---
_id: '63827'
abstract:
- lang: eng
  text: Light-emitting diodes (LEDs) are becoming increasingly important across various
    sectors of the lighting industry and are being used more frequently. In the field
    of symbolic projection, research is increasingly focusing on implementing light
    modulation using energy-efficient, incoherent LEDs rather than lasers. Since light
    modulation in micro- and nano-optics is typically achieved through phase modulation,
    Finite-Difference Time-Domain (FDTD) simulations are employed for analysis. The
    objective of this article is to investigate different approaches for approximating
    incoherent monochromatic light sources within FDTD simulations. To this end, two
    approaches based on dipole sources are considered, as well as a method involving
    plane waves with modulated wavefronts based on Cosine–Fourier functions and a
    method based on the superposition of Gaussian beams. These methods are evaluated
    in terms of their accuracy using a two-dimensional double-slit configuration and
    are compared against a fully incoherent analytical reference.
article_number: '128'
article_type: original
author:
- first_name: Dominik
  full_name: Metzner, Dominik
  last_name: Metzner
- first_name: Jens
  full_name: Potthoff, Jens
  last_name: Potthoff
- first_name: Thomas
  full_name: Zentgraf, Thomas
  id: '30525'
  last_name: Zentgraf
  orcid: 0000-0002-8662-1101
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
citation:
  ama: Metzner D, Potthoff J, Zentgraf T, Förstner J. Approximating Incoherent Monochromatic
    Light Sources in FDTD Simulations. <i>Photonics</i>. 2026;13(2). doi:<a href="https://doi.org/10.3390/photonics13020128">10.3390/photonics13020128</a>
  apa: Metzner, D., Potthoff, J., Zentgraf, T., &#38; Förstner, J. (2026). Approximating
    Incoherent Monochromatic Light Sources in FDTD Simulations. <i>Photonics</i>,
    <i>13</i>(2), Article 128. <a href="https://doi.org/10.3390/photonics13020128">https://doi.org/10.3390/photonics13020128</a>
  bibtex: '@article{Metzner_Potthoff_Zentgraf_Förstner_2026, title={Approximating
    Incoherent Monochromatic Light Sources in FDTD Simulations}, volume={13}, DOI={<a
    href="https://doi.org/10.3390/photonics13020128">10.3390/photonics13020128</a>},
    number={2128}, journal={Photonics}, publisher={MDPI AG}, author={Metzner, Dominik
    and Potthoff, Jens and Zentgraf, Thomas and Förstner, Jens}, year={2026} }'
  chicago: Metzner, Dominik, Jens Potthoff, Thomas Zentgraf, and Jens Förstner. “Approximating
    Incoherent Monochromatic Light Sources in FDTD Simulations.” <i>Photonics</i>
    13, no. 2 (2026). <a href="https://doi.org/10.3390/photonics13020128">https://doi.org/10.3390/photonics13020128</a>.
  ieee: 'D. Metzner, J. Potthoff, T. Zentgraf, and J. Förstner, “Approximating Incoherent
    Monochromatic Light Sources in FDTD Simulations,” <i>Photonics</i>, vol. 13, no.
    2, Art. no. 128, 2026, doi: <a href="https://doi.org/10.3390/photonics13020128">10.3390/photonics13020128</a>.'
  mla: Metzner, Dominik, et al. “Approximating Incoherent Monochromatic Light Sources
    in FDTD Simulations.” <i>Photonics</i>, vol. 13, no. 2, 128, MDPI AG, 2026, doi:<a
    href="https://doi.org/10.3390/photonics13020128">10.3390/photonics13020128</a>.
  short: D. Metzner, J. Potthoff, T. Zentgraf, J. Förstner, Photonics 13 (2026).
date_created: 2026-02-02T07:18:03Z
date_updated: 2026-02-02T21:38:34Z
department:
- _id: '15'
- _id: '230'
- _id: '289'
- _id: '623'
- _id: '61'
doi: 10.3390/photonics13020128
intvolume: '        13'
issue: '2'
keyword:
- tet_topic_opticalantenna
- tet_topic_numerics
- tet_topic_meta
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.mdpi.com/2304-6732/13/2/128
oa: '1'
publication: Photonics
publication_identifier:
  issn:
  - 2304-6732
publication_status: published
publisher: MDPI AG
quality_controlled: '1'
status: public
title: Approximating Incoherent Monochromatic Light Sources in FDTD Simulations
type: journal_article
user_id: '158'
volume: 13
year: '2026'
...
