Novel Volume Integral Equation Approach for Low-Frequency E-Field Dosimetry of Transcranial Magnetic Stimulation.

A new volume integral equation (VIE) approach is introduced to study transcranial magnetic stimulation (TMS) and high-contrast media at low frequencies. This new integral equation offers a simple solution to the high-contrast breakdown observed in low-frequency electric field (E-field) dosimetry of conductive media. Specifically, we employ appropriate approximations that are valid for low frequencies and stabilize the VIE by introducing a basis expansion set that removes solutions associated with high eigenvalues in the equation.

Nano-antenna synthesis for an arbitrary far-field radiation pattern and polarization based on vector spherical wave functions expansion.

A systematic method is proposed to synthesize a nano-antenna based on theoretical principles. This nano-antenna, which is composed of a set of small dielectric spheres, is designed to have a desired far-field radiation pattern and polarization. The basis of the proposed method is expanding all electromagnetic waves into the series of vector spherical wave functions.