An efficient iterative algorithm for computation of scattering from dielectric objects

Liao, Shaolin; Gopalsami, N.; Venugopal, Aneesh; Heifetz, Alexander; Raptis, A.C.

doi:10.1364/oe.19.003304

Cited by 22 publications

(13 citation statements)

References 9 publications

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“…3, at Φ L0 = 4 1 4 π, the four modes degenerates to two doubly-degenerated eigen modes, as expected in the analytical result given in Eq. (16). The one of the two doubly-degenerated eigen modes is a mode with loss and the other one is a mode with gain because κ = 1/4 ∈ 0, 3 − √ 5 /2 .…”

Section: A Dispersion Curvesmentioning

confidence: 98%

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High-Q Interstitial Square Coupled Microring Resonators Arrays

Liao

2020

IEEE J. Quantum Electron.

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The properties of the square array of coupled Microring Resonators (MRRs) with interstitial rings are studied. Dispersion behavior of the interstitial square coupled MRRs is obtained through the transfer matrix method with the Floquet-Bloch periodic condition. Analytical formulas of the eigen wave vectors, band gaps and eigen mode vectors are derived for the special cases of the interstitial square coupled MRRs array with identical couplers and the regular square coupled MRRs array without the interstitial rings. Then, the eigen modes' field distribution are calculated for each of the four eigen wave vectors for a given frequency through the secular equation. Finally, numerical simulation is performed for an interstitial square coupled MRRs array with identical couplers and a regular square coupled MRRs array. The simulation result verifies the analytical analysis. Finally, the loaded quality factors of the interstitial 5-ring configuration, the regular 4-ring configuration and the 1-ring configuration are obtained. It is found that the loaded quality factor of the interstitial 5-ring configuration is up to 20 times and 8 times as high as those of the 1-ring configuration and the regular 4-ring configuration respectively, mainly due to the degenerated eigen modes at the resonant frequency. Thus, the interstitial square coupled MRRs array has the great potential to form high-quality integrated photonics components, including filters and resonance based sensing devices like the parity-time symmetric sensors.

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Section: A Dispersion Curvesmentioning

confidence: 98%

“…The eigen wave vectors are obtained as k (1,2) x = j0.52π/p and k (3,4) x = −j0.52π/p, verifying the analytical result given in Eq. (16). Also, the bottom plot of Fig.…”

Section: A Dispersion Curvesmentioning

confidence: 99%

High-Q Interstitial Square Coupled Microring Resonators Arrays

Liao

2020

IEEE J. Quantum Electron.

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“…For electromagnetic scattering from metallic objects, the Method of Moments (MoM [7]) has been extensively used for computation of electromagnetic scattering of metallic objects. The MoM solves the Maxwell's equations based on the the Electric Field Integral Equation (EFIE [8] ), one of the Surface Integral Equations (SIEs [9], [10]). For objects other than metals such as dielectric objects, the Magnetic Field Integral Equation (MFIE) and the combination of the EFIE and the MFIE, i.e., the Combined Field Integral Equation (CFIE) Shaolin Liao (Corresponding Author: liaoshlin@mail.sysu.edu.cn) is with School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, Guangdong Province, China.…”

Section: Introductionmentioning

confidence: 99%

“…Firstly, the MoM only requires calculation of the electromagnetic field and storage of the surface current on the boundary surface, greatly reducing the computational effort and storage resource. Secondly, fast electromagnetic field propagation methods such as the Fast Multipole Method (FMM [14]) and the Fast Fourier Transform (FFT [10], [15]) method are readily available to accelerate the MoM impedance matrix computation. At last but not the least, efficient matrix inverse algorithms [16], [17], [18] such as the iterative Generalized Minimal REsidual Method (GMRES [18]) can be used to solve the MoM equation.…”

Section: Introductionmentioning

confidence: 99%

An Electromagnetic Ping-Pong Algorithm forPlanar Reflector Antennas of Arbitrary Shapes

Liao¹,

Ou²

2021

Preprint

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An efficient Ping-Pong algorithm is presented to deal with electromagnetic scattering from planar reflector antennas of arbitrary geometric shapes. The proposed Computational Electromagnetics (CEM) algorithm does not require formation, storage and inverse of the impedance matrix used by the Method of Moments (MoM). Instead, a rigorous formula is obtained for computation of the surface current from the scattering electric field. Besides, the algorithm only contains convolution operations with the scalar Green’s function and second derivatives operations to iteratively update the surface currents and scattering electric field. Also, hypersingular integration arising from the singularities of the surface current and scattering electric field is properly regularized. Furthermore, the algorithm converges fast and satisfactory results are obtained after a few iterations. Besides, the first iteration gives the solution for reflector antennas on perfect absorption substrates. Numerical solutions are obtained for some typical antennas and comparisons are made to those in the literature and from the MoM.

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“…Following the pioneering theoretical work by El-Ganainy et al [21], the feasibility of translating this quantum-inspired symmetry to the optics regime has been demonstrated in a various contributions and, specifically, in coupled optical structures [22][23][24][25][26][27]. Later, it has also been demonstrated in the electromagnetic and acoustic systems [28,29], whose governing Helmholtz equation [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] is similar to the Schrödinger equation in the quantum physics. These PT-symmetric wave systems are usually realized by introducing the spatial distribution of balanced gain-loss profiles.…”

Section: Introductionmentioning

confidence: 99%

Rigorous Quantum Formulation of Parity-Time Symmetric Coupled Resonators

Liao¹,

Ou²

2020

PIER M

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Rigorous quantum formulation of the Parity-Time (PT) symmetry phenomenon in the RF/microwave regime for a pair of coil resonators with lump elements has been presented. The coil resonator is described by the lump-element model that consists of an inductor (L), a resistor (R), and a capacitor (C). Rigorous quantum Hamiltonian for the coupled RLC coil resonators system has been derived through twice basis transforms of the original basis. The first basis transform rotates the original basis such that off-diagonal terms of the governing matrix of the equation system of the coupled coil resonators is reduced to constants. Then a second basis transform obtains the quantum Hamiltonian, including the diagonal effective complex frequencies and off-diagonal coupling terms, together with the transformed basis. With the obtained quantum Hamiltonian, the eigenvalues and eigenvectors of the coupled coil resonators can be obtained as usual as the quantum Hamiltonian. Finally, numerical simulation verifies the correctness of the theory. The quantum formulation of the coupled coil resonators can provide better guideline to design a better PT-symmetric system.

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An efficient iterative algorithm for computation of scattering from dielectric objects

Cited by 22 publications

References 9 publications

High-Q Interstitial Square Coupled Microring Resonators Arrays

High-Q Interstitial Square Coupled Microring Resonators Arrays

An Electromagnetic Ping-Pong Algorithm forPlanar Reflector Antennas of Arbitrary Shapes

Rigorous Quantum Formulation of Parity-Time Symmetric Coupled Resonators

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