A Decoupled Formulation of the Vector Wave Equation in Orthogonal Curvilinear Coordinates, with Application to Ferrite-Filled and Curved Waveguides of General Cross Section

Pseudo-Analytical Modeling for Electromagnetic Well-Logging Tools in Complex Geophysical Formations

“…To proceed, we will use a procedure introduced in [51,144], in which new transversal fields are defined by…”

“…To decouple these equations, we follow the process shown in [51,Ch. 2] and [144]. To take the decouple process we need to combine these equations in such a way that the axial (E and H) and transversal (E t and H t ) fields come together in a form involving a single combinations.…”

“…The approach proposed here allow us to decouple the differential equations for the axial fields (by means of the auxiliary fields G ± ) merely by carrying out a matrix digitalization, instead of employing a bi-complex variable as in [51,144].…”

Eigenvalue Analysis of Curved Open Waveguides Using a Finite Difference Frequency Domain Method Employing Orthogonal Curvilinear Coordinates

“…Considering wave propagation toward the positive u 3 -direction as ∝ e −jβu3 , then ∂/∂u 3 −→ −jβ, provided that the metric factor h 3 is independent of u 3 , according to Lewin,[8]. This propagation assumption restricts the curve of the guide axis to shapes in which ∂h 3 /∂u 3 = 0, or curves of constant curvature.…”

“…(4) we have to impose certain restrictions on the metric coefficients h 1 and h 2 . Again, according to Lewin [8], these must be also independent of u 3 , namely ∂h 1 /∂h 3 = 0, ∂h 2 /∂h 3 = 0.…”