---
_id: '4581'
author:
- first_name: Yevgen
  full_name: Grynko, Yevgen
  id: '26059'
  last_name: Grynko
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
citation:
  ama: 'Grynko Y, Förstner J. Application of the Discontinuous Galerkin Time Domain
    Method in Nonlinear Nanoplasmonics. In: <i>2018 IEEE 17th International Conference
    on Mathematical Methods in Electromagnetic Theory (MMET)</i>. IEEE; 2018. doi:<a
    href="https://doi.org/10.1109/mmet.2018.8460261">10.1109/mmet.2018.8460261</a>'
  apa: Grynko, Y., &#38; Förstner, J. (2018). Application of the Discontinuous Galerkin
    Time Domain Method in Nonlinear Nanoplasmonics. In <i>2018 IEEE 17th International
    Conference on Mathematical Methods in Electromagnetic Theory (MMET)</i>. IEEE.
    <a href="https://doi.org/10.1109/mmet.2018.8460261">https://doi.org/10.1109/mmet.2018.8460261</a>
  bibtex: '@inproceedings{Grynko_Förstner_2018, title={Application of the Discontinuous
    Galerkin Time Domain Method in Nonlinear Nanoplasmonics}, DOI={<a href="https://doi.org/10.1109/mmet.2018.8460261">10.1109/mmet.2018.8460261</a>},
    booktitle={2018 IEEE 17th International Conference on Mathematical Methods in
    Electromagnetic Theory (MMET)}, publisher={IEEE}, author={Grynko, Yevgen and Förstner,
    Jens}, year={2018} }'
  chicago: Grynko, Yevgen, and Jens Förstner. “Application of the Discontinuous Galerkin
    Time Domain Method in Nonlinear Nanoplasmonics.” In <i>2018 IEEE 17th International
    Conference on Mathematical Methods in Electromagnetic Theory (MMET)</i>. IEEE,
    2018. <a href="https://doi.org/10.1109/mmet.2018.8460261">https://doi.org/10.1109/mmet.2018.8460261</a>.
  ieee: Y. Grynko and J. Förstner, “Application of the Discontinuous Galerkin Time
    Domain Method in Nonlinear Nanoplasmonics,” in <i>2018 IEEE 17th International
    Conference on Mathematical Methods in Electromagnetic Theory (MMET)</i>, 2018.
  mla: Grynko, Yevgen, and Jens Förstner. “Application of the Discontinuous Galerkin
    Time Domain Method in Nonlinear Nanoplasmonics.” <i>2018 IEEE 17th International
    Conference on Mathematical Methods in Electromagnetic Theory (MMET)</i>, IEEE,
    2018, doi:<a href="https://doi.org/10.1109/mmet.2018.8460261">10.1109/mmet.2018.8460261</a>.
  short: 'Y. Grynko, J. Förstner, in: 2018 IEEE 17th International Conference on Mathematical
    Methods in Electromagnetic Theory (MMET), IEEE, 2018.'
date_created: 2018-10-04T22:21:39Z
date_updated: 2022-01-06T07:01:14Z
ddc:
- '530'
department:
- _id: '61'
doi: 10.1109/mmet.2018.8460261
file:
- access_level: closed
  content_type: application/pdf
  creator: fossie
  date_created: 2018-10-04T22:25:59Z
  date_updated: 2018-10-04T22:25:59Z
  file_id: '4582'
  file_name: 2018-09 Grynko - MMET (preprint).pdf
  file_size: 1131678
  relation: main_file
  success: 1
file_date_updated: 2018-10-04T22:25:59Z
has_accepted_license: '1'
keyword:
- tet_topic_numerics
- tet_topic_shg
language:
- iso: eng
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic
  Theory (MMET)
publication_identifier:
  isbn:
  - '9781538654385'
publication_status: published
publisher: IEEE
status: public
title: Application of the Discontinuous Galerkin Time Domain Method in Nonlinear Nanoplasmonics
type: conference
user_id: '158'
year: '2018'
...
