Boundary conditions of the electromagnetic field

Approximate Boundary Relations on Anisotropic Sheets

“…Regarding the notation, the field quantities in the form A I , A II in (8) and the rest of the paper denote the limiting values of a vector A as one approaches on a point on S from the related regions, while the subscripts t and n indicate the components of any field quantity tangential and normal to S which satisfy A = A t +nA n = (n × A) ×n +n(n · A). The relations (8), (9) were first introduced byİdemen in [6,7] for the special case of a planar interface. In virtue of Theorem A3, the fields (6) are supposed to possess singularities of finite order which also renders the dimension of the sets of the compatibility equations finite and consequently yield the following theorems regarding the orders of singularity on an arbitrary material sheet.…”

Electrodynamics of transformation-based invisibility cloaking

“…[43][44][45] This set of boundary conditions can be categorized into a more general mathematical form of boundary conditions in the sense of the Schwartz distribution theory. 46,47 Recent studies are interested in the metamaterial models that can potentially realize this particular set of boundary conditions.…”

Relativistic Electromagnetic Boundary Conditions

“…3 Our intuitive wiev point will be verified in Footnote 4. 4 Except that one spatial dimension is reduced, four-vector (cσ, K) is similar to the one written in Eq. (11.128) of Ref.…”

“…However, a literature survey can show that electromagnetic boundary conditions are questioned from time to time [1][2][3][4] , although their derivations are of standard textbook knowledge [5]. The present study proposes an analytical examination of the e.m. boundary conditions in an orthogonal curvilinear coordinate system which conforms locally and instantaneously to the boundary surface at a specified point on it.…”