy Programme, grant number EP/G036861/1 (Oxford Centre for Doctoral Training in Healthcare Innovation).]

Zero refractive index in time-Floquet acoustic metamaterials

New scientific investigations of artificially structured materials and experiments have exhibited wave manipulation to the extreme. In particular, zero refractive index metamaterials have been on the front line of wave physics research for their unique wave manipulation properties and application potentials. Remarkably, in such exotic materials, time-harmonic fields have an infinite wavelength and do not exhibit any spatial variations in their phase distribution. This unique feature can be achieved by forcing a Dirac cone to the center of the Brillouin zone (Γ point), as previously predicted and experimentally demonstrated in time-invariant metamaterials by means of accidental degeneracy between three different modes. In this article, we propose a different approach that enables true conical dispersion at Γ with twofold degeneracy and generates zero index properties. We break time-reversal symmetry and exploit a time-Floquet modulation scheme to demonstrate a time-Floquet acoustic metamaterial with zero refractive index. This behavior, predicted using stroboscopic analysis, is confirmed by full-wave finite element simulations. Our results establish the relevance of time-Floquet metamaterials as a novel reconfigurable platform for wave control.

Realizable design of field taper via coordinate transformation.

Complex electromagnetic structures can be designed by exploiting the concept of spatial coordinate transformations. In this paper, we define a coordinate transformation scheme that enables one to taper the electric field between two waveguides of different cross-sections. The electromagnetic field launched from the wide input waveguide is compressed in the proposed field tapering device and guided into the narrow output waveguide. In closed rectangular waveguide configurations, the taper can further play the role of a mode selector due to the output waveguide's cut-off frequency. Realizable permittivity and permeability values that can be achieved with common existing metamaterials are determined from the transformation equations and simplified by a proposed parameter reduction method. Both a 2D continuous design model and a potential 3D discretized realization model are presented at microwave frequencies and the performances of the tapering devices are verified by full-wave finite element numerical simulations. Finally, near-field distributions are shown to demonstrate the field tapering functionality.

Numerical Modeling and De-Embedding of Non-Planar Periodic Guided-Wave Structures via Short-Open Calibration in 3-D FEM Algorithm

In this paper, a numerical short-open calibration (SOC) technique is presented to numerically model and de-embed a variety of non-planar periodic guided-wave structures based on the 3-D full-wave finite element method (FEM). A simple current source or lumped-port model is introduced in formulation of a determinant FEM algorithm. By incorporating the SOC in the FEM solver, the intrinsic port discontinuity caused by this port model is then fully removed or calibrated out of the core non-planar periodic guided-wave structure during the calibration process. Because of the 3-D nature of FEM, the effective per-unit-length parameters of the core periodic guided-wave structure, i.e., effective propagation constant and effective characteristic impedance, are extracted successfully. Two numerical examples, including microstrip line with periodical loading of shorting pins and metal–insulator–metal composite right/left handed structure, are numerically modeled for demonstration and verification. Extracted results have validated the feasibility and accuracy of the presented FEM-SOC, thereby exhibiting its advanced capability in numerical modeling and de-embedding of non-planar structures with complicated configurations.

Elastic metasurfaces for splitting SV- and P-waves in elastic solids

Although recent advances have made it possible to manipulate electromagnetic and acoustic wavefronts with sub-wavelength metasurface slabs, the design of elastodynamic counterparts remains challenging. We introduce a novel but simple design approach to control SV-waves in elastic solids. The proposed metasurface can be fabricated by cutting an array of aligned parallel cracks in a solid such that the materials between the cracks act as plate-like waveguides in the background medium. The plate array is capable of modulating the phase change of SV-wave while keeping the phase of P-wave unchanged. An analytical model for SV-wave incidence is established to calculate the transmission coefficient and the transmitted phase through the plate-like waveguide explicitly. A complete 2π range of phase delay is achieved by selecting different thicknesses for the plates. An elastic metasurface for splitting SV- and P-waves is designed and demonstrated using full wave finite element simulations. Two metasurfaces for focusing plane and cylindrical SV-waves are also presented.

