Huygens Surface Research Articles

A Multiple Huygens Surface-Based Ray Tracing Framework With GPU Acceleration

A Multiple Huygens Surface-Based Ray Tracing Framework With GPU Acceleration

Updated Radiative Transfer Model for Titan in the Near-infrared Wavelength Range: Validation against Huygens Atmospheric and Surface Measurements and Application to the Cassini/VIMS Observations of the Dragonfly Landing Area

We present an analysis of Titan data acquired by the Cassini Visual and Infrared Mapping Spectrometer (VIMS) at the landing site of the Dragonfly mission, using a new version of our radiative transfer model for Titan, with significant updates for the spectroscopic parameters of atmospheric gases and photochemical aerosols. Our updated radiative transfer model is validated against the in situ spectroscopic measurements of the Huygens probe during its descent and once landed. We confirm that aerosols with a fractal dimension of 2.3–2.4 provide the best fit to the observations. We apply our radiative transfer model to four VIMS data cubes over the Selk crater region including the Dragonfly landing and exploration areas, further validating our model by producing consistent aerosol population and surface albedo maps. These infrared albedo maps, further corrected from the photometry, enable us to study the Selk crater region in terms of surface composition, landscape formation, and evolution. Our results suggest that the Selk crater is in an intermediate state of degradation and that the mountainous terrains of the area (including the crater rim and ejecta) are likely to be dominated by fine grains of tholin-like sediment. This organic sediment would be transported to the lowlands (crater floor and surrounding plains), possibly with water ice particles, by rivers, and further deposited and processed to form the sand particles that feed the neighboring dune fields. These results provide information for the operational and scientific preparation of the Dragonfly mission, paving the way for future exploration of Titan’s surface composition and geology.

Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects.

We investigated how to construct low-order subspace basis sets to accurately represent electromagnetic fields generated within inhomogeneous arbitrary objects by radio-frequency sources external to a Huygen's surface. The basis generation relies on the singular value decomposition of Green's functions integro-differential operators which makes it feasible to derive a reduced-order yet stable model. We present a detailed study of the theoretical and numerical requisites for generating such basis, and show how it can be used to calculate performance limits in magnetic resonance imaging applications. Finally, we propose a novel numerical framework for the computation of characteristic modes of arbitrary inhomogeneous objects. We validated accuracy and convergence properties of the numerical basis against a complete analytical basis in the case of a uniform spherical object. We showed that the discretization of the Huygens's surface has a minimal effect on the accuracy of the calculations, which mainly depended on the electromagnetic solver resolution and order of approximation.

An Explicit Time-Domain Finite-Element Boundary Integral Method for Analysis of Electromagnetic Scattering

A numerical scheme, which hybridizes the element-level dual-field time-domain finite-element domain decomposition method (ELDDM) and the time-domain boundary integral (TDBI) method to accurately and efficiently analyze open-region transient electromagnetic scattering problems, is proposed. Element-level decomposition decouples Maxwell equations on a discretization element from those on its neighboring elements using equivalent currents defined on their faces. For any element inside the computation domain, the equivalent currents are obtained from fields in the neighboring elements. For any element on the boundary of the computation domain, the equivalent currents are obtained using the fields generated by TDBI. To generate these fields, TDBI “radiates” equivalent currents on a Huygens surface enclosing the scatterer. This approach when combined with a leapfrog-type time updates results in a fully explicit numerical scheme that allows ELDDM and TDBI to use different time steps. Numerical results that demonstrate the applicability of the proposed method to concave and disconnected scatterers are presented.

Radiation and Scattering of EM Waves in Large Plasmas Around Objects in Hypersonic Flight

The hypersonic flight regime is conventionally defined for Mach > 5; in these conditions, the flying object becomes enveloped in a plasma. This plasma is densest in thin surface layers, but, in typical situations of interest, it impacts electromagnetic wave propagation in an electrically large volume. We address this problem with a hybrid approach. We employ the equivalence theorem to separate the inhomogeneous plasma region from the surrounding free space via an equivalent (Huygens) surface and the Eikonal approximation to Maxwell equations in the large inhomogeneous region for obtaining equivalent currents on the separating surface. Then, we obtain the scattered field via (exact) free-space radiation of these surface equivalent currents. The method is extensively tested against reference results and then applied to a real-life reentry vehicle with full 3-D plasma computed via computational fluid dynamic (CFD) simulations. We address both scattering [radar cross section (RCS)] from the entire vehicle and radiation from the onboard antennas. From our results, significant radio link path losses can be associated with plasma spatial variations (gradients) and collisional losses to an extent that matches well the usually perceived blackout in crossing layers in the cutoff. Furthermore, we find good agreement with existing literature concerning significant alterations of the radar response (RCS) due to the plasma envelope.

