Sensitivity analysis of waveguide eigenvalue problems

Burschäpers, N.; Fiege, Sabrina; Schuhmann, Rolf; Walther, Andrea

doi:10.5194/ars-9-85-2011

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…Note however, that the method that we will present in this work can be used with any numerical solver able to calculate the derivatives of an objective function with respect to the design parameters. Other examples are the finite difference time domain method [24], the beam propagation method [25] or the eigenmode expansion method [26]- [28], to name a few.…”

Section: A Finite Element Methods With Shape Derivativesmentioning

confidence: 99%

Bayesian Optimization With Improved Scalability and Derivative Information for Efficient Design of Nanophotonic Structures

Garcia-Santiago

Burger

Rockstuhl

et al. 2021

J. Lightwave Technol.

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We propose the combination of forward shape derivatives and the use of an iterative inversion scheme for Bayesian optimization to find optimal designs of nanophotonic devices. This approach widens the range of applicability of Bayesian optmization to situations where a larger number of iterations is required and where derivative information is available. This was previously impractical because the computational efforts required to identify the next evaluation point in the parameter space became much larger than the actual evaluation of the objective function. We demonstrate an implementation of the method by optimizing a waveguide edge coupler.

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Section: A Finite Element Methods With Shape Derivativesmentioning

confidence: 99%

Bayesian Optimization With Improved Scalability and Derivative Information for Efficient Design of Nanophotonic Structures

Garcia-Santiago

Burger

Rockstuhl

et al. 2021

J. Lightwave Technol.

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show abstract

“…Also, for photonic crystals, the band structure is calculated using model order reduction (MOR) in Scheiber et al (2011). A sensitivity analysis for a waveguide eigenvalue problem has finally also been demonstrated in Burschäpers et al (2011), here with permittivity values as parameters in the context of a simple inverse problem.…”

Section: Introductionmentioning

confidence: 99%

Higher-order sensitivity analysis of periodic 3-D eigenvalue problems for electromagnetic field calculations

Jorkowski

Schuhmann

2017

Adv. Radio Sci.

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Abstract. An algorithm to perform a higher-order sensitivity analysis for electromagnetic eigenvalue problems is presented. By computing the eigenvalue and eigenvector derivatives, the Brillouin Diagram for periodic structures can be calculated. The discrete model is described using the Finite Integration Technique (FIT) with periodic boundaries, and the sensitivity analysis is performed with respect to the phase shift ϕ between the periodic boundaries.For validation, a reference solution is calculated by solving multiple eigenvalue problems (EVP). Furthermore, the eigenvalue derivatives are compared to reference values using finite difference (FD) formulas.

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“…For resonance problems, left and right eigenmodes are in general not identical, which increases the computational effort, and normalization requires additional attention. There are specialized approaches that, e.g., exploit magnetic fields for extracting the left eigenmodes 20 , introduce an adjoint system for computing sensitivities 21 , or that rely on internal and external electric fields at the boundaries of the nanoresonators 22 . It is also possible to completely omit the use of eigenmodes for sensitivity analysis 23 .…”

mentioning

confidence: 99%

Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators

et al. 2022

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Resonances are omnipresent in physics and essential for the description of wave phenomena. We present an approach for computing eigenfrequency sensitivities of resonances. The theory is based on Riesz projections and the approach can be applied to compute partial derivatives of the complex eigenfrequencies of any resonance problem. Here, the method is derived for Maxwell’s equations. Its numerical realization essentially relies on direct differentiation of scattering problems. We use a numerical implementation to demonstrate the performance of the approach compared to differentiation using finite differences. The method is applied for the efficient optimization of the quality factor of a nanophotonic resonator.

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Sensitivity analysis of waveguide eigenvalue problems

Cited by 6 publications

References 10 publications

Bayesian Optimization With Improved Scalability and Derivative Information for Efficient Design of Nanophotonic Structures

Bayesian Optimization With Improved Scalability and Derivative Information for Efficient Design of Nanophotonic Structures

Higher-order sensitivity analysis of periodic 3-D eigenvalue problems for electromagnetic field calculations

Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators

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