Field Theory Handbook

Current Distribution and Impedance of a Cylindrical Antenna in an Isotropic Compressible Plasma

“…If we are in source-free regions, Helmholtz•s Principle [Moon, 1961], which states that any v~ctor fie}d well behaved at infinity can be completely specified as the sum of an irrotational vector field and a solenoidal vector field, may be applied to justify the modal decomposition. The opticd mo.de would then be solenoidal, and the plasma mode would be irrotationa1.…”

Ray Optics at a Deep-Subwavelength Scale: A Transformation Optics Approach

“…We realize that metamaterials with rapidly varying optical properties can still comply with the ray optics approximations under certain conditions: the existence of an equivalent space, in which the light experiences an effective homogeneous medium along its propagation and flows along linear ray trajectories. The invariance of the Maxwell equation under conformal transformation 23 ensures that the ray-like behavior will be sustained in the original space, where the light propagates along curVed ray trajectories ( Figure 1b).…”

“…and represented by the coordinate system (u, V), which can be easily extended to a three-dimensional space by translation or rotation. 23 The light flows in the form of ray trajectories along the V axis (Figure 1b). We define s b ) (ε, µ) and s b′ ) (ε′, µ′) to be the diagonalized constituents of the permittivity and permeability along the (u, V, w) axes in the Cartesian and curvilinear representations of (u, V, w), respectively (e.g., Figures S1 and S2 in the Supporting Information).…”

“…18 The degeneracy (h u ) h V ) originates from the Cauchy-Riemann relationships (∂x/∂u ) ∂y/∂V, ∂x/∂V ) -∂y/∂u) 23 and simplifies the design and analysis of the optical system. A diffraction-free propagation throughout the medium requires dispersion relations k V (k u ), where the V axis is the light flow direction, in the form of…”

“…In Figure 3a, the coordinates are represented by the blue lines (V axis) and the interfaces between the layers (u axis). Such curvilinear coordinates are mapped onto the Cartesian space (x, y, z) through bipolar transformations 23 x -iy ) R coth ( u 1 + iV 1 2 ) for region I,…”