Efficient implementation of B-spline modal method for lamellar gratings

Granet, Gérard

doi:10.1364/josaa.31.000332

Cited by 13 publications

(11 citation statements)

References 18 publications

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“…Most proposed implementations of the modal method use a set of predetermined basis functions to express the eigenfunctions such as the complex Fourier series used in the FMM (RCWA), orthogonal polynomials adopted in polynomial expansion modal methods 19,20 or B -splines 21,22 . Eigenmodes may be computed also by finite-difference approach 9,23 or by pseudospectral methods 24,25 .…”

Section: Methodsmentioning

confidence: 99%

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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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Section: Methodsmentioning

confidence: 99%

“…It can be seen that replacement of S-matrix technique by direct solution of Eq. (22) or by iterative algorithms can reduce computational time more than twice when precise results are required. The next example of application of the methods discussed in this work is with the structure examined in 9,20-25 .…”

Section: Number Of Modes Number Of Modesmentioning

confidence: 99%

Iterative approach as alternative to S-matrix in modal methods

Semenikhin¹,

Zanuccoli

2014

SPIE Proceedings

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“…The eigenvalues are required as the zeros of a transcendental equation. In a second approach, the eigenfunctions are expanded on a set of basis functions [7][8][9][10][11][12][13][14][15][16][17]. The main differences between these variants of modal methods is the choice of the expansion and test functions.…”

Section: Introductionmentioning

confidence: 99%

Numerical scheme for the modal method based on subsectional Gegenbauer polynomial expansion: application to biperiodic binary grating

Edee

Plumey

2015

J. Opt. Soc. Am. A

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The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution.

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“…[1][2][3][4] The B-Spline modal method (BMM), which was recently developped, [5][6][7][8][9] is an interesting alternative to the FMM. Indeed, it enables the use of algorithms for solving the eigenvalue equations which are specific to sparse matrices, thus reducing significantly the calculation time.…”

Section: Introductionmentioning

confidence: 99%

Simulating the focusing of light onto 1D nanostructures with a B-spline modal method

et al. 2015

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Focusing the light onto nanostructures thanks to spherical lenses is a first step to enhance the field, and is widely used in applications, in particular for enhancing non-linear effects like the second harmonic generation. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam can not be described by the simple ray tracing formalism. Here, we present a method to compute the response to a focused beam, based on the B-spline modal method. The simulation of a gaussian focused beam is obtained thanks to a truncated decomposition on plane waves computed on a single period, which limits the computation burden.

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Efficient implementation of B-spline modal method for lamellar gratings

Cited by 13 publications

References 18 publications

Iterative approach as alternative to S-matrix in modal methods

Iterative approach as alternative to S-matrix in modal methods

Numerical scheme for the modal method based on subsectional Gegenbauer polynomial expansion: application to biperiodic binary grating

Simulating the focusing of light onto 1D nanostructures with a B-spline modal method

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