Resonant scattering and third-harmonic generation by cubically polarizable grating structures

Angermann, Lutz; Yatsyk, Vasyl V.; Yatsyk, M. V.

doi:10.1109/msmw.2016.7538124

Cited by 7 publications

(21 citation statements)

References 7 publications

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“…The present paper complements our previous works [11][12][13][14][15][16]. In the setting of a coupled system approach, a numerical investigation of the energy characteristics of the radiation of the third harmonic by a nonlinear layer is performed on the basis of a block-wise iterative scheme for the computational analysis of the resonance properties of wave radiation by a nonlinear layered object in the vicinity of the eigenvalues of induced eigenvalue problems.…”

Section: Introductionmentioning

confidence: 87%

“…The quantities {Φnκ} 3 n=1 at the multiple frequencies nκ are coupled by the condition of phase synchronism of the waves, see Figure 1 and [12][13][14][15]:…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…The algorithm for the solution of (6) is realized by means of an iterative scheme, at each step of which the following system of linearized complex algebraic equations of second kind is solved [11][12][13][14][15][16]:…”

Section: Solution Of the Coupled Nonlinear Equation Systemmentioning

confidence: 99%

“…Applying the principle of analytic continuation, the nonlinear problems (6) are continued into the complex space of values of the frequency parameter, thereby allowing an investigation of induced eigenvalue problems [12][13][14][15][16]. That is, we want to determine the eigenvalues and the nontrivial solutions of the homogeneous non-self-adjoint linear problems with the induced permittivities (4):…”

Section: The Eigen Modes Of the Induced Eigenvalue Problemsmentioning

confidence: 99%

“…see [11][12][13][14][15][16]18]. The indices specify the number of local maxima |Ex| (or |U|, since |U| = |Ex|, see (5), (9)) along the coordinate axes in the space filled by the dielectric layer, see Figure 1.…”

Section: Numerical Investigation Of the Electrodynamic Properties Of mentioning

confidence: 99%

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Energy characteristics of a nonlinear layer at resonant frequencies of wave scattering and generation

Angermann

Yatsyk

2019

Open Physics

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This work presents a mathematical model, a computational scheme and experimental results describing the electrodynamic characteristics of a nonmagnetic, isotropic, E-polarized, nonlinear layered dielectric object with a cubically polarizable medium. The nonlinear object is irradiated by a quasi-homogeneous field, where the incident field constitutes of a packet of phase-synchronized plane oscillations. In the case under consideration the excitation may consist both of a highly intense electromagnetic field at a basic (fundamental) frequency, which results in the generation of the third harmonic, as well as of weakly intense fields at multiples of the basic frequency which produce no harmonics, but only have an influencing effect on the processes of wave radiation. The investigations were carried out within the setting of a coupled system approach at resonant excitation frequencies determined by the eigenvalues of the induced eigenvalue problems. A verification of the energy balance law is carried out. By means of estimations for the conditionalities of the occuring matrices, the level of degeneration of the induced non-self-adjoint spectral problems as well as the sensitivity of the coupled system of nonlinear boundary value problems with respect to computational errors are verified.

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Section: Introductionmentioning

confidence: 87%

“…The quantities {Φnκ} 3 n=1 at the multiple frequencies nκ are coupled by the condition of phase synchronism of the waves, see Figure 1 and [12][13][14][15]:…”

Section: The Mathematical Modelmentioning

confidence: 99%

Section: Solution Of the Coupled Nonlinear Equation Systemmentioning

confidence: 99%

Section: The Eigen Modes Of the Induced Eigenvalue Problemsmentioning

confidence: 99%

Section: Numerical Investigation Of the Electrodynamic Properties Of mentioning

confidence: 99%

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Energy characteristics of a nonlinear layer at resonant frequencies of wave scattering and generation

Angermann

Yatsyk

2019

Open Physics

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Conclusion and Outlook

Angermann¹,

Yatsyk²

2018

Resonant Scattering and Generation of Waves

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Time Domain Finite Element Method for Maxwell’s Equations

Anees

Angermann

2019

IEEE Access

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In this paper, we discuss a time domain finite element method for the approximate solution of Maxwell's equations. A weak formulation is derived for the electric and magnetic fields with appropriate initial and boundary conditions, and the problem is discretized both in space and time. In space, Nédeléc curl-conforming and Raviart-Thomas div-conforming finite elements are used to discretize the electric and magnetic fields, respectively. The backward Euler and symplectic schemes are applied to discretize the problem in time. For this system, we prove an error estimate. In addition, computational experiments are presented to validate the method, the electric and magnetic fields are visualized. The method also allows treating complex geometries of various physical systems coupled to electromagnetic fields in 3D.INDEX TERMS Backward Euler method, error estimates, Maxwell's equations, time domain finite element methods, simulation, symplectic method, visualization.

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Resonant scattering and third-harmonic generation by cubically polarizable grating structures

Cited by 7 publications

References 7 publications

Energy characteristics of a nonlinear layer at resonant frequencies of wave scattering and generation

Energy characteristics of a nonlinear layer at resonant frequencies of wave scattering and generation

Conclusion and Outlook

Time Domain Finite Element Method for Maxwell’s Equations

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