On the Formulation and Implementation of the Love’s Condition Constraint for the Source Reconstruction Method

Design and Experimental Evaluation of Cascaded Metasurface Pairs

“…This can be understood by the equivalent interpretation of ( 11)-( 12) (which describe forward and reflected waves); when transformed into ( 13)-( 14), the equations instead represent an enforcement of Love's condition. Since this can be made irrespective of the geometry of the equivalent problem [16], [17], it follows that the IE-based algorithm can be applied to metasurface pairs with arbitrary shapes and orientations.…”

“…The IE-based approach can be derived in a similar manner to the PWS-based approach. To begin, as in [10], we apply Love's equivalence principle [16]- [18] to the internal region bounded by the metasurface pair (but not including the metasurfaces themselves), generating an equivalent problem for this region. This requires the imposition of equivalent electric ( ⃗ J) and magnetic ( ⃗ M ) currents on the closed (and rectangular) surface S (see Fig 1) which produce the forward and reflected travelling waves in the internal region.…”

“…In the optimization step, we minimize both the LPC cost functional and this constraint. A careful consideration of ( 13)-( 14) will show that this is equivalent to a Love's constraint [16], [17]; i.e., this constraint has the effect of enforcing the zero-field condition outside of the equivalent region.…”

Stabilized Single Current Inverse Source Formulations Based on Steklov–Poincaré Mappings

“…Moreover, it should also be noted that it is not necessary to solve both (15) and ( 16) to obtain both currents: once one of the two currents has been computed (discretized with RWGs), the discretization of the other as a linear combination of BCs can be obtained after back substitution in (12). In addition, only one current is required to compute the probed field in the outside region by using (13) or (14), respectively, following the discretization strategies delineated above with the sole difference that the leftmost operators must be evaluated in the point of interest, and not tested with primal or dual functions. Finally, it is noted that the introduced single-source formulations need the additional inversion of first and second kind operators in ( 16) and ( 15) respectively.…”

“…Another feature of interest among inverse source schemes is their capacity to find equivalent Love currents-that are directly related to the tangential fields-which is considered in the literature particularly useful for antenna diagnostics [6], [12]. The Love currents can be obtained by adding further constraints to double current formulations [6], [13], [14] or by filtering any of the solution via Calderón projection [15]. Another interesting approach, leveraging Huygens radiators and valid for plane waves, has been proposed in [16] to reduce the size of the Love-constrained problem to that of a single current formulation, at the price of an approximation.…”