---
_id: '3743'
abstract:
- lang: eng
  text: Frequently, optical integrated circuits combine elements (waveguide channels,
    cavities), the simulation of which is well established through mature numerical
    eigenproblem solvers. It remains to predict the interaction of these modes. We
    address this task by a general, “Hybrid” variant (HCMT) of Coupled Mode Theory.
    Using methods from finite-element numerics, the properties of a circuit are approximated
    by superpositions of eigen-solutions for its constituents, leading to quantitative,
    computationally cheap, and easily interpretable models.
author:
- first_name: Manfred
  full_name: Hammer, Manfred
  id: '48077'
  last_name: Hammer
  orcid: 0000-0002-6331-9348
citation:
  ama: 'Hammer M. Guided Wave Interaction in Photonic Integrated Circuits — A Hybrid
    Analytical/Numerical Approach to Coupled Mode Theory. In: Agrawal A, ed. <i>Recent
    Trends in Computational Photonics</i>. Vol 204. 204th ed.  Springer Series in
    Optical Sciences book series. Springer; 2017:77-105.'
  apa: Hammer, M. (2017). Guided Wave Interaction in Photonic Integrated Circuits
    — A Hybrid Analytical/Numerical Approach to Coupled Mode Theory. In A. Agrawal
    (Ed.), <i>Recent Trends in Computational Photonics</i> (204th ed., Vol. 204, pp.
    77–105). Springer.
  bibtex: '@inbook{Hammer_2017, edition={204}, series={ Springer Series in Optical
    Sciences book series}, title={Guided Wave Interaction in Photonic Integrated Circuits
    — A Hybrid Analytical/Numerical Approach to Coupled Mode Theory}, volume={204},
    booktitle={Recent Trends in Computational Photonics}, publisher={Springer}, author={Hammer,
    Manfred}, editor={Agrawal, ArtiEditor}, year={2017}, pages={77–105}, collection={
    Springer Series in Optical Sciences book series} }'
  chicago: Hammer, Manfred. “Guided Wave Interaction in Photonic Integrated Circuits
    — A Hybrid Analytical/Numerical Approach to Coupled Mode Theory.” In <i>Recent
    Trends in Computational Photonics</i>, edited by Arti Agrawal, 204th ed., 204:77–105.  Springer
    Series in Optical Sciences Book Series. Springer, 2017.
  ieee: M. Hammer, “Guided Wave Interaction in Photonic Integrated Circuits — A Hybrid
    Analytical/Numerical Approach to Coupled Mode Theory,” in <i>Recent Trends in
    Computational Photonics</i>, 204th ed., vol. 204, A. Agrawal, Ed. Springer, 2017,
    pp. 77–105.
  mla: Hammer, Manfred. “Guided Wave Interaction in Photonic Integrated Circuits —
    A Hybrid Analytical/Numerical Approach to Coupled Mode Theory.” <i>Recent Trends
    in Computational Photonics</i>, edited by Arti Agrawal, 204th ed., vol. 204, Springer,
    2017, pp. 77–105.
  short: 'M. Hammer, in: A. Agrawal (Ed.), Recent Trends in Computational Photonics,
    204th ed., Springer, 2017, pp. 77–105.'
date_created: 2018-08-01T10:44:00Z
date_updated: 2022-01-06T06:59:34Z
department:
- _id: '61'
edition: '204'
editor:
- first_name: Arti
  full_name: Agrawal, Arti
  last_name: Agrawal
intvolume: '       204'
keyword:
- tet_topic_waveguide
- tet_topic_numerics
language:
- iso: eng
page: 77-105
publication: Recent Trends in Computational Photonics
publication_identifier:
  isbn:
  - 978-3-319-55438-9
publication_status: published
publisher: Springer
series_title: ' Springer Series in Optical Sciences book series'
status: public
title: Guided Wave Interaction in Photonic Integrated Circuits — A Hybrid Analytical/Numerical
  Approach to Coupled Mode Theory
type: book_chapter
user_id: '55706'
volume: 204
year: '2017'
...