Terahertz attenuators based on dielectric stacks with alternating refractive indices

This article demonstrates the design of dielectric terahertz (THz) attenuators comprising of periodically placed x-cut and z-cut ion-sliced lithium niobate dielectric layers. Changes introduced in the propagating wave due to alternating refractive indices of a ferroelectric material have been exploited for the design of an effective attenuator. The electrical and optical properties gathered from experimental investigations have been used to study the influence of different crystalline orientations on the design. The conduit comprising the periodically placed dielectric slabs has been configured as a tristate switch by modulating the amplitude of the traversing THz wave by altering its angle of incidence. Full-wave finite-element simulations have been conducted over a series of parametric configurations to come up with the optimized design. A modulation depth as high as 94.76% is achieved. The proposed low-cost, easily configurable THz dielectric attenuators operating around 0.625 THz can be potentially used as an external modulator for THz quantum cascade lasers.

Effective media properties of hyperuniform disordered composite materials.

The design challenge of new functional composite materials consisting of multiphase materials has attracted an increasing interest in recent years. In particular, understanding the role of distributions of ordered and disordered particles in a host media is scientifically and technologically important for designing novel materials and devices with superior spectral and angular properties. In this work, the effective medium property of disordered composite materials consisting of hyperuniformly distributed hard particles at different filling fractions is investigated. To accurately extract effective permittivity of a disordered composite material, a full-wave finite element method and the transmission line theory are used. Numerical results show that the theory of hyperuniformity can be conveniently used to design disordered composite materials with good accuracy compared with those materials with randomly dispersed particles. Furthermore, we demonstrate that a Luneburg lens based on the proposed hyperuniform media has superior radiation properties in comparison with previously reported metamaterial designs and it may open up a new avenue in electromagnetic materials-by-design.

Shielding Effectiveness Simulation of SMT EMI Gaskets Utilizing ANSYS HFSS

Abstract As more components populate smaller board areas, the risk of unwanted coupling between components increases. Shielding and radiated emissions tests outlined by IEEE standards such as IEC 61000-4-21 and ASTM4935D identify measurement techniques to quantify shielding effectiveness. In a PCB topology, shields enclose components to create a Faraday cage, but necessitate a method to ground and fasten the shield to the PCB. Typical methods include the use of gaskets, sealants and clips. This paper reviews a gasket methodology and validates a parameterized ANSYS HFSS simulation with the measured relationship between gasket configuration and shielding effectiveness. Surface mount, rectangular, compressible gaskets manufactured by W.L. Gore & Associates, Inc. are used in several configurations to shield a PCB radiator. Radiated emissions measurements are performed in an ETS-Lindgren reverberation chamber to evaluate shielding effectiveness for each configuration. ANSYS HFSS, a full wave Finite Element Method (FEM) electromagnetic simulation solver, is used to simulate each geometric configuration and is verified with measured results.

Time-of-flight dependency on transducer separation distance in a reflective-path guided-wave ultrasonic flow meter at zero flow conditions.

Transit-time flow meters based on guided ultrasonic wave propagation in the pipe spool have several advantages compared to traditional inline ultrasonic flow metering. The extended interrogation field, obtained by continuous leakage from guided waves traveling in the pipe wall, increases robustness toward entrained particles or gas in the flow. In reflective-path guided-wave ultrasonic flow meters (GW-UFMs), the flow equations are derived from signals propagating solely in the pipe wall and from signals passing twice through the fluid. In addition to the time-of-flight (TOF) through the fluid, the fluid path experiences an additional time delay upon reflection at the opposite pipe wall due to specular and non-specular reflections. The present work investigates the influence of these reflections on the TOF in a reflective-path GW-UFM as a function of transducer separation distance at zero flow conditions. Two models are used to describe the signal propagation through the system: (i) a transient full-wave finite element model, and (ii) a combined plane-wave and ray-tracing model. The study shows that a range-dependent time delay is associated with the reflection of the fluid path, introducing transmitter-receiver distance dependence. Based on these results, the applicability of the flow equations derived using model (ii) is discussed.

Topological edge states in acoustic Kagome lattices

We demonstrate that an acoustic Kagome lattice formed by an array of interconnected resonant cavities exhibits a new class of topological states protected by C3 symmetry, and it is characterised by a topological invariant in the form of a winding number in Pauli vector space. This acoustic topological metamaterial can be considered as the two-dimensional analogue of the Su–Schrieffer–Heeger model, exhibiting a topological transition when a detuning is introduced between the inter-cell and intra-cell hopping amplitudes. The topological transition caused by such detuning is accompanied by the opening of a complete topological band gap, which may host edge states. The edge states emerge on either truncated ends of the lattice terminated by a cladding layer or at the domain walls between topologically nontrivial and trivial domains. First-principles simulations based on full-wave finite element method are used to design the lattice and confirm our analytical predictions.

Coupled-mode-theory framework for nonlinear resonators comprising graphene.