Identifying Interference From Multiple Noise Sources Using Only Magnetic Near Fields

As electronic products become increasingly more complicated, multiple noise sources are likely to simultaneously interfere with the radio frequency (RF) receiver. It will be very helpful if the dominant noise source can be identified when solving the RF interference issue in a complex system. This article proposes a method to separately calculate the contributions from multiple noise sources at their overlapped frequencies so that the worse noise source could be identified even when multiple sources radiate simultaneously. The proposed method creatively employs the decomposition method based on the reciprocity theory to calculate the interference contribution from different sources. Furthermore, in the interest of reducing the near-field scanning time and complexity, the magnetic field only scanning method is developed by using the finite-element method (FEM). In the proposed method, Huygens's surface is established for each source. The tangential magnetic near fields on each Huygens's surface were then applied to solve the corresponding tangential electric fields by the FEM. Subsequently, the sources are removed while the corresponding Huygens's surfaces are maintained. The victim structure is excited under these conditions to obtain the tangential magnetic fields on Huygens's surfaces, and a novel FEM procedure is applied to obtain the tangential electric fields. Finally, based on the electric and magnetic fields, the interference from each noise source can be separately estimated based on the reciprocity theory. This method is validated by a numerical example and measurement. This approach can assist engineers in identifying the contribution of coupling from different sources and in efficiently resolving electromagnetic interference issues.

Accuracy and Conditioning of Surface-Source Based Near-Field to Far-Field Transformations

The conditioning and accuracy of various inverse surface-source formulations are investigated. First, the normal systems of equations are discussed. Second, different implementations of the zero-field condition are analyzed regarding their effect on solution accuracy, conditioning, and source ambiguity. The weighting of the Love-current side constraint is investigated in order to provide an accurate problem-independent methodology. The transformation results for simulated and measured near-field data show a comparable behavior regarding accuracy and conditioning for most of the formulations. Advantages of the Love-current solutions are found only in diagnostic capabilities. Regardless of this, the Love side constraint is a computationally costly way to influence the iterative solver threshold, which is more conveniently controlled with the appropriate type of normal equation. The solution behavior of the inverse surface-source formulations is mostly influenced by the choice of the reconstruction surface. A spherical Huygens surface leads to the best conditioning, whereas the most accurate solutions are found with a tight, possibly convex hull around the antenna under test.

Design of high-efficiency all-dielectric polymer meta-surfaces beam deflection blazed grating

Optical meta-surface element is a kind of two-dimensional ultra-thin device based on the regular arrangement of single-layer or multi-layer sub-wavelength nanostructure array. It can realize the sudden operation of optical amplitude, phase, polarization, the wavelength in a subwavelength scale. In this paper, we design a Huygens meta-surface based on low loss all-dielectric, which can approach the phase control of the outgoing beam after the parallel beam incident on the meta-surface. By the single-layer dielectric nanostructure array, so called Huygens surface, the abnormal transmission without reflection and low loss meta-atoms are realized. Five different beam deflectors were design by these meta-atoms. The different performance of five beam deflectors were discussed, and the effect of wavelength for different beam deflector was investigated next. The highest efficiency of beam deflector is around 85%. The largest deflection angle is 13.248˚ for one polymer grating. These silicon-based beam deflection meta-surfaces may be applied as blazed grating in the monochromator r, precision measurement, and laser shaping.

Method for the Sea Clutter Characterization in HF Surface Wave Radars From the Fields Diffracted by the Sea Surface

A new method for the characterization of the sea clutter in high-frequency surface wave radars is presented. The method is applied for the bistatic and the monostatic case. This method is based on the discretization of the sea surface in multiple patches. The fields diffracted by each patch are determined. Subsequently, the voltage that the diffracted fields induce on the receiving antenna is calculated. The sum of the voltages induced by all the patches is the sea clutter to be characterized. The fields diffracted by the sea patches are characterized in the form of field charts on a Huygens surface surrounding each patch. Field charts are modeled by analytical expressions. The current induced on the receiving antenna by the diffracted fields is calculated by means of the Lorentz reciprocity theorem. The feasibility of the method of characterization of the sea clutter is verified by means of the characterization of the fields diffracted by a single patch. The calculation of the induced current is done using the diffracted fields that are reconstructed from the analytical expressions that model them. It is also verified that the transmitting and receiving antenna can be replaced by plane wave sources, in order to simplify the calculations of the radiated fields that take part in the Lorentz reciprocity theorem. As a validation of the proposed method, the Doppler spectrum of a moving sea surface is calculated for the monostatic case.

