New fast and memory-sparing method for rigorous electromagnetic analysis of 2D periodic dielectric structures

Щербаков, А. А.; Tishchenko, A.V.

doi:10.1016/j.jqsrt.2011.09.019

Cited by 28 publications

(48 citation statements)

References 34 publications

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“…The linear spectra are determined by using the generalized-source method (GSM). 42 To validate these results, the transmission spectra are also calculated by using CST Microwave Studio. The positions of the resonances in the calculated spectra are in a good agreement with the experimental data, corresponding to an electric resonance at approximately 640 nm and a magnetic one at 790 nm.…”

Section: ■ Theoretical Insightsmentioning

confidence: 99%

Enhanced Magnetic Second-Harmonic Generation from Resonant Metasurfaces

et al. 2015

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We study, both experimentally and theoretically, the second-order nonlinear response from resonant metasurfaces composed of metal−dielectric nanodisks. We demonstrate that by exciting the resonant optical modes of the composite nanoparticles we can achieve strong enhancement of the second-harmonic signal from the metasurface. By employing a multipole expansion method for the generated second-harmonic radiation, we show that the observed SHG enhancement is due to the magnetic dipolar and electric quadrupolar second-order nonlinear response of the metasurface.T he nonlinear optical properties of nanostructures are known to differ substantially from those of bulk media because they are affected by strong confinement and local resonances. 1−7 It is well established that the strong field enhancement through formation of "hot spots" can dramatically boost nonlinear effects in metallic nanoparticles. 8−11 Importantly, in the case of metamaterials, the nanopatterning leads not only to more efficient nonlinear interaction but also to completely new nonlinear regimes due to the magnetic optical response of the constituent "meta-atoms". While exciting applications of the linear magnetic response of metamaterials for both metallic 12−16 and dielectric 17−19 structures have been readily achieved at infrared and even optical frequencies, the magnetic nature of nonlinear optical phenomena in metamaterials is still largely unexplored.We focus our attention on the process of second-harmonic generation (SHG), which is an even-order nonlinear process that vanishes in centrosymmetric materials in the electric dipole approximation. 20 For small nanoparticles, efficient SHG may be observed due to several factors, including local field enhancement, deviation of the particle shapes from a symmetric one, and surface effects. 21 Importantly, the resonances in plasmonic and dielectric nanoparticles, combined with a strong enhancement of the optical near-field, as well as the effective overlap of the interacting optical modes, allow for multifold enhancement of SHG. 22−24 The enhancement of efficiency of second-harmonic generation within extremely small nanoscopic volumes is of paramount interest in surface science, 25,26 colloidal chemistry, 27 and catalytic chemistry. 28 Due to its nature, second-harmonic generation is extremely sensitive to surface adsorbents. As such, even a single-molecule layer adsorbed onto a surface can completely change the surface nonlinear susceptibility. This sensitivity to changes of the chemical environment has found many applications to the study of the symmetry properties of surfaces, the nature of adsorbates at surfaces or interfaces, or noninvasive probing of buried interfaces.It was recognized that the local field distribution depends drastically on the size, shape, and mutual orientation of the nanoparticles, thus providing a way for the design of artificial materials with required nonlinear optical properties. 29−31 Such nonlinearity engineering resembles the engineering of nonlinear materials by che...

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Section: ■ Theoretical Insightsmentioning

confidence: 99%

Enhanced Magnetic Second-Harmonic Generation from Resonant Metasurfaces

et al. 2015

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“…(3) from the vector field F in Eq. (6). To this end, we start from the spatial-domain relations between the electric field and electric flux density on the one hand and the definition of the vector field F on the other.…”

Section: B Revised Normal-vector-field Formulationmentioning

confidence: 99%

“…The concept of normal-vector fields, as introduced in [1], has been adopted in several computational frameworks to improve the convergence in a Fourier basis, in particular in the differential method [1,2], the rigorous coupled wave analysis (RCWA) [3], and more recently in the volume-integral method [4][5][6]. The basic idea behind this concept is that normalvector fields can separate the components of the electric field (E) and the electric flux density D. Via this separation, we can access the continuous components of both E and D across material interfaces and construct a vector field F that is continuous everywhere, with the possible exception of isolated points and lines that correspond to geometrical edges and corners of the scattering object under investigation.…”

Section: Introductionmentioning

confidence: 99%

Local normal vector field formulation for periodic scattering problems formulated in the spectral domain

Beurden

Setija

2017

J. Opt. Soc. Am. A

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We present two adapted formulations, one tailored to isotropic media and one for general anisotropic media, of the normal-vector field framework previously introduced to improve convergence near arbitrarily shaped material interfaces in spectral simulation methods for periodic scattering geometries. The adapted formulations enable the definition and generation of the normal-vector fields to be confined to a region of prolongation that includes the material interfaces but is otherwise limited. This allow for a more flexible application of geometrical transformations like rotation and translation per scattering object in the unit cell. Moreover, these geometrical transformations enable a cut-and-connect strategy to compose general geometries from elementary building blocks. The entire framework gives rise to continuously parameterized geometries.

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“…Recently, due to rapidly increasing of the complexity of simulated devices and the rising demands of accuracy that leads to the need of solving very large systems of linear equations, the iterative methods have been considered more promising. To date a number of algorithms have been developed to solve Maxwell's equations with iterative approach [4][5][6][7][8][9] . Its implementation can significantly reduce the computational time.…”

Section: Introductionmentioning

confidence: 99%

Iterative approach as alternative to S-matrix in modal methods

Semenikhin¹,

Zanuccoli

2014

SPIE Proceedings

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The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell's equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of 3 M operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct-iterative approaches. The possibility to diminish the impact of 3 M -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to 2 M by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches.

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New fast and memory-sparing method for rigorous electromagnetic analysis of 2D periodic dielectric structures

Cited by 28 publications

References 34 publications

Enhanced Magnetic Second-Harmonic Generation from Resonant Metasurfaces

Enhanced Magnetic Second-Harmonic Generation from Resonant Metasurfaces

Local normal vector field formulation for periodic scattering problems formulated in the spectral domain

Iterative approach as alternative to S-matrix in modal methods

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