Generalized Modal Expansion of Electromagnetic Field in 2-D Bounded and Unbounded Media

Dai, Qi I.; Chew, Weng Cho; Lo, Yat Hei; Liu, Y. G.; Jiang, Li Jun

doi:10.1109/lawp.2012.2215571

Cited by 16 publications

(11 citation statements)

References 8 publications

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“…They have less generality and limited applications. The present work demonstrates a generalized modal expansion analysis leading to a unified treatment for arbitrary 3-D vector-wave problems, which is an extension of the recent paper addressing simple 2-D scalar problems [22]. In this work, we implement an efficient conformal finite-difference (FD) scheme to model several real devices, and interpret the complicated wave-matter interactions by using a reduced modal picture of CEM data.…”

Section: Introductionmentioning

confidence: 94%

“…Furthermore, we can obtain the nondegenerate orthogonality conditions as (19) Similar to the original problem, the degenerate curl-free modes of the auxiliary system satisfy where are eigensolutions of (20) and (21) for lossy and non-reciprocal problems, respectively. Again, for , we have (22) For other degenerate cases, we can also apply the Gram-Schmit orthogonalization process. Thus, the field solution due to any source excitation can be expanded in terms of the complete set (assumed to be) of eigenbasis [3], where can be calculated in a simple form of (23) Besides the perfectly conducting boundaries, we can use the periodic boundary conditions (PBCs) to bound the inhomogeneity.…”

Section: A Bounded Casementioning

confidence: 99%

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Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Dai¹,

Lo²,

Chew

et al. 2014

IEEE Trans. Antennas Propagat.

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A generalized modal expansion theory for investigating arbitrary 3-D bounded and unbounded electromagnetic fields is presented. When an inhomogeneity is enclosed with impenetrable boundaries, the field excited by arbitrary sources is expanded with a complete set of eigenmodes, which are classified into trapped modes and radiation modes. As the boundaries tend to infinity, trapped modes remain unchanged, while radiation modes form a continuum. To illustrate the theory, several real-life structures are investigated with a conformal finite-difference technique in the frequency domain. Perfectly matched layers (PMLs) are imposed at finite extent to emulate the unbounded problems. Numerical examples show that, only a few system modes are prominent in expanding an excited field, leading to a reduced modal picture which provides a quick guidance as well as useful physical insight for engineering design and optimization of electromagnetic devices and components.

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Section: Introductionmentioning

confidence: 94%

Section: A Bounded Casementioning

confidence: 99%

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Dai¹,

Lo²,

Chew

et al. 2014

IEEE Trans. Antennas Propagat.

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“…Several fast and universal eigenvalue solvers have been developed for an arbitrary electromagnetic system (Dai et al 2012(Dai et al , 2013(Dai et al , 2014Sha et al 2014). …”

Section: Weak Coupling and Strong Coupling Regimesmentioning

confidence: 99%

“…On the other hand, the well-documented literature on natural mode analysis mainly focuses on bounded or semi-bounded systems (even dielectric resonator antennas are normally enclosed by impenetrable boundaries when their modal shapes are sought for). Recent effort addresses bounded and unbounded problems using a general framework based on natural mode expansion, which offers useful physical insight into antenna operation, as well as an alternative of CMA for modal design and engineering (Dai et al 2012(Dai et al , 2014.…”

Section: Modal Analysis For Antenna Designmentioning

confidence: 99%

Numerical Modeling in Antenna Engineering

Chew

Jiang

Sun

et al. 2015

Handbook of Antenna Technologies

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The principal computational electromagnetics techniques for solving antenna problems are reviewed. An introduction is given on a historical review of how antenna problems were solved in the past. The call for precise solutions calls for the use of numerical methods as found in computational electromagnetics. A brief introduction on differential equation solutions and integral solutions is given. The Green's function concept is introduced to facilitate the formulation of integral equations. Numerical methods and fast algorithms to solve these equations are discussed.Then an overview of how electromagnetic theory relates to circuit theory is presented. Then the concept of partial element equivalence circuit is introduced to facilitate solutions to more complex problems. In antenna technology, one invariably has to have a good combined understanding of the wave theory and circuit theory.Next, the discussion on the computation of electromagnetic solutions in the "twilight zone" where circuit theory meets wave theory was presented. Solutions valid for the wave physics regime often become unstable facing low-frequency catastrophe when the frequency is low.Due to advances in nanofabrication technology, antennas can be made in the optical frequency regime. But their full understanding requires the full solutions of Maxwell's equations. Also, many models, such as perfect electric conductors, which are valid at microwave frequency, are not valid at optical frequency. Hence, many antenna concepts need rethinking in the optical regime.Next, an emerging area of the use of eigenanalysis methods for antenna design is discussed. This can be the characteristic mode analysis or the natural mode analysis. These analysis methods offer new physical insight not possible by conventional numerical methods.Then the discussion on the use of the domain decomposition method to solve highly complex and multi-scale antenna structures is given. Antennas, due to the need to interface with the circuit theory, often have structures ranging from a fraction of a wavelength to a tiny fraction of a wavelength. This poses a new computational challenge that can be overcome by the domain decomposition method.Many antenna designs in the high-frequency regime or the ray optics regime are guided by ray physics and the adjoining mathematics. These mathematical techniques are often highly complex due to the rich physics that come with ray optics. The discussion on the use of these new mathematical techniques to reduce computational workload and offering new physical insight is given.A conclusion section is given to summarize this chapter and allude to future directions.

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“…9,[20][21][22][23] Discreteness stems from imposing Sommerfeld radiation boundary conditions to account for radiation. 24 The imaginary part of the complex eigenfrequency relates to the finite lifetime or decay rate of energy to all loss channels. However, complex eigenfrequencies introduce their own implementational and interpretational difficulties, such as a difficult-to-solve non-linear eigenvalue problem, unphysical exponentially diverging fields, and the need to define permittivities at complex frequencies.…”

Section: Introductionmentioning

confidence: 99%

Generalizing Normal Mode Expansion of Electromagnetic Green’s Tensor to Open Systems

2019

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We generalize normal mode expansion of Green's tensorḠ(r, r ) to lossy resonators in open systems, resolving a longstanding open challenge. We obtain a simple yet robust formulation, whereby radiation of energy to infinity is captured by a complete, discrete set of modes, rather than a continuum. This enables rapid simulations by providing the spatial variation ofḠ(r, r ) over both r and r in one simulation. Few eigenmodes are often necessary for nanostructures, facilitating both analytic calculations and unified insight into computationally intensive phenomena such as Purcell enhancement, radiative heat transfer, van der Waals forces, and Förster resonance energy transfer. We bypass all implementation and completeness issues associated with the alternative quasinormal eigenmode methods, by defining modes with permittivity rather than frequency as the eigenvalue. We obtain true stationary modes that decay rather than diverge at infinity, and are trivially normalized. Completeness is achieved both for sources located within the inclusion and the background through use of the Lippmann-Schwinger equation. Modes are defined by a linear eigenvalue problem, readily implemented using any numerical method. We demonstrate its simple implementation on COMSOL Multiphysics, using the default inbuilt tools. Results were validated against direct scattering simulations, including analytical Mie theory, attaining arbitrarily accurate agreement regardless of source location or detuning from resonance. arXiv:1711.00335v1 [physics.optics] 1 Nov 2017

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Generalized Modal Expansion of Electromagnetic Field in 2-D Bounded and Unbounded Media

Cited by 16 publications

References 8 publications

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

Numerical Modeling in Antenna Engineering

Generalizing Normal Mode Expansion of Electromagnetic Green’s Tensor to Open Systems

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