---
_id: '3828'
abstract:
- lang: eng
  text: "The 3D implementation of a hybrid analytical/numerical variant of the coupled-mode
    theory is discussed.\r\nEigenmodes of the constituting dielectric channels are
    computed numerically. The frequency-domain\r\ncoupled-mode models then combine
    these into fully vectorial approximations for the optical electromagnetic\r\nfields
    of the composite structure. Following a discretization of amplitude functions
    by 1D finite elements, pro-\r\ncedures from the realm of finite-element numerics
    are applied to establish systems of linear equations for the then-\r\ndiscrete
    modal amplitudes. Examples substantiate the functioning of the technique and allow
    for some numerical\r\nassessment. The full 3D simulations are highly efficient
    in memory consumption, moderately demanding in com-\r\nputational time, and, in
    regimes of low radiative losses, sufficiently accurate for practical design. Our
    results\r\ninclude the perturbation of guided modes by changes of the refractive
    indices, the interaction of waves in parallel,\r\nhorizontally or vertically coupled
    straight waveguides, and a series of crossings of potentially overlapping channels\r\nwith
    fairly arbitrary relative positions and orientations."
article_type: original
author:
- first_name: Manfred
  full_name: Hammer, Manfred
  id: '48077'
  last_name: Hammer
  orcid: 0000-0002-6331-9348
- first_name: Samer
  full_name: Alhaddad, Samer
  last_name: Alhaddad
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
citation:
  ama: 'Hammer M, Alhaddad S, Förstner J. Hybrid coupled-mode modeling in 3D: perturbed
    and coupled channels, and waveguide crossings. <i>Journal of the Optical Society
    of America B</i>. 2017;34(3):613-624. doi:<a href="https://doi.org/10.1364/josab.34.000613">10.1364/josab.34.000613</a>'
  apa: 'Hammer, M., Alhaddad, S., &#38; Förstner, J. (2017). Hybrid coupled-mode modeling
    in 3D: perturbed and coupled channels, and waveguide crossings. <i>Journal of
    the Optical Society of America B</i>, <i>34</i>(3), 613–624. <a href="https://doi.org/10.1364/josab.34.000613">https://doi.org/10.1364/josab.34.000613</a>'
  bibtex: '@article{Hammer_Alhaddad_Förstner_2017, title={Hybrid coupled-mode modeling
    in 3D: perturbed and coupled channels, and waveguide crossings}, volume={34},
    DOI={<a href="https://doi.org/10.1364/josab.34.000613">10.1364/josab.34.000613</a>},
    number={3}, journal={Journal of the Optical Society of America B}, publisher={The
    Optical Society}, author={Hammer, Manfred and Alhaddad, Samer and Förstner, Jens},
    year={2017}, pages={613–624} }'
  chicago: 'Hammer, Manfred, Samer Alhaddad, and Jens Förstner. “Hybrid Coupled-Mode
    Modeling in 3D: Perturbed and Coupled Channels, and Waveguide Crossings.” <i>Journal
    of the Optical Society of America B</i> 34, no. 3 (2017): 613–24. <a href="https://doi.org/10.1364/josab.34.000613">https://doi.org/10.1364/josab.34.000613</a>.'
  ieee: 'M. Hammer, S. Alhaddad, and J. Förstner, “Hybrid coupled-mode modeling in
    3D: perturbed and coupled channels, and waveguide crossings,” <i>Journal of the
    Optical Society of America B</i>, vol. 34, no. 3, pp. 613–624, 2017.'
  mla: 'Hammer, Manfred, et al. “Hybrid Coupled-Mode Modeling in 3D: Perturbed and
    Coupled Channels, and Waveguide Crossings.” <i>Journal of the Optical Society
    of America B</i>, vol. 34, no. 3, The Optical Society, 2017, pp. 613–24, doi:<a
    href="https://doi.org/10.1364/josab.34.000613">10.1364/josab.34.000613</a>.'