A general framework combining perturbation theory and coupled-mode theory is developed for analyzing nonlinear resonant structures comprising dispersive bulk and sheet materials. To allow for conductive sheet materials, a nonlinear current term is introduced in the formulation in addition to the more common nonlinear polarization. The framework is applied to model bistability in a graphene-based traveling-wave resonator system exhibiting third-order nonlinearity. We show that the complex conductivity of graphene disturbs the equality of electric and magnetic energies on resonance (a condition typically taken for granted), due to the reactive power associated with the imaginary part of graphene's surface conductivity. Furthermore, we demonstrate that the dispersive nature of conductive materials must always be taken into account, since it significantly impacts the nonlinear response. This is explained in terms of the energy stored in the surface current, which is zeroed-out when linear dispersion is neglected. The results obtained with the proposed framework are compared with full-wave nonlinear finite-element simulations with excellent agreement. Very low characteristic power for bistability is obtained, indicating the potential of graphene for nonlinear applications.

A coupling model for quasi-normal modes of photonic resonators

We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a generalized eigenvalue problem involving small size dense matrices. We apply this technique to dielectric rod dimmer of rectangular cross section for transverse electric polarization in a two-dimensional setup. The results of our model show excellent agreement with full wave finite element simulations. We provide a convergence analysis, and a simplified model with a few modes to study the influence of the relative position of the two resonators. This model provides interesting physical insights on the coupling scheme at stake in such systems and pave the way for systematic and efficient design and optimization of resonances in more complicated systems, for applications including sensing, antennae and spectral filtering.

Full-wave feasibility study of anti-radar diagnostic of magnetic field based on O-X mode conversion and oblique reflectometry imaging.

An innovative millimeter wave diagnostic is proposed to measure the local magnetic field and edge current as a function of the minor radius in the tokamak pedestal region. The idea is to identify the direction of minimum reflectivity at the O-mode cutoff layer. Correspondingly, the transmissivity due to O-X mode conversion is maximum. That direction, and the angular map of reflectivity around it, contains information on the magnetic field vector B at the cutoff layer. Probing the plasma with different wave frequencies provides the radial profile of B. Full-wave finite-element simulations are presented here in 2D slab geometry. Modeling confirms the existence of a minimum in reflectivity that depends on the magnetic field at the cutoff, as expected from mode conversion physics, giving confidence in the feasibility of the diagnostic. The proposed reflectometric approach is expected to yield superior signal-to-noise ratio and to access wider ranges of density and magnetic field, compared with related radiometric techniques that require the plasma to emit electron Bernstein waves. Due to computational limitations, frequencies of 10-20 GHz were considered in this initial study. Frequencies above the edge electron-cyclotron frequency (f > 28 GHz here) would be preferable for the experiment, because the upper hybrid resonance and right cutoff would lie in the plasma, and would help separate the O-mode of interest from spurious X-waves.

Substrate-integrated waveguide diplexers with improved Y-junctions

Y-junctions are often adopted to design diplexers since their characteristics can conveniently satisfy the constraints for optimum performance of diplexer design. In order to decrease the size of the Y-junction diplexer, the two branches of the junction can be bent to yield parallel outputs. However, this parallel configuration can degrade the characteristic of the Y-junction. In this letter, two improved novel configurations of Y-junction diplexers are introduced, analyzed with an efficient mode-matching based approach and optimized for best performance. For illustration, the method is applied to two diplexers in substrate-integrated waveguide technology realized using band-pass post filters. For each diplexer, the fractional bandwidths of operation for the up and down channels are 2.70% and 2.44% at 7.4 GHz and 8.2 GHz respectively. The viability of the design approach is validated by full-wave finite-element simulations using Ansys HFSS and measurements on the two fabricated diplexers. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:1384–1388, 2016

Effective power delivery filtering of mixed-signal systems with negligible radiated emission

In this paper, an effective noise isolation filter, implemented between the power delivery planes of a mixedsignal system is designed and tested. The filter can be placed between the analog and digital circuits to minimize the wideband noise leakage from digital circuits to narrow-band and sensitive analog devices. The filter is established by an array of semi-lumped element resonators designed to electromagnetically connect the ground and power planes at the operating frequency of analog circuits. The filter is designed at 3.6 GHz and fabricated on a four layer FR4 board. To further reduce the noise coupling and electromagnetic radiations from the PCB, the application of microwave absorbers on the edges of the board are investigated. To compare the results, a full-wave finite element solver is employed.