Notice of Retraction: Identifying Interference From Multiple Noise Sources by Magnetic Near Fields Only

As electronic products become more and more complicated, multiple noise sources very likely interfere with the radio frequency receiver simultaneously. This paper proposes a method to identify the interference from different noise sources separately, even when they are radiating at the same time. This method converts magnetic fields to electric fields by the finite-element method (FEM) and employs the decomposition method based on reciprocity theory. In the proposed method, Huygens's surface will be set up for each source. The tangential magnetic near fields on each Huygens's surface are used to solve tangential electric fields correspondingly by the FEM. Then, the sources are removed but their Huygens's surfaces are kept. The victim structure is excited in this case to get the tangential magnetic fields on Huygens's surfaces. A creative FEM processing procedure is applied to obtain tangential electric fields in this situation. Finally, with these two groups of fields, the interference from each noise source can be estimated separately based on reciprocity theory. This method is validated by a numerical example. It is very helpful for engineers to be able to identify the contribution of the coupling from different sources and further solve the electromagnetic interference issues efficiently.

A new multilevels Huygens sub-gridding finite difference time domain based on a tree structure and object oriented programming

In this article, an efficient sub-gridding finite-difference time-domain is developed for the simulation of multiscaled electromagnetic problems. The proposed technique is based on using the Huygens surfaces for interfacing electromagnetic fields between different grids. The use of the Object Oriented Programming for modeling FDTD simulations facilitates the imbrication of multiple sub-grids. That heightens the spatial ratio without affecting the accuracy and stability of the sub-gridding technique. Spatiotemporal interpolation is used to evaluate the electromagnetic fields in Huygens surface location among the coarse grid. Results of numerical experiments prove that the use of imbricated sub-grids and spatiotemporal interpolation in the Huygens sub-gridding is more efficient than the use of a single sub-grid with only spatial interpolation.

A Broad-Band Huygens Surface Source Model for Near-Field to Near-Field Transformations

A broad-band Huygens surface method requiring only the measurement of the magnetic field for near-field to near-field transformations is presented. The proposed method is valid down to near dc and supports arbitrary shaped Huygens surfaces. The method relies on an augmented-integral equation formulation that is used to predict the electric field on the Huygens surface. The proposed formulation is discretized using a high-order locally corrected Nystrom method. The surface magnetic and electric fields can then be used to compute external electric and magnetic fields. The method is validated using electromagnetic fields radiated by a three-phase motor showing excellent results over several Fourier harmonics of the motor fields, including the zeroth harmonic. The method is also validated at high frequency for a dipole antenna array.

Investigating the Influence of Spatial Constraints on Ultimate Receive Coil Performance for Monkey Brain MRI at 7 T.

The RF receive coil array has become increasingly vital in current MR imaging practice due to its extended spatial coverage, maintained high SNR, and improved capability of accelerating data acquisition. The performance of a coil array is intrinsically determined by the current patterns generated in coil elements as well as by the induced electromagnetic fields inside the object. Investigations of the ultimate performance constrained by a specific coil space, which defines all possible current patterns flowing within, offer the opportunity to evaluate coil-space parameters (i.e., coverage, coil-to-object distance, layer thickness, and coil element type) without the necessity of considering the realistic coil element geometry, coil elements layout, and number of receive channels in modeling. In this paper, to mimic 7-T monkey RF head coil design, seven hypothetical ultimate coil arrays with different coil-space configurations were mounted over a numerical macaque head model; by using Huygens's surface approximation method, the influences of coil-space design parameters were systematically investigated through evaluating the spatial constrained ultimate intrinsic SNR and ultimate g-factor. Moreover, simulations were also conducted by using four coil arrays with limited number of loop-only elements, in order to explore to what extent the ultimate coil performance can be achieved by using practical coil designs, and hence several guidelines in RF coil design for monkey brain imaging at 7 T have been tentatively concluded. It is believed that the present analysis will offer important implications in novel receive array design for monkey brain MR imaging at ultra-high field.

All-dielectric two-dimensional metasurfaces based on electric and magnetic dipolar Mie resonances

We present a design paradigm of two-dimensional metasurfaces composed of homogenous dielectric nanowires only, which can reliably work at the near-infrared and visible-light frequencies. The design principle is based on the coherent interference between electric and magnetic dipolar modes of a single nanowire, in conjunction with the near-field coupling interactions between neighbouring nanowires in a periodic array. No complicated refractive index profiles or lossy metallic components are needed. By assembling different nanowires into a super cell structure and choosing an appropriate lattice constant, we present an actual physical implementation of the Huygens surface. An effective manipulation on the transmitted wave direction is achieved with a close-to-unity transmittance. A metasurface-based planar lens with short focal distance is unambiguously demonstrated, and potential applications in the related fields are expected.

