Novel boundary condition for the finite-element solution of arbitrary planar junctions

PadÉ Boundary Conditions for the Finite-Element Modeling of Arbitrary Planar Junctions

“…An alternative 2-D/FEM scheme that avoids the MEBC was recently reported [14]. Though essentially analogous to our PBC algorithm [4], that 2-D/FEM scheme however, does not seem to be straightforwardly generalized to schemes of higher order accuracy.…”

“…In order to calculate the boundary integrals in the right-hand side (RHS) of (3), we express the field at the port in terms of the corresponding slowly varying envelopes, such that (4) where is the reference refractive index for port . For instance, considering Fig.…”

“…A HIGHLY accurate technique, widely used for the simulation of optical junctions and discontinuities, consists of expanding the fields over the ports in terms of the corresponding accessing waveguides modes [1]- [3]. An accurate boundary condition relating the field and its normal derivative then arises, which is called the mode-expansion boundary condition (MEBC) [4]. However, this technique is in general highly time consuming, since the calculation of a large number of modes is normally requested.…”

“…Recently, we reported a simple boundary condition for the two-dimensional finite-element method (2-D/FEM) which permits the simulation of accessing waveguides without the need of calculating waveguide modes, by using a paraxial approximation for the fields' longitudinal variation at the ports [4]. This method, which is called the paraxial boundary condition (PBC), requires less computational effort than the MEBC and performs reasonable well in a wide number of cases, producing more reliable outcomes than the well-known "simple" (impedance) boundary condition (SIBC) in which only one guided mode is assumed to propagate along the access waveguides [4].…”

Aplicação de Redes Neurais Artificiais em Conjunto com o Método Vetorial da Propagação de Feixes na Análise de um Acoplador Direcional Baseado em Fibra Ótica

“…Essas aplicações têm sido alvo da atenção de diferentes autores, por exemplo: divisores de potência [9], [10], [11], [12], [13] e [14]; guias de variação longitudinal [13], [15], [16], [17] e [18]; filtros óticos; multiplexadores; demultiplexadores; roteadores; ressoadores óticos [14] e [11]; grades de Bragg [17]; chaveadores [18], [9] e [13]; estruturas fotônicas periódicas magneto-ótico [19], [20] e [21] etc.…”