Dyadic Green's Function Method Research Articles

A Ray Tracing Tool for Propagation Modeling in Layered Media: A Case Study at the Chip Scale

Nowadays, many wireless applications require the exchange of electromagnetic waves through propagation environments that look like to stratified media to some extent. This may concern both natural scenarios, e.g., air/vegetation/ground, and artificial structures, like meta-materials, photonic devices, solar cells or systems-on-chip. The characterization of the layered propagation channel is therefore important for the design and deployment of effective devices and systems. To this aim, the Dyadic Green Function method has been often leveraged, although its use is usually limited to simple sources, like short dipoles or current elements. Furthermore, it seems unsuited to assess the dispersive properties of the channel, which are known to become important when high data-rate must be conveyed. In this paper, a ray-based approach to propagation inside layers is proposed. As the layered environment can be quite reverberating, a great number of rays may be needed, to the extent that the corresponding computational burden might be hardly afforded by general purpose ray tracing tools. Therefore, the ray tracing engine here presented is specifically conceived for the layered case, and mostly relies on analytical formulation. The accuracy of the model is checked against measurement carried out at chip scale at optical frequency, as a reference study case.

On Surface-Wave Suppression of Differential Circular Microstrip Antennas

Differential microstrip antennas have received considerable attention in the design of highly integrated radio transceivers for wireless communications. A study of the surface waves excited by the single-ended and differential feeds is presented for the circular microstrip antennas. The cavity-mode theory and the dyadic Green's function method are combined to rigorously calculate the surface-wave field excited by each mode for the circular microstrip antennas under single-ended and differential feedings, respectively. The vertical monopole probe antenna is used to measure the TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -mode surface wave excited by the single-ended and differential circular microstrip antennas, respectively. The measured and calculated results confirm that the surface wave excited by the differential feeding is smaller than that excited by the single-ended counterpart.

A Simple Approach to Evaluate Near Field Thermal Radiation From Emitters With Layered Structures and Temperature Variations in One Direction

Abstract A simple analytical calculation scheme to determine near field radiation through decomposing an emission domain into lots of thin thermal current sheets is presented. Through finding the orthogonal modes of thermal current of each thin layer, the thin current sheets can be treated as radiation sources of electromagnetic waves with determined analytical solutions. The outgoing electromagnetic waves from each thin current sheets can be either in transverse electric (TE) or transverse magnetic (TM) modes depending on the orientations of the current in the thin current sheets with respect to the directions of amplitude modulations of the orthogonal modes. Electromagnetic waves arriving to a collection domain are related to the electromagnetic waves leaving from each thin current thermal sheet with transfer coefficients. Transfer coefficient for TE and TM waves can be determined analytically with transfer matrix method or scattering matrix methods. Compared with existing dyadic Green's function method, the new calculation scheme allows material and temperature variations along one direction of the emission domain based on determined analytical expressions of TE and TM waves leaving from each thin current sheets. The simple calculation scheme is especially useful in near field radiation of layered structures with different material such as hyperbolic material with negative refractive indices. With this new approach, we recovered analytical solutions of near field radiation between two semi-infinite domains with uniform temperature and derived closed form solution of near field radiation between two semi-infinite domains with temperature profiles with/without laminated structures.

Spontaneous emission and energy shifts of a Rydberg rubidium atom close to an optical nanofiber

In this paper, we report on numerical calculations of the spontaneous emission rates and Lamb shifts of a $^{87}\text{Rb}$ atom in a Rydberg-excited state $\left(n\leq30\right)$ located close to a silica optical nanofiber. We investigate how these quantities depend on the fiber's radius, the distance of the atom to the fiber, the direction of the atomic angular momentum polarization as well as the different atomic quantum numbers. We also study the contribution of quadrupolar transitions, which may be substantial for highly polarizable Rydberg states. Our calculations are performed in the macroscopic quantum electrodynamics formalism, based on the dyadic Green's function method. This allows us to take dispersive and absorptive characteristics of silica into account; this is of major importance since Rydberg atoms emit along many different transitions whose frequencies cover a wide range of the electromagnetic spectrum. Our work is an important initial step towards building a Rydberg atom-nanofiber interface for quantum optics and quantum information purposes.

