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Time-domain 3-D lattice Green's function (LGF) sequences can be evaluated using a single-lattice point recurrence scheme, and play an important role in finite-difference Green's function diakoptics. Asymptotically, at large distances, the LGFs in three dimensions can be described in terms of six wave constituents, each oscillating with its own instantaneous complex or real frequency. All instantaneous...
The wireless communication range of E-Band point-to-point antenna systems can be extended by increasing the effective isotropic radiated power (EIRP). By employing a focal plane arrays (FPA), the reflector antenna can generate a high EIRP with electronic beam steering. By axially displacing the FPA towards the reflector, the field pattern across the FPA will be broader. Therefore the number of active...
Micromachined microwave cavity filters offer a light-weight, high-Q and highly integrated alternative in the frequency range of 20 GHz–100 GHz as compared to conventional filter types. The filter technology shows potential for use in 5G portable devices and as such, the design of a duplexer operating in the 28 GHz band is demonstrated.
The robust and speedy evaluation of lattice Green's functions LGFs) is crucial to the effectiveness of finite-difference Green's function diakoptics schemes. We have recently determined a generic recurrence scheme for the construction of scalar LGF sequences at arbitrary points on a 3-D cubic lattice. For this recurrence scheme, proper care must be taken to retain sufficient accuracy. For certain...
We have previously reported on the use of Zeil-berger's algorithm to construct a third-order recurrence scheme with polynomial coefficients of the sixth degree, by which 2-D finite-difference time-domain (FDTD) Green's function sequences can be generated on-the-fly. For 3-D cubic lattices, we have managed to find recurrence schemes for lattice points along the symmetry directions. In the non-diagonal...
Modeling strategies for weakly-guiding optical fibres often rely on the weak-guidance approximation. We revisit the vectorial modal field equations in the guise of a modal impedance-angle formalism, and discover that three distinct levels of weak-guidance approximations lead to propagation coefficient solutions that are O(Δn), n = 1,2,3 with respect tot the weak-guidance parameter Δ.
The lookback boundary Green's function diakoptics (GFD) schemes reported on before act on field quantities at the boundary set of disjoint domains. This seems a logical and desirable property, but induces computational complexities. It is also possible to construct a domain-based GFD lookback scheme, akin to a discrete Green's function method developed by Vazquez and Parini. We discuss these limited...
Earlier, we have analysed a finite-difference timedomain (FDTD) toy problem for a configuration with two disjoint domains, each consisting of a single point, using a Green's function diakoptics unlimited lookback scheme, based on the inverse of the stability function. We have developed an analogous scheme for non-trivial problems involving at least one interior point in one of the domains that occurs...
We present the extension of the linear embedding via Green's operators (LEGO) scheme to problems that involve elementary sources localized inside complex structures made of different dielectric media with inclusions. We show how this new feature allows solving problems of wave propagation within, e.g., devices based on electromagnetic band-gap structures.
The discrete space-time-domain wave interaction between distant computational domains can efficiently be described via Green's function diakoptics. For a toy problem with a computational domain consisting of two non-adjacent points, the inverse of the stability function facilitates the derivation of a stable unlimited lookback scheme. This approach permits the use of inter-domain continuous Green's...
Linear embedding via Green's operators (LEGO) is a domain decomposition method for solving electromagnetic problems which involve composite 3-D structures. By combining the standard Method of Moments with a set of macro basis functions obtained through the Arnoldi iteration, the algebraic system of LEGO can be effectively compressed. However, under general circumstances it is not easy to choose the...
We present an efficient formulation based on the linear embedding via Green's operators (LEGO) and the eigencurrent expansion method to optimize composite wave interaction structures, e.g., photonic-crystal based devices. In LEGO, a composite structure is broken up into "bricks" that are characterized through scattering operators and the interaction among them is captured using transfer...
We have extended the linear embedding via Green's operators (LEGO) method to the solution of complicated structures comprised of many different penetrable and conducting media. By combining LEGO with the Arnoldi basis functions, we are able to substantially reduce the size of the relevant algebraic system that arises from the application of the Method of Moments. We review the basics of the overall...
We tackle the scattering from a finite dielectric host medium containing a regular arrangement of (metallic or penetrable) inclusions by using the linear embedding via Green's operators method. After “dicing” the structure into “bricks”, we state an integral equation which we turn into a weak form via the Method of Moments (MoM) with subdomain basis functions. Then, to proceed i) we compress the off-diagonal...
In Green's function diakoptics, wave-field interactions between disjoint domains in space are described in terms of interacting multi-port subsystems. In addition to integral-equation based Green's function diakoptics for time-harmonic fields, a demonstrably stable discrete space-time Green's function diakoptics scheme has been reported to be effective for proximate regions. For distant regions it...
Linear embedding via Green's operators (LEGO) [1,2] is a domain decomposition method in which the electromagnetic scattering by an aggregate of Np bodies (immersed in a homogeneous background medium) is tackled by enclosing each object within an arbitrarily-shaped bounded domain T>k (brick), k = 1,... ,Nd (e.g., see Fig. 1). The bricks are characterized electromagnetically by means of scattering...
We combine the linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) to efficiently deal with 2-D electrically large electromagnetic band-gap (EBG) structures. In LEGO, the composite structure is broken up into elements called “bricks” that are characterized through scattering operators by invoking Love's equivalence principle. The problem is then formulated through...
We combine the linear embedding via Green's operators method with an electric field integral equation (EFIE) to solve the problem of an antenna system which radiates in close proximity of a large 3-D structure. Upon rearranging the relevant equations we include the contribution of the large structure into the EFIE posed over the antenna surface — which results in a “modified” EFIE. The latter can...
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