  short: M. Hammer, S. Alhaddad, J. Förstner, Journal of the Optical Society of America
    B 34 (2017) 613–624.
date_created: 2018-08-07T08:40:41Z
date_updated: 2022-01-06T06:59:38Z
ddc:
- '530'
department:
- _id: '61'
doi: 10.1364/josab.34.000613
file:
- access_level: open_access
  content_type: application/pdf
  creator: hclaudia
  date_created: 2018-08-07T09:46:13Z
  date_updated: 2018-09-03T14:09:04Z
  file_id: '3829'
  file_name: 2017-02 Hammer_Hybrid coupled mode modelling in 3D_Perturbed and coupled
    channels and waveguide crossings_Coupled Mode Theory JOSA B.pdf
  file_size: 5539592
  relation: main_file
file_date_updated: 2018-09-03T14:09:04Z
has_accepted_license: '1'
intvolume: '        34'
issue: '3'
keyword:
- tet_topic_waveguide
- tet_topic_numerics
language:
- iso: eng
oa: '1'
page: 613-624
publication: Journal of the Optical Society of America B
publication_identifier:
  issn:
  - 0740-3224
  - 1520-8540
publication_status: published
publisher: The Optical Society
status: public
title: 'Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide
  crossings'
type: journal_article
urn: '38287'
user_id: '158'
volume: 34
year: '2017'
...
---
_id: '3836'
abstract:
- lang: eng
  text: We apply the Discontinuous Galerkin Time Domain (DGTD) method for numerical
    simulations of the second harmonic generation from various metallic nanostructures.
    A Maxwell–Vlasov hydrodynamic model is used to describe the nonlinear effects
    in the motion of the excited free electrons in a metal. The results are compared
    with the corresponding experimental measurements for split-ring resonators and
    plasmonic gap antennas.
author:
- first_name: Yevgen
  full_name: Grynko, Yevgen
  id: '26059'
  last_name: Grynko
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
citation:
  ama: 'Grynko Y, Förstner J. Simulation of Second Harmonic Generation from Photonic
    Nanostructures Using the Discontinuous Galerkin Time Domain Method. In: Agrawal
    A, ed. <i>Recent Trends in Computational Photonics</i>. Cham: Springer International
    Publishing; 2017:261-284. doi:<a href="https://doi.org/10.1007/978-3-319-55438-9_9">10.1007/978-3-319-55438-9_9</a>'
  apa: 'Grynko, Y., &#38; Förstner, J. (2017). Simulation of Second Harmonic Generation
    from Photonic Nanostructures Using the Discontinuous Galerkin Time Domain Method.
    In A. Agrawal (Ed.), <i>Recent Trends in Computational Photonics</i> (pp. 261–284).
    Cham: Springer International Publishing. <a href="https://doi.org/10.1007/978-3-319-55438-9_9">https://doi.org/10.1007/978-3-319-55438-9_9</a>'
  bibtex: '@inbook{Grynko_Förstner_2017, place={Cham}, title={Simulation of Second
    Harmonic Generation from Photonic Nanostructures Using the Discontinuous Galerkin
    Time Domain Method}, DOI={<a href="https://doi.org/10.1007/978-3-319-55438-9_9">10.1007/978-3-319-55438-9_9</a>},
    booktitle={Recent Trends in Computational Photonics}, publisher={Springer International
    Publishing}, author={Grynko, Yevgen and Förstner, Jens}, editor={Agrawal, ArtiEditor},
    year={2017}, pages={261–284} }'
  chicago: 'Grynko, Yevgen, and Jens Förstner. “Simulation of Second Harmonic Generation
    from Photonic Nanostructures Using the Discontinuous Galerkin Time Domain Method.”
    In <i>Recent Trends in Computational Photonics</i>, edited by Arti Agrawal, 261–84.
