A Frequency-Domain Near-Field-to-Far-Field Transform for Planar Layered Media

Abstract

Abstract-We report a frequency-domain near-field-to-far-field transform (NFFFT) for the numerical modeling of radiation and scattering in planar multilayered spaces. Although the results are equivalent to those of Demarest et al. (1996), the formulation is more compact, more stable, and applicable to observation angles in the lower half space. Furthermore, the results are presented in a vector-potential formalism that is more easily adaptable to existing free-space implementations. The NFFFT algorithm can be used in any differential-equation-based finite numerical method, including but not limited to the finite-difference time-domain (FDTD) method and the finite-element method (FEM).Index Terms-FDTD methods, finite difference methods, finite element methods, near-field far-field transformation.

Angora: A Free Software Package for Finite-Difference Time-Domain Electromagnetic Simulation

“…The phasor-domain nearfi eld-to-far-fi eld transformation is supported for an arbitrary number of layers with any permittivity, perme ability, and electric-conductivity values (see Section 5), whereas the timedomain near-fi eld-to-far-fi eld transformation is supported for up to three lossless planar layers. The phasor-domain near-fi eld-tofar-fi eld transformation for arbitrary lay ering was described (as an extension and generalization of the results in [13]) in [14], and the time-domain near-fi eld-to-far-fi eld transformation for a three-layered medium was described in [15].…”

Extension and Optimization of the Axisymmetric 2.5-D Eigensolver: Toward Far-Field Calculations in Stratified Backgrounds

“…The NFFFT can be derived through either of the two ways: 1) Stratton-Chu formulas [16], [32] or the 2) surfaceequivalence principle [24], [37], [38]. Although both provide the same NFFFT formulas in UBs, the latter has a broader application [37], [38].…”

“…To the best of our knowledge, the NFFFT for 2.5-D eigensolver has not been applied for the cases other than uniform backgrounds (UBs) [16], [32]. The treatment of the NFFFT in SBs should take account of the influence of the scattering within each layer [17], [37]- [39]. Here, we suggest two NFFFTs for SBs: closedsurface and open-surface transformations.…”

Computation of tightly-focused laser beams in the FDTD method

“…The scattered electromagnetic field can then be collected outside the TF/SF boundary (e.g. using a near-field-to-far-field transform for multilayered spaces [25]) and processed suitably to yield a wealth of information. In this subsection, we will numerically calculate the microscope image of a scatterer under focused-beam illumination.…”

“…7. Using the scattered field outside the TF/SF boundary, and propagating it to the far (Fraunhofer) zone using a multilayer NFFFT [25], a numerical microscope image of the scatterer can be synthesized [27]. In Fig.…”