On the complexity of aperiodic Fourier modal methods for finite periodic structures

Pisarenco, Maxim; Setija, I.D.

doi:10.1016/j.jcp.2013.12.051

Cited by 10 publications

(13 citation statements)

References 39 publications

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“…In this geometry, the cell is composed with all the periods of the scatterer as well as empty space on the cell sides, in order to minimize the effect of the periodicity thanks to the decay of the field in the empty sides. This method it is however not rigorous, in the sense that the radiation condition is imposed indirectly by expanding the computational domain . Guizal et al.…”

Section: Numerical Modelingmentioning

confidence: 99%

“…Lalanne and co‐workers have introduced the use of absorbing boundary conditions and perfectly matched layers (PMLs) at the boundaries of the unit cell in order to build and numerically analyze finite structures . A review of different approaches for ARCWA is given by Pisarenco and Setija . Figure shows an example of computation for the fields in a finite grating with 32 lines using different ARCWA approaches and comparing the solution to the standard RCWA.…”

Section: Numerical Modelingmentioning

confidence: 99%

“…This method it is however not rigorous, in the sense that the radiation condition is imposed indirectly by expanding the computational domain. [75] Guizal et al have developed a method called aperiodic RCWA (ARCWA), which can be applied to an aperiodic lamellar structure under a finite size beam illumination. [76] The electromagnetic field in the grating and in the surrounding medium is expressed in terms of Fourier integrals, leading to an integro-differential equation which can be solved numerically using a discretization in Fourier space; note that several hundreds of harmonics are required for convergence of the solution.…”

Section: Rigorous Coupled Wave Analysismentioning

confidence: 99%

“…[77,78] A review of different approaches for ARCWA is given by Pisarenco and Setija. [75] Figure 5 shows an example of computation for the fields in a finite grating with 32 lines using different ARCWA approaches and comparing the solution to the standard RCWA. The radiation field in homogeneous space is also calculated using these different approaches (not shown here).…”

Section: Rigorous Coupled Wave Analysismentioning

confidence: 99%

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Recent Advances in Resonant Waveguide Gratings

Quaranta

Basset

Martin

et al. 2018

Laser & Photonics Reviews

307

199

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Resonant waveguide gratings (RWGs), also known as guided mode resonant (GMR) gratings or waveguide‐mode resonant gratings, are dielectric structures where these resonant diffractive elements benefit from lateral leaky guided modes from UV to microwave frequencies in many different configurations. A broad range of optical effects are obtained using RWGs such as waveguide coupling, filtering, focusing, field enhancement and nonlinear effects, magneto‐optical Kerr effect, or electromagnetically induced transparency. Thanks to their high degree of optical tunability (wavelength, phase, polarization, intensity) and the variety of fabrication processes and materials available, RWGs have been implemented in a broad scope of applications in research and industry: refractive index and fluorescence biosensors, solar cells and photodetectors, signal processing, polarizers and wave plates, spectrometers, active tunable filters, mirrors for lasers and optical security features. The aim of this review is to discuss the latest developments in the field including numerical modeling, manufacturing, the physics, and applications of RWGs. Scientists and engineers interested in using RWGs for their application will also find links to the standard tools and references in modeling and fabrication according to their needs.

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Section: Numerical Modelingmentioning

confidence: 99%

Section: Numerical Modelingmentioning

confidence: 99%

Section: Rigorous Coupled Wave Analysismentioning

confidence: 99%

Section: Rigorous Coupled Wave Analysismentioning

confidence: 99%

See 2 more Smart Citations

Recent Advances in Resonant Waveguide Gratings

Quaranta

Basset

Martin

et al. 2018

Laser & Photonics Reviews

307

199

View full text Add to dashboard Cite

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“…For the two outer layers the equations are simpler since the coefficients of ongoing waves are known. For instance the structure of the matrix of system (22) for TM-case for three layers is:…”

Section: B Calculation Of the Expansion Coefficients By Iterative Mementioning

confidence: 99%

Application of the iterative approach to modal methods for the solution of Maxwell's equations

Semenikhin¹,

Zanuccoli²

2015

Journal of Computational Physics

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Abstract. In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is based on the calculation of the eigenmodes part by part by using shift-and-invert iterative technique and by applying the iterative approach to solve linear equations to compute eigenmodes expansion coefficients. As practical implementation, the iterative modal methods based on polynomials and trigonometric functions as well as on finitedifference scheme are developed. Alternatives to the scattering matrix (S-matrix) technique which are based on pure iterative or mixed direct-iterative approaches allowing to markedly reduce the number of required numerical operations are discussed. Additionally, the possibility of diminishing the memory demand of the whole algorithm from second to first power of the number of modes by implementing the iterative approach is demonstrated. This allows to carry out calculations up to hundreds of thousands eigenmodes without using a supercomputer.

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