Efficient vertical mode expansion method for scattering by arbitrary layered cylindrical structures

Shi, Hua‐Tian; Lu, Ya Yan

doi:10.1364/oe.23.014618

Cited by 12 publications

(7 citation statements)

References 39 publications

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“…The NMM methods are also applicable to three-dimensional (3D) rotationally symmetric structures that are piecewise uniform in the radial variable [15,22]. There is also a related method for more general 3D structures without the rotational symmetry [28,27]. The techniques developed in this paper, namely, the Robin-type boundary condition for terminating the PML and the fast method for computing reference solutions for cylindrical incident waves, should also be useful in these NMM and related methods for 3D structures.…”

Section: Discussionmentioning

confidence: 99%

A Numerical Mode Matching Method for Wave Scattering in a Layered Medium with a Stratified Inhomogeneity

Lu¹,

Lu²,

Song³

2019

SIAM J. Sci. Comput.

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Numerical mode matching (NMM) methods are widely used for analyzing wave propagation and scattering in structures that are piecewise uniform along one spatial direction. For open structures that are unbounded in transverse directions (perpendicular to the uniform direction), the NMM methods use the perfectly matched layer (PML) technique to truncate the transverse variables. When incident waves are specified in homogeneous media surrounding the main structure, the total field is not always outgoing, and the NMM methods rely on reference solutions for each uniform segment. Existing NMM methods have difficulty handing gracing incident waves and special incident waves related to the onset of total internal reflection, and are not very efficient at computing reference solutions for non-plane incident waves. In this paper, a new NMM method is developed to overcome these limitations. A Robin-type boundary condition is proposed to ensure that non-propagating and non-decaying wave field components are not reflected by truncated PMLs. Exponential convergence of the PML solutions based on the hybrid Dirichlet-Robin boundary condition is established theoretically. A fast method is developed for computing reference solutions for cylindrical incident waves. The new NMM is implemented for two-dimensional structures and polarized electromagnetic waves. Numerical experiments are carried out to validate the new NMM method and to demonstrate its performance.

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Section: Discussionmentioning

confidence: 99%

A Numerical Mode Matching Method for Wave Scattering in a Layered Medium with a Stratified Inhomogeneity

Lu¹,

Lu²,

Song³

2019

SIAM J. Sci. Comput.

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“…For practical applications, the cylinders of finite height must be studied. These studies may benefit from the recently developed vertical mode expansion method (VMEM) for scattering problems involving multiple non-circular cylinders of finite height [35][36][37] Appendix A For a system with N circular cylinders surrounded by a homogeneous medium of refractive index n 0 , the matrix A in Eq. ( 5) is an N × N block matrix, b is a vector with N blocks, and they are…”

Section: Discussionmentioning

confidence: 99%

Exceptional points for resonant states on parallel circular dielectric cylinders

Abdrabou

2019

J. Opt. Soc. Am. B

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Exceptional points (EPs) are special parameter values of a non-Hermitian eigenvalue problem where eigenfunctions corresponding to a multiple eigenvalue coalesce. In optics, EPs are associated with a number of counter-intuitive wave phenomena, and have potential applications in lasing, sensing, mode conversion and spontaneous emission processes. For open photonic structures, resonant states are complex-frequency solutions of the Maxwell's equations with outgoing radiation conditions. For open dielectric structures without material gain or loss, the eigenvalue problem for resonant states can have EPs, since it is non-Hermitian due to radiation losses. For applications in nanophotonics, it is important to understand EPs for resonant states on small finite dielectric structures consisting of conventional dielectric materials. To achieve this objective, we study EPs of resonant states on finite sets of parallel infinitely-long circular dielectric cylinders with subwavelength radii. For systems with two, three and four cylinders, we develop an efficient numerical method for computing EPs, present examples for second and third order EPs, and highlight their topological features. Our work provides insight to understanding EPs on more complicated photonic structures, and can be used as a simple platform to explore applications of EPs.

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“…Although general numerical methods, such as the FEM, are available for computing resonant modes even when the media are dispersive, our method is simple, efficient and robust. For scattering problems, the VMEM is applicable to more general structures including cylinders with arbitrary cross sections [39], multiple cylinders [40,41] and periodic arrays of cylinders [42]. We are extending the method for computing resonant modes for such more general structures.…”

Section: Discussionmentioning

confidence: 99%

Computing resonant modes of circular cylindrical resonators by vertical mode expansions

Shi

2019

Phys. Rev. E

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Open subwavelength cylindrical resonators of finite height are widely used in various photonics applications. Circular cylindrical resonators are particularly important in nanophotonics, since they are relatively easy to fabricate and can be designed to exhibit different resonance effects. In this paper, an efficient and robust numerical method is developed for computing resonant modes of circular cylinders which may have a few layers and may be embedded in a layered background. The resonant modes are complex-frequency outgoing solutions of the Maxwell's equations with no sources or incident waves. The method uses field expansions in one-dimensional (1D) "vertical" modes to reduce the original three-dimensional eigenvalue problem to 1D problems, and uses Chebyshev pseudospectral method to compute the 1D modes and set up the discretized eigenvalue problem. In addition, a new iterative scheme is developed so that the 1D nonlinear eigenvalue problems can be reliably solved. For metallic cylinders, the resonant modes are calculated based on analytic models for the dielectric functions of metals. The method is validated by comparisons with existing numerical results, and it is also used to explore subwavelength dielectric cylinders with high-Q resonances and analyze gold nanocylinders.

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Efficient vertical mode expansion method for scattering by arbitrary layered cylindrical structures

Cited by 12 publications

References 39 publications

A Numerical Mode Matching Method for Wave Scattering in a Layered Medium with a Stratified Inhomogeneity

A Numerical Mode Matching Method for Wave Scattering in a Layered Medium with a Stratified Inhomogeneity

Exceptional points for resonant states on parallel circular dielectric cylinders

Computing resonant modes of circular cylindrical resonators by vertical mode expansions

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