Generalized additional boundary conditions for wire media

Multilayered Wire Media: Generalized Additional Boundary Conditions and Applications

“…However, when two wire mediums are connected with a PEC patch at the junction (see Fig. 4(b), for the multilayer structure with PEC patches), GABCs similar to those proposed in [13] (for the PEC patches) have to be considered at the connection x = x 0 :…”

“…where C is the capacitance of the wires and C 0 is the capacitance of the metallic patch which depends on the period a and gap g (the values of C and C 0 are defined in [13]). These ABCs are accurate for moderate and large gaps between the patches, provided the distance h between the metallic patches in adjacent layers is much greater than g. When the gap between the patches reduces and C 0 → ∞, we have a perfect electric conducting ground plane with the ABCs (9), (10) reduced to dJ c (x)/dx|…”

“…This is because the presence of metallic patches at the wire ends diminishes charge buildup in such a way that, upon homogenization, the mushroom structure can be treated as a uniaxial continuous Epsilon-Negative (ENG) material loaded with a capacitive grid of patches. Further, in [13] generalized additional boundary conditions (GABCs) have been derived for wire media terminated with distributed loads (metallic patch arrays acting as parallel loads to the wires) and lumped loads (arbitrary impedance insertions acting as series loads to the wires) or a combination of both at the junction, with the latter case presented in [18,19]. Although, the GABCs derived in [13] are applied at the wire-to-patch connection with the finite size of the patch (with certain restrictions imposed on the size of the gap between the patches with respect to the separation of adjacent patch arrays), these boundary conditions are valid only for perfect electric conductor terminations.…”

“…Further, in [13] generalized additional boundary conditions (GABCs) have been derived for wire media terminated with distributed loads (metallic patch arrays acting as parallel loads to the wires) and lumped loads (arbitrary impedance insertions acting as series loads to the wires) or a combination of both at the junction, with the latter case presented in [18,19]. Although, the GABCs derived in [13] are applied at the wire-to-patch connection with the finite size of the patch (with certain restrictions imposed on the size of the gap between the patches with respect to the separation of adjacent patch arrays), these boundary conditions are valid only for perfect electric conductor terminations. However, when the metallic terminations (patches) are thin (resistive) (or for no patch case [10]), the charge accumulation and diffusion at the wire-to-patch interface (or charge accumulation at the open wire end interface) becomes important (spatial dispersion effects have to be considered), necessitating a new additional boundary condition at this interface [16], which takes into account the finite conductivity of the material at the connection points.…”

“…This is because the non-local character of the material enables it to support extra (or extraordinary) waves, which in general are not supported by materials with local responses. To overcome this, uniquely solved ABCs [9][10][11]13] which are pertinent to the specific problem (composition of the structure) can be introduced.…”