A Unified Mode Solver for Optical Waveguides Based on Mapped Barycentric Rational Chebyshev Differentiation Matrix

Zhu, Jianxin; Zhang, Xuecang; Song, Rencheng

doi:10.1109/jlt.2010.2048891

Cited by 5 publications

(1 citation statement)

References 45 publications

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“…Alternatively, the perfectly matched layer (PML) technique has been adopted in several studies to simulate the half-infinite substrate (Huang et al 1996;Treyssede et al 2014) because the PML technique results in a linear eigenvalue problem. One of the main drawbacks of PML is the appearance of the so-called Berenger modes that only depend on the PML parameters (Zhu et al 2010). Careful modal sifting is required to filter the Berenger modes out of the modal solutions (Treyssede et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Calculation of normal and leaky modes for horizontal stratified models based on a semi-analytical spectral element method

Shi,

Ren,

et al. 2022

Geophysical Journal International

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Summary The dispersion curves of surface waves controlled by normal modes have been widely used for the retrieval of subsurface structures. However, only the S-wave velocity structures can be retrieved in most cases because normal modes are primarily sensitive to S-wave velocities. Compared with normal modes, leaky modes, which depend on subsurface structures as well and are more sensitive to P-wave velocities, are rarely applied for subsurface imaging. Besides the difficulties of extracting leaky modes from field data, the calculation of leaky modes also prevents the practical application because traditional methods need to search the leaky-mode roots in the complex frequency-wavenumber domain and thus suffer from root skipping. Recently, some new observation methods support the extraction of multi-order leaky mode dispersion, an effective method for calculating leaky modes is consequently required for further investigation. In this paper, a semi-analytical spectral element method (SASEM) is proposed to solve for the normal and leaky modes of elastic waves propagating in a stratified model with a half-space substrate. The transparent boundary condition and semi-infinite element method are used to model the elastic wavefields in the half-space substrate. Then, a linear eigenvalue problem is derived for the modal calculation. Through simple eigenvalue decomposition, we can obtain the solutions of both normal and leaky modes stably and efficiently without any prior estimations, which makes SASEM very friendly to forward modeling and inversion. Several numerical tests were performed to verify the effectiveness of SASEM, as well as to demonstrate its features of high accuracy and no root skipping. Besides the models composed of several homogeneous layers, SASEM was applied to a vertically inhomogeneous offshore model to demonstrate its wide applicability. Analyses on the oscillations of the solved modes show that the leaky modes differ from the normal modes because of the increasing wavefields in the half-space. Moreover, modal analyses confirm that a part of the leaky modes (guided-P modes) is more dependent on the P waves, whereas the other modes are primarily determined by the S waves. Consequently, the effective calculation of leaky modes makes it possible to constrain the P-wave velocity using leaky-mode dispersion curves.

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Section: Introductionmentioning

confidence: 99%

Calculation of normal and leaky modes for horizontal stratified models based on a semi-analytical spectral element method

Shi,

Ren,

et al. 2022

Geophysical Journal International

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Calculation of normal and leaky modes in planar waveguides based on a semi-analytical spectral element method

Shi¹,

Ren²,

Li³

et al. 2021

Preprint

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A semi-analytical spectral element method (SASEM) is proposed to solve for the normal and leaky modes of elastic waves propagating in a planar waveguide with a half-space substrate. For the SH-wave modes, the transparent boundary condition is used to model the SH wavefields in the half-space substrate. To solve for the PSV-wave normal modes on the (+, +) Riemann sheet and leaky modes on the (+, -) Riemann sheet, the elastic wavefields in the finite-thickness layers are modeled using the displacements, whereas the wavefields in the half-space are modeled using the P-and S-wave potentials. In the substrate, the transparent boundary condition is used for the shear wavefields, whereas semi-infinite elements are introduced to treat the radiative boundary condition of the P wavefields. Then, a polynomial eigenvalue problem is derived, which can be transformed into a standard linear eigenvalue problem. Solving the eigenvalue problem, we can obtain the solutions of the normal and leaky modes. Several numerical tests were performed to verify the effectiveness of SASEM, as well as to demonstrate its high accuracy. Modal analyses of the oscillations of the solved modes demonstrate that the leaky modes differ from the normal modes because of the increasing wavefields in the half-space. Moreover, the guided-P modes are confirmed to be more dependent on the P-waves, whereas the normal and organ-pipe modes are primarily determined by the S-waves. Besides the crustal model composed of several homogeneous layers, SASEM is applied to a vertically inhomogeneous offshore model to demonstrate its applicability. The good agreement between the theoretical guided-P modes and the dispersion spectra not only shows the correctness of SASEM when analyzing waveguides composed of gradient layers but also indicates the potential for constraining the P-wave velocity using the guided-P modes.

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High accuracy modal analysis and beam propagation method for nano-waveguides

Zhang

2012

Opt Quant Electron

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A Unified Mode Solver for Optical Waveguides Based on Mapped Barycentric Rational Chebyshev Differentiation Matrix

Cited by 5 publications

References 45 publications

Calculation of normal and leaky modes for horizontal stratified models based on a semi-analytical spectral element method

Calculation of normal and leaky modes for horizontal stratified models based on a semi-analytical spectral element method

Calculation of normal and leaky modes in planar waveguides based on a semi-analytical spectral element method

High accuracy modal analysis and beam propagation method for nano-waveguides

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