A boundary element technique applied to the analysis of waveguides with periodic surface corrugations

Floquet Multipliers of Periodic Waveguides via Dirichlet-to-Neumann Maps

“…The smaller x-extent of 1 is 2/π. This example makes frequent appearances in the literature; see, e.g., [3].…”

“…Because of the dispersion relation some of the entries in the matrix depend on γ in a highly nonlinear fashion. The numerical method used for this problem is to solve det A(γ ) = 0 by either Newton's or Muller's method [3]. However, discretizations lead to large ill-conditioned systems and hence the determinant is a bad indicator for the numerical rank of a matrix.…”

Entire domain integral equation analysis of periodic dielectric waveguides

“…Then, we need to restrict (x,z) in (8) on the gratings domains. Thus, we consider a) (x,z) on S g 1 and b) (x,z) on S g 2 and expand u in (8) in the Fourier series (7). In addition, we take the inner products of both sides of (8) with the test functions (conjugates of the expansion functions of (7)) 6 …”

“…The propagation phenomena in dielectric grating waveguides have been investigated by a number of methodologies including: the coupled-mode theory [5], the Floquet-Bloch theory [6], and sub-domain integral equation techniques in connection with the boundary element method [7]. The first method incorporates several approximations, while the accuracy of the latter two depends on the numerical evaluation of the resulting integrals or solutions of differential equations systems and on the discretization in boundary elements.…”

The Waveguide Eigenvalue Problem and the Tensor Infinite Arnoldi Method

“…Benchmark example. In order to illustrate properties of our approach, we consider a waveguide previously analyzed in [31,9]. We set the wavenumber as in Figure 5.1, where K 1 = √ 2.3 ω, K 2 = √ 3 ω, K 3 = ω and ω = π.…”