Hello!
Reading up on simulations of electromagnetic scattering with DG-FEM and trying some myself, I got stuck.
In some of papers I have read, a scattering field formulation is used, in which the total field is linearly decomposed in incident field and scattering field:
[itex] E^{T}=E^{S}+E^{I}[/itex]
And, the 2D equations for the scattering field in a lossless, isotropic medium are:
[itex] \epsilon_{r} \frac{\partial E^{S}}{\partial t} = \nabla \times H^{S} - (\epsilon_{r} - \epsilon_{r}^{I}) \frac{\partial E^{i}}{\partial t} [/itex]
[itex] \mu_{r} \frac{\partial H^{S}}{\partial t} = -\nabla \times E^{S} - (\mu_{r} - \mu_{r}^{I}) \frac{\partial H^{i}}{\partial t} [/itex]
My problem is in the interpretation of the "scattering field" and "incident field" in this context. In every use I see of this formulation [itex]\epsilon_{r}[/itex] is space dependent, while [itex]\epsilon_{r}^{I}[/itex] is a constant - specifically, the incident medium's permittivity (same for the permeability). How can this work for multi-substrate cases, where, if I am thinking correctly, the medium considered incident should change?
(I am quite confused with the affair in general, so any clarifications are quite welcome)
Reading up on simulations of electromagnetic scattering with DG-FEM and trying some myself, I got stuck.
In some of papers I have read, a scattering field formulation is used, in which the total field is linearly decomposed in incident field and scattering field:
[itex] E^{T}=E^{S}+E^{I}[/itex]
And, the 2D equations for the scattering field in a lossless, isotropic medium are:
[itex] \epsilon_{r} \frac{\partial E^{S}}{\partial t} = \nabla \times H^{S} - (\epsilon_{r} - \epsilon_{r}^{I}) \frac{\partial E^{i}}{\partial t} [/itex]
[itex] \mu_{r} \frac{\partial H^{S}}{\partial t} = -\nabla \times E^{S} - (\mu_{r} - \mu_{r}^{I}) \frac{\partial H^{i}}{\partial t} [/itex]
My problem is in the interpretation of the "scattering field" and "incident field" in this context. In every use I see of this formulation [itex]\epsilon_{r}[/itex] is space dependent, while [itex]\epsilon_{r}^{I}[/itex] is a constant - specifically, the incident medium's permittivity (same for the permeability). How can this work for multi-substrate cases, where, if I am thinking correctly, the medium considered incident should change?
(I am quite confused with the affair in general, so any clarifications are quite welcome)