A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures.
Saved in:
| Title: | A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures. |
|---|---|
| Authors: | Vidal-Codina, F.1 (AUTHOR) fvidal@mit.edu, Nguyen, N.-C.1 (AUTHOR) cuongng@mit.edu, Ciracì, C.2 (AUTHOR) cristian.ciraci@iit.it, Oh, S.-H.3 (AUTHOR) sang@umn.edu, Peraire, J.1 (AUTHOR) peraire@mit.edu |
| Source: | Journal of Computational Physics. Mar2021, Vol. 429, pN.PAG-N.PAG. 1p. |
| Subjects: | Galerkin methods, Maxwell equations, Second harmonic generation, Degrees of freedom, Linear systems |
| Abstract: | We develop a nested hybridizable discontinuous Galerkin (HDG) method to numerically solve the Maxwell's equations coupled with a hydrodynamic model for the conduction-band electrons in metals. The HDG method leverages static condensation to eliminate the degrees of freedom of the approximate solution defined in the elements, yielding a linear system in terms of the degrees of freedom of the approximate trace defined on the element boundaries. This article presents a computational method that relies on a degree-of-freedom reordering such that the HDG linear system accommodates an additional static condensation step to eliminate a large portion of the degrees of freedom of the approximate trace, thereby yielding a much smaller linear system. For the particular metallic structures considered in this article, the resulting linear system obtained by means of nested static condensations is a block tridiagonal system, which can be solved efficiently. We apply the nested HDG method to compute second harmonic generation on a triangular coaxial periodic nanogap structure. This nonlinear optics phenomenon features rapid field variations and extreme boundary-layer structures that span a wide range of length scales. Numerical results show that the ability to identify structures which exhibit resonances at ω and 2 ω is essential to excite the second harmonic response. • A nested HDG method to economize the solution of traditional HDG systems. • A computational framework combining nested HDG with the structure of the problem for additional computational savings. • Model order reduction strategy to identify geometries that lead to resonances at ω , 2 ω. • Ability to simulate nonlocal second harmonic generation plasmonic phenomena on realistic 3-D nanostructures. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 148473401 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Vidal-Codina%2C+F%2E%22">Vidal-Codina, F.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fvidal@mit.edu</i><br /><searchLink fieldCode="AR" term="%22Nguyen%2C+N%2E-C%2E%22">Nguyen, N.-C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cuongng@mit.edu</i><br /><searchLink fieldCode="AR" term="%22Ciracì%2C+C%2E%22">Ciracì, C.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> cristian.ciraci@iit.it</i><br /><searchLink fieldCode="AR" term="%22Oh%2C+S%2E-H%2E%22">Oh, S.-H.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> sang@umn.edu</i><br /><searchLink fieldCode="AR" term="%22Peraire%2C+J%2E%22">Peraire, J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> peraire@mit.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Mar2021, Vol. 429, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Maxwell+equations%22">Maxwell equations</searchLink><br /><searchLink fieldCode="DE" term="%22Second+harmonic+generation%22">Second harmonic generation</searchLink><br /><searchLink fieldCode="DE" term="%22Degrees+of+freedom%22">Degrees of freedom</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We develop a nested hybridizable discontinuous Galerkin (HDG) method to numerically solve the Maxwell's equations coupled with a hydrodynamic model for the conduction-band electrons in metals. The HDG method leverages static condensation to eliminate the degrees of freedom of the approximate solution defined in the elements, yielding a linear system in terms of the degrees of freedom of the approximate trace defined on the element boundaries. This article presents a computational method that relies on a degree-of-freedom reordering such that the HDG linear system accommodates an additional static condensation step to eliminate a large portion of the degrees of freedom of the approximate trace, thereby yielding a much smaller linear system. For the particular metallic structures considered in this article, the resulting linear system obtained by means of nested static condensations is a block tridiagonal system, which can be solved efficiently. We apply the nested HDG method to compute second harmonic generation on a triangular coaxial periodic nanogap structure. This nonlinear optics phenomenon features rapid field variations and extreme boundary-layer structures that span a wide range of length scales. Numerical results show that the ability to identify structures which exhibit resonances at ω and 2 ω is essential to excite the second harmonic response. • A nested HDG method to economize the solution of traditional HDG systems. • A computational framework combining nested HDG with the structure of the problem for additional computational savings. • Model order reduction strategy to identify geometries that lead to resonances at ω , 2 ω. • Ability to simulate nonlocal second harmonic generation plasmonic phenomena on realistic 3-D nanostructures. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=148473401 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jcp.2020.110000 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Galerkin methods Type: general – SubjectFull: Maxwell equations Type: general – SubjectFull: Second harmonic generation Type: general – SubjectFull: Degrees of freedom Type: general – SubjectFull: Linear systems Type: general Titles: – TitleFull: A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Vidal-Codina, F. – PersonEntity: Name: NameFull: Nguyen, N.-C. – PersonEntity: Name: NameFull: Ciracì, C. – PersonEntity: Name: NameFull: Oh, S.-H. – PersonEntity: Name: NameFull: Peraire, J. IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 03 Text: Mar2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 00219991 Numbering: – Type: volume Value: 429 Titles: – TitleFull: Journal of Computational Physics Type: main |
| ResultId | 1 |
