Analysis of electromagnetic wave interactions on nonlinear scatterers using time domain volume integral equations

Handle URI:
http://hdl.handle.net/10754/556248
Title:
Analysis of electromagnetic wave interactions on nonlinear scatterers using time domain volume integral equations
Authors:
Ulku, Huseyin Arda ( 0000-0003-4682-3902 ) ; Sayed, Sadeed Bin; Bagci, Hakan ( 0000-0003-3867-5786 )
Abstract:
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half and full Schubert-Wilton-Glisson (SWG) functions, respectively. Equations are Galerkin tested in space and the resulting semi-discrete system is integrated in time for the unknown expansion coefficients using the aforementioned predictor-corrector scheme. The explicitness of the MOT scheme allows for incorporation of the nonlinearities as simple discretized function evaluations on the right hand side of the system. Numerical results that demonstrate the accuracy, efficiency, and applicability of the proposed nonlinear MOT-TDVIE solver will be presented.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
IEEE
Journal:
Radio Science Meeting (Joint with AP-S Symposium), 2014 USNC-URSI
Issue Date:
6-Jul-2014
DOI:
10.1109/USNC-URSI.2014.6955421
Type:
Abstract
Additional Links:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6955421
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorUlku, Huseyin Ardaen
dc.contributor.authorSayed, Sadeed Binen
dc.contributor.authorBagci, Hakanen
dc.date.accessioned2015-06-04T11:02:58Zen
dc.date.available2015-06-04T11:02:58Zen
dc.date.issued2014-07-06en
dc.identifier.doi10.1109/USNC-URSI.2014.6955421en
dc.identifier.urihttp://hdl.handle.net/10754/556248en
dc.description.abstractEffects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half and full Schubert-Wilton-Glisson (SWG) functions, respectively. Equations are Galerkin tested in space and the resulting semi-discrete system is integrated in time for the unknown expansion coefficients using the aforementioned predictor-corrector scheme. The explicitness of the MOT scheme allows for incorporation of the nonlinearities as simple discretized function evaluations on the right hand side of the system. Numerical results that demonstrate the accuracy, efficiency, and applicability of the proposed nonlinear MOT-TDVIE solver will be presented.en
dc.publisherIEEEen
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6955421en
dc.rights(c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.en
dc.titleAnalysis of electromagnetic wave interactions on nonlinear scatterers using time domain volume integral equationsen
dc.typeAbstracten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalRadio Science Meeting (Joint with AP-S Symposium), 2014 USNC-URSIen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Electronics Engineering Gebze Institute of Technology, Kocaeli, Turkeyen
kaust.authorUlku, Huseyin Ardaen
kaust.authorBagci, Hakanen
kaust.authorSayed, Sadeed Binen
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