Constrained power focusing of vector fields: an innovative globally optimal strategy

Abstract

This paper introduces and discusses an innovative approach to focus the electromagnetic power carried by a vector field into a target point, while keeping the field level bounded elsewhere. To overcome the complexity of the underlying NP-hard problem, we introduce a multi-objective optimization framework based on convex programming subproblems. Notably, such a strategy has the unique capability of achieving the globally optimal solution by means of local search algorithms. A numerical analysis is reported to assess the methods' performance, including a comparison with previous contributions. The proposed approach is herein presented in the case of 2D vector fields (transverse electric polarization) but it can be easily extended to the general 3D case.

Thermal and Microwave Constrained Focusing for Patient-Specific Breast Cancer Hyperthermia: A Robustness Assessment

“…Accordingly, ongoing activities are devoted to an extension of the developed tools and analysis of the 3-D case [31]. Moreover, the possibility of achieving multiple-focusing hyperthermia applicators by exploiting superposition effects and multiobjective optimization is also under consideration.…”

An Overview on Synthesis Techniques for Near-Field Focused Antennas

“…Another direct optimization approach is presented in [24,25]. Although [24] is intended for a scalar case in multifocusing applications and [25] is presented as a method for a complete optimization of the radiated field, accounting for its three components, both methods are based on the maximization of the real part of the field radiated at the focal points with additional constraints to vanish the imaginary part of the field and to control the field level at positions apart from the focal points. The choice of a real value field at the focal point does not reduce the degrees of freedom of the problem as far as it represents a simple change of the overall phase reference.…”

“…In case of the methods presented in [24,25], it is also important to point out the differences between the scalar and vector cases, as the scalar case seems to represent a simplified formulation perfectly suitable for focusing applications, while the vector case fits a complete shaping of the 3D NF distribution, accounting for the three components of the radiated field.…”

Near-Field Multibeam Generation by Tensorial Metasurfaces

“…A fast optimization scheme capable of shaping the intensity (norm) of the electric field of continuous radiating apertures is here introduced. Despite the fact that the proposed scheme is not optimal (optimization-wise), as convex ones are [16], [17], it can mold the near field in complex shapes extremely efficiently. In the discussion to follow, normal font characters correspond to scalar quantities, bold symbols to vectors and bold symbols with a double underscore indicate dyadics.…”