General model of optical frequency conversion in homogeneous media: Application to second-harmonic generation in an ε -near-zero waveguide

Traditional optical frequency conversion model is well improved in this work. In terms of the dyadic Green's function method, a set of coupled-amplitude equations is reduced under a proposed transition layer assumption, accompanying the simultaneous integral equations. The model, as a generalization of the current frequency conversion theory, is aimed at any one-dimensional thin film or bulk nonlinear structure, allowing for arbitrary optical anisotropy and absorption without pumping and propagating limitations. The assumption reasonably simplifies the strict nonlinear boundary conditions and enables the equations to yield exact radiative field solutions. A field-enhanced phase-matching configuration is designed for second harmonic generation in a lossy $\ensuremath{\epsilon}$-near-zero material. The high contrast of refractive indices between a substrate (silicon) and the material traps the harmonic wave inside and constructs a natural mirror reflection waveguide. A simulation in the lowest guided mode predicts an efficiency enhancement proportional to the relative wave impedance to the fifth power under a resonant condition.

High-performance electroluminescent refrigeration enabled by photon tunneling

Electroluminescent refrigeration, though theoretically proposed half a century ago, is rarely reported due to the requirement of extremely low nonidealities. Here, we theoretically show that by operating the device in the near-field regime with a vacuum gap down to 10nm, photon tunneling through evanescent waves can increase the tolerance of non-intrinsic nonradiative recombination to 31.6%. More importantly, the refrigeration rate may be enhanced by 2000-fold over the far-field scenario. In addition, the lowest achievable cooling temperature against the ambient condition of 300K extends from 284.2K to 270.6K. A self-consisted model based on the fluctuation-dissipation theory combined with dyadic Green's function method is developed considering the effect of the chemical potential of photons on the energy of Planck's quantum oscillators. This work opens a route to greatly enhance electroluminescent refrigeration, while relieving the strict material's requirement, for solid-state noncontact thermal management.

Analysis of imaging properties of a microlens based on the method for a dyadic Green's function

The dyadic Green's function (DGF) is applied to examine the effect of focal shift in a spherical microlens with the variation of the numerical aperture for a given Fresnel number when a monochromatic plane wave with x linear polarization is incident on the microlens. By comparing the results based on the method for the vector Kirchhoff diffraction theory [J. Opt. Soc. Am. A22, 68-76 (2005)], the effect of the spherical aberration on focal shift in a microlens is evaluated, and the influences of NA as well as the spherical aberration on the transverse electric energy density distribution in the focal plane are also investigated. In contrast with other vector formulations of imaging theory, which mainly focus on the focal shift in an aplanatic system, the DGF method is more practical and effective to locate the principal maximum energy density along the normal axis and to study transverse electric energy density distribution, because the actual shape of a microlens and the effects of aberrations are considered.

Thermal radiation in 1D photonic crystals

Optical properties of periodic structures, or photonic crystals, have been studied extensively over the last two decades. While thermal radiation from surface grating structures has also been investigated, radiation inside a photonic crystal has not been investigated completely. We have developed a method to analyze thermal radiation in 1D periodic layered media using a modified dyadic Green's function method and the fluctuation–dissipation theorem. Using the method, thermal radiation between layers in periodic structures made of ultra-thin metallic films is analyzed. The unusual features of thermal radiation in such structures are explained.

Electromagnetic fields inside a lossy, multilayered spherical head phantom excited by MRI coils: models and methods

The precise evaluation of electromagnetic field (EMF) distributions inside biological samples is becoming an increasingly important design requirement for high field MRI systems. In evaluating the induced fields caused by magnetic field gradients and RF transmitter coils, a multilayered dielectric spherical head model is proposed to provide a better understanding of electromagnetic interactions when compared to a traditional homogeneous head phantom. This paper presents Debye potential (DP) and Dyadic Green's function (DGF)-based solutions of the EMFs inside a head-sized, stratified sphere with similar radial conductivity and permittivity profiles as a human head. The DP approach is formulated for the symmetric case in which the source is a circular loop carrying a harmonic-formed current over a wide frequency range. The DGF method is developed for generic cases in which the source may be any kind of RF coil whose current distribution can be evaluated using the method of moments. The calculated EMFs can then be used to deduce MRI imaging parameters. The proposed methods, while not representing the full complexity of a head model, offer advantages in rapid prototyping as the computation times are much lower than a full finite difference time domain calculation using a complex head model. Test examples demonstrate the capability of the proposed models/methods. It is anticipated that this model will be of particular value for high field MRI applications, especially the rapid evaluation of RF resonator (surface and volume coils) and high performance gradient set designs.

