Scattering of an arbitrary plane wave by a dielectric wedge: Integral equations and fields near the edge

Abstract

[1] The behavior of the field components near the edge has been shown to be that of the static fields, which is derived here without rigor for an infinite wedge. Fields scattered by a finite dielectric wedge illuminated by an arbitrary plane monochromatic wave are computed using either singular or hypersingular integral equations (SIEs or HIEs), derived by the single integral equation method. Field components are then computed near the edge of a finite wedge. Longitudinal components of the fields behave like constants, other components of the electric field behave like those in the transverse magnetic mode, and other components of the magnetic field behave like those in the transverse electric mode. Exceptions occur when approaching the wedge along the bisector. Boundary functions and transverse field components computed with SIEs rise more sharply than predicted approaching the edge after a range in which the agreement with those computed with HIEs is good.

On the Convergence and Accuracy of Numerical Mode Computations of Surface Plasmon Waveguides

“…However, it is apparent from studies conducted to date that the transverse electric and magnetic fields diverge near the edge of the wedge, but that the longitudinal fields remain finite. 48 One could then surmise that the transverse SPP mode fields supported by a 90 metal corner should also diverge as the corner is approached, a hypothesis that is further encouraged (but not verified) by the field distributions of Figures 7 and 9. Field divergence near corners causes slow convergence in the computation of modes in dielectric waveguides, especially for strongly guiding structures.…”

“…[48] and references therein). However, it is apparent from studies conducted to date that the transverse electric and magnetic fields diverge near the edge of the wedge, but that the longitudinal fields remain finite.…”

“…This is sensible considering that the fields might diverge according to a similar power law as dielectric corners, 48 limiting the divergence to an area considerably smaller than the mode size. The rate of convergence also depends on the angle of the metal corner (90 here), so convergence studies should be undertaken for other angles, for example, pertaining to the metal channel or wedge.…”

Integral Equations for 3-D Scattering: Finite Strip on a Substrate

“…Once the integral equations are solved, the electromagnetic fields are obtained by integration. For the two-dimensional configuration the unknown functions diverge at the edges [2], which we expect to be the case in the three-dimensional problem as well. At the vertices P i the divergences could be worse.…”

Electromagnetic fields near plasmonic wedges

“…Meixner's theory is valuable because of its simplicity, but it is approximate; disagreements with numerical methods were reported in the behavior of field components near a dielectric wedge [3] and under different excitation conditions [4]. In the absence of an accurate theory, several approaches have been presented, such as physical optics approximations [5][6][7] and integral equation methods [3,[8][9][10]. Hypersingular integral equations (HIEs) developed by Marx calculate rigorously the fields scattered by a dielectric wedge [8].…”