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We present an efficient numerical method for simulating the scattering of electromagnetic fields by a multilayered medium with random interfaces. The elements of this algorithm, the Monte Carlo–transformed field expansion method, are (i) an interfacial problem formulation in terms of impedance-impedance operators, (ii) simulation by a high-order perturbation of surfaces approach (the transformed field expansions method), and (iii) efficient computation of the wave field for each random sample by forward and backward substitutions. Our perturbative formulation permits us to solve a sequence of linear problems featuring an operator that isdeterministic, and its LU decomposition matrices can be reused, leading to significant savings in computational effort. With an extensive set of numerical examples, we demonstrate not only the robust and high-order accuracy of our scheme for small to moderate interface deformations, but also how Padé summation can be used to address large deviations.
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On analyticity of scattered fields in layered structures with interfacial graphene
Abstract Two‐dimensional materials such as graphene have become crucial components of most state‐of‐the‐art plasmonic devices. The possibility of not only generating plasmons in the terahertz regime, but also tuning them in real time via chemical doping or electrical gating make them compelling materials for engineers seeking to build accurate sensors. Thus, the faithful modeling of the propagation of linear waves in a layered, periodic structure with such materials at the interfaces is of paramount importance in many branches of the applied sciences. In this paper, we present a novel formulation of the problem featuring surface currents to model the two‐dimensional materials which not only is free of the artificial singularities present in related approaches, but also can be used to deliver a proof of existence, uniqueness, and analytic dependence of solutions. We advocate for a surface integral formulation which is phrased in terms of well‐chosen Impedance–Impedance Operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet–Neumann Operators that appear in classical formulations. With a High‐Order Perturbation of Surfaces approach we are able to give a straightforward demonstration of this new well‐posedness result which only requires the verification that a finite collection of explicitly stated transcendental expressions be nonzero. We further illustrate the utility of this formulation by displaying results of a High‐Order Spectral numerical implementation which is flexible, rapid, and robust.
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- Award ID(s):
- 1813033
- PAR ID:
- 10450090
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Studies in Applied Mathematics
- Volume:
- 147
- Issue:
- 2
- ISSN:
- 0022-2526
- Page Range / eLocation ID:
- p. 527-576
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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