Direct Integration of Field Equations - Abstract

In this work the integral expressions of the field equations in electrostatics, magnetostatic, and electrodynamics are derived first with the aid of a scale-vector Green's theorem. The results can be interpreted by the proper sets of potential functions. For the electrodynamic case we call attention to the fact that Schelkunoff's formulas derived by applying the equivalence principle are equivalent to Stratton and Chu's. The superior nature of Franz's formulas based on the method of dyadic Green Functions is then reviewed and shown to contain the missing line integrals deliberately added by Stratton and Chu, which are also missing in Schelkunoff's formula.

A full-wave model for EMI prediction in planar microstrip circuits excited in the near-field of a short electric dipole

A full-wave model to evaluate the interference induced in planar microstrip lines of arbitrary shape exposed to the near-field of an elementary electric dipole is presented. The analysis of the line response, consisting in the evaluation of the surface current excited along the microstrip line, is based on the electric dyadic Green's function method. The surface current induced on the metal strip which, for the sake of generality, is considered as embedded in the dielectric substrate, is obtained solving by means of the spectral-domain approach (SDA) the electric integral equation, which enforces the boundary condition of zero tangential electric field on the surface of the strip. The induced current is computed for different line geometries and loads, and for various positions (inside or outside the dielectric substrate) and orientations of the dipolar source. Indications towards reducing the level of the signal induced on the loads of the line are inferred.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the time‐domain response of microstrip dipoles embedded in a low‐loss grounded dielectric slab

AbstractA space‐time analysis of the field radiated from microstrip dipoles embedded in a low‐loss grounded dielectric slab is proposed. The analysis is based on the dyadic Green's function method. The radiation mechanism as well as the structure electrical and geometrical parameters influencing the radiation phenomenon are analyzed. Design guidelines to reduce the amplitude of the radiated field, or its distortion, are suggested. © 1993 John Wiley &amp; sons, Inc.

Reduced angular sensitivity frequency selective surface

A new FSS geometry consisting of an open ring loaded with a square patch is proposed and analysed using a dyadic Green function method. It is shown that the square patch reduces the angular sensitivity of the reflection coefficient, which is further reduced by increasing the open circuit gap size.

Application of the dyadic Green's function method to calculate the heat generated by a direct contact applicator.

A rigorous formalism using the dyadic Green's function to determine the relative heating pattern in a two-layer fat-muscle medium of a dipole-corner reflector applicator in direct contact with the finite fat layer is described. The results are compared with the earlier approximate calculations of Guy and Lehmann. Though the two theories give identical results for the relative heat produced in the muscle layer, the relative heating patterns predicted by the present theory in the fat layer are different.

Radiation Characteristics of an Electric Dipole in a Warm, Anisotropic Plasma

By means of the dyadic Green's function method, a formula is derived for the impedance matrix of an electric-current source immersed in a warm plasma under the influence of an external static magnetic field. A dispersion equation is given. The results are expressed in terms of the components of the compressivity and the permittivity tensors. It is shown that the power radiated by an electric dipole in such a medium can be written as the Hermitian form associated with the impedance matrix. Some numerical results are also included.

Microwave circuit characteristics of bulk GaAs oscillators

The microwave circuit characteristics of bulk GaAs transit-time mode and limited space-charge accumulation (LSA) mode oscillators have been evaluated experimentally and theoretically. Experimental measurements were performed with a waveguide-coaxial microwave circuit having two experimental degrees of freedom in which the circuit radiation impedance at the device contacts was evaluated by a dyadic Green's function method. Experiments conducted in three rectangular waveguide circuits at fixed bias voltage have established that the LSA mode frequency tuning range is determined by the magnitude and variation of the circuit series inductive reactance X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> relative to the device low-field resistance R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> . At a bias voltage which is twice threshold the tuning range is given by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2.4\leq X_{L}/R_{0}\leq 2.4</tex> . No fixed, linear equivalent circuit characterizes the LSA mode. Analysis and experimental results indicate that the device impedance of small-signal transit-time mode oscillators changes from a passive parallel RC impedance well below threshold to an impedance just above threshold which can be approximated by a series RLC circuit. The series L and C decrease linearly with transit-time mode harmonic order number.