An Integral Equation Approach Towards the Design of Compact Metasurface Pairs

Design and Experimental Evaluation of Cascaded Metasurface Pairs

“…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 order for the equivalent problem to be consistent, we ensure that the fields radiated by these currents result in the very same fields given by ( 7)- (10). This can be succinctly described by the following equations [10]…”

“…In the case of the latter, the goal is to find the fields in the bounded space between the metasurface pair that satisfy the LPC condition for a desired field transformation. The algorithms to design cascaded metasurface pairs can roughly be classified into the following categories: iterative Fourierbased techniques [7], optimization techniques based on the plane wave spectrum (PWS) [6], [8], [9], and optimization algorithms based on integral equation (IE) formulations [10], [11]. The majority of the literature regarding cascaded metasurface pair design relies on simulation data.…”

“…This design algorithm is itself based on [6] and extends it to be fully automated. The other is an IE-based approach which follows [10]. For a particular design problem, we first present simulation data using different metasurface unit cell models.…”

“…The goal of the metasurface pair design algorithms considered herein is to find the internal forward and reflected waves, u fwd and u ref , such that the LPC condition is met at each unit cell of both metasurfaces. The unknowns to be found in either or both design methods are highlighted in red (based on the figure from [10]).…”