Internally Combined Volume-Surface Integral Equation for EM Analysis of Inhomogeneous Negative Permittivity Plasma Scatterers

A well-conditioned internally combined volume-surface integral equation (ICVSIE) for analyzing electromagnetic scattering from perfect electrically conducting (PEC) surfaces coated with negative permittivity plasmas is presented. Existing integral equations pertinent to these problems oftentimes yield ill-conditioned systems of equations. The ill-conditioning stems from the presence of interfaces between a positive permittivity background medium and the negative permittivity plasma and/or is due to low-frequency breakdown. To tackle these issues, the proposed ICVSIE wraps the negative permittivity plasma into a Huygens surface and exploits surface equivalence principles to artificially change the sign of the permittivity of the medium in which equivalent volumetric polarization currents radiate. Next, it combines a Muller combined field integral equation on the Huygens surface with a volume-surface integral equation for the negative permittivity plasma that coats the PEC surface in a manner that circumvents low-frequency breakdown. The accuracy, efficiency, and stability of the proposed ICVSIE are demonstrated via its application to various canonical scatterers and a plasma-engulfed reentry vehicle.

Singularity Problem With the One-sheet Huygens Subgridding Method

The Huygens subgridding (HSG) relies on the connection of two finite-difference time-domain (FDTD) grids by means of Huygens surfaces. An earlier work has presented that the Huygens surfaces can be reduced to one sheet of current in place of the usual two sheets. This letter shows that the resulting simplified HSG may be at the origin of inaccuracy in the computed results because of the singularity of the field at the edges of perfect electric or magnetic conductors. The difficulty can be easily overcome in two dimensions but not easily in three dimensions, where it is preferable to use the one sheet implementation only for the outer Huygens surface.

Internally Combined Volume-Surface Integral Equation for a 3-D Electromagnetic Scattering Analysis of High-Contrast Media

An internally combined volume surface integral equation (ICVSIE) for analyzing three-dimensional (3-D) electromagnetic scattering from heterogeneous high-contrast (HC) dielectric objects is proposed. Iteratively solved (generalized) volume integral equations [(g)VIEs] often converge slowly when applied to the analysis of electromagnetic interactions involving dielectric objects with permittivities much higher than those of the surrounding medium [HC breakdown] or discretized using mesh elements much smaller than the wavelength [low-frequency (LF) breakdown]. The proposed ICVSIE hybridizes a VIE and a surface integral equation (SIE) in a manner that eliminates both breakdown phenomena. Just as in previous hybrid VIE–SIE approaches, the ICVSIE invokes Huygens surface equivalence principle to transform the original problem into coupled equivalent exterior and interior scenarios. In the exterior scenario, surface currents radiate in the original surrounding medium; in the interior problem, surface and volume polarization currents radiate in a medium with permittivity closer to that of the object. By judiciously combining integral equations pertinent to both scenarios, the ICVSIE system is assembled. Numerical results show that the proposed ICVSIE is both HC and LF stable when applied to the analysis of 3-D scattering problems.

Huygens Excitation in Debye Media in the FDTD Method

The total-field/scattered-field method, also called the Huygens surface method, is a common method to enforce an incident wave in a finite-difference time domain grid filled with a vacuum. In this communication, it is shown that it can also be used in such dispersive media as the Debye media. The incident wave to be enforced on the Huygens surface is computed either by an analytical calculation in the general case or by means of the auxiliary grid technique in special cases. As in a vacuum, the leakage of energy outside the Huygens surface is lower than −40 dB with the analytical incident wave and it can be far lower with the auxiliary grid incident wave.

All-dielectric circular polarizer with nearly unit transmission efficiency based on cascaded tensor Huygens surface.

In this paper, we demonstrate a high-efficiency and broadband circular polarizer based on cascaded tensor Huygens surface capable of operating in the near-infrared region. The high efficiency originates from the simultaneous excitation of the Mie-type electric and magnetic dipole resonances within an all-dielectric rotationally twisted strips array. Due to the symmetry breaking of the structure in the light propagation, one state of the circularly polarized light can pass through freely, while the other state is largely blocked. The maximum polarization transmission reaches 0.97 with a polarization suppression ratio of 911:1, which represents a major advance in the performance compared with previously reported circular polarizers. The proposed metamaterial possessing the merits of high efficiency and simple inclusions has potentials for applications in biological detector, optical communication and sensor.

High-efficiency beam manipulation combining geometric phase with anisotropic Huygens surface

Conventional geometric metasurfaces relying on space-variant metal antennas for beam manipulation suffer from strong Ohmic loss and incomplete polarization conversion. The efficiency is often limited to rather small values, especially when operating in transmission mode. Here, we tackle this challenge by deliberately constructing an equivalent sheet with anisotropic surface electric and magnetic polarizabilities using cross-shaped dielectric antennas. An incident circularly polarized light can be almost fully converted to a transmitted light of opposite helicity with an unprecedented efficiency up to 98%. Such a transmissive metasurface possessing the merits of high-efficiency, non-dispersion, and robust against variations can serve as an outstanding candidate for flat optics, such as anomalous refraction and beam focusing.