On the active manipulation of fields and applications: I. The quasistatic case

Abstract

Following the ideas proposed in [10] and [11] on active exterior cloaking, we present here a systematic integral equation method to generate suitable quasistatic fields for cloaking, illusions and energy focusing (with given accuracy) in multiple regions of interests. In the quasistatic regime, the central issue is to design appropriate source functions for the Laplace equation so that the resulting solution will satisfy the required properties. We show the existence and non-uniqueness of solutions to the problem and study the physically relevant unique L 2 -minimal energy solution. we also provide some numerical evidences on the feasibility of the proposed approach.

Active manipulation of EM fields in open waveguides

“…The following result shows the existence of a minimal energy solution for (2.20) and follows immediately from Proposition 2.1 by using similar ideas as in [44] or [45].…”

“…As our next step, we combined eight dipoles in a single plane with placement at 0, 45,90,135,180,225,270, and 315 degrees with each dipole at 0.06 off the central waveguide axis (that is, r 0 = 0.06): all dipoles are oriented parallel to the central axis of the waveguide and are in the plane defined by x = 0. The resulting pattern for this ring of eight dipoles (a sub-array) is shown below in Figure 6; in this figure black refers to the pattern at r = 0.07 and x = 0.005, magenta refers to r = 0.07 and x = 0.01, and blue refers to r = 0.07 and x = 0.015.…”

“…One of the authors of the present paper (Onofrei) has developed a general approach, based on the theory of boundary layer potentials [45], for the active manipulation of quasi-static fields with just one active source (antenna) in three dimensions. This approach provides a compact quiet zone exterior to the active source.…”

On the synthesis of acoustic sources with controllable near fields

“…In a recent development in [22] (see also [23] for the low frequency approximation), a general analytical approach based on the theory of boundary layer potentials was proposed for the active acoustic control problem in homogeneous environments. Then, in [24], building up on [22], the authors presented a thorough two dimensional sensitivity analysis for the synthesis of time-harmonic weak radiators with controllable patterns in some exterior region and proved that such acoustic sources will be feasible only if the region of control is in the reactive near-field of the source.…”

Active Radar Cross Section Reduction of an Object Using Microstrip Antennas

“…In these works, cancellation of both electrostatic fields has been shown, as well as time‐varying scalar fields in two and three dimensions by using integral representation theorems. More recently, in Onofrei (, ), Onofrei proposed a unified integral equation method for the construction of a class of approximate solutions for the problem of scalar field manipulation using scalar sources. A sensitivity study for this design in the context of scalar field scattering cancellation was proposed in Norris et al () and Hubenthal and Onofrei ().…”