    Cham: Springer International Publishing, 2017. <a href="https://doi.org/10.1007/978-3-319-55438-9_9">https://doi.org/10.1007/978-3-319-55438-9_9</a>.'
  ieee: 'Y. Grynko and J. Förstner, “Simulation of Second Harmonic Generation from
    Photonic Nanostructures Using the Discontinuous Galerkin Time Domain Method,”
    in <i>Recent Trends in Computational Photonics</i>, A. Agrawal, Ed. Cham: Springer
    International Publishing, 2017, pp. 261–284.'
  mla: Grynko, Yevgen, and Jens Förstner. “Simulation of Second Harmonic Generation
    from Photonic Nanostructures Using the Discontinuous Galerkin Time Domain Method.”
    <i>Recent Trends in Computational Photonics</i>, edited by Arti Agrawal, Springer
    International Publishing, 2017, pp. 261–84, doi:<a href="https://doi.org/10.1007/978-3-319-55438-9_9">10.1007/978-3-319-55438-9_9</a>.
  short: 'Y. Grynko, J. Förstner, in: A. Agrawal (Ed.), Recent Trends in Computational
    Photonics, Springer International Publishing, Cham, 2017, pp. 261–284.'
date_created: 2018-08-07T10:42:30Z
date_updated: 2022-01-06T06:59:41Z
ddc:
- '530'
department:
- _id: '61'
doi: 10.1007/978-3-319-55438-9_9
editor:
- first_name: Arti
  full_name: Agrawal, Arti
  last_name: Agrawal
file:
- access_level: request
  content_type: application/pdf
  creator: fossie
  date_created: 2018-08-16T08:05:50Z
  date_updated: 2022-01-06T06:59:40Z
  file_id: '3916'
  file_name: Recent-Trends-in-Computational-Photonics - chapter 9 - Grynko - SHG DG.pdf
  file_size: 2798215
  relation: main_file
file_date_updated: 2022-01-06T06:59:40Z
has_accepted_license: '1'
keyword:
- tet_topic_numerics
- tet_topic_shg
- tet_topic_meta
language:
- iso: eng
page: 261-284
place: Cham
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '53'
  name: TRR 142
- _id: '54'
  name: TRR 142 - Project Area A
- _id: '62'
  name: TRR 142 - Subproject A5
publication: Recent Trends in Computational Photonics
publication_identifier:
  isbn:
  - '9783319554372'
  - '9783319554389'
  issn:
  - 0342-4111
  - 1556-1534
publication_status: published
publisher: Springer International Publishing
status: public
title: Simulation of Second Harmonic Generation from Photonic Nanostructures Using
  the Discontinuous Galerkin Time Domain Method
type: book_chapter
user_id: '158'
year: '2017'
...
---
_id: '3934'
abstract:
- lang: eng
  text: Typical optical integrated circuits combine elements, like straight and curved
    waveguides, or cavities, the simulation and design of which is well established
    through numerical eigenproblem-solvers. It remains to predict the interaction
    of these modes. We address this task by a ”Hybrid” variant (HCMT) of Coupled Mode
    Theory. Using methods from finite-element numerics, the optical properties of
    a circuit are approximated by superpositions of eigen-solutions for its constituents,
    leading to quantitative, low-dimensional, and interpretable models in the frequency
    domain. Spectral scans are complemented by the direct computation of supermode
    properties (spectral positions and linewidths, coupling-induced phase shifts).
    This contribution outlines the theoretical background, and discusses briefly limitations
    and implementational details, with the help of an example of a 2-D coupled-resonator-optical-waveguide
    configuration.
author:
- first_name: Manfred
  full_name: Hammer, Manfred
  id: '48077'
  last_name: Hammer
  orcid: 0000-0002-6331-9348
citation:
  ama: 'Hammer M. Wave interaction in photonic integrated circuits: Hybrid analytical
    / numerical coupled mode modeling. In: Broquin J-E, Nunzi Conti G, eds. <i>Integrated
    Optics: Devices, Materials, and Technologies XX</i>. SPIE; 2016:975018-975018-8.
    doi:<a href="https://doi.org/10.1117/12.2214331">10.1117/12.2214331</a>'
  apa: 'Hammer, M. (2016). Wave interaction in photonic integrated circuits: Hybrid
    analytical / numerical coupled mode modeling. In J.-E. Broquin &#38; G. Nunzi
    Conti (Eds.), <i>Integrated Optics: Devices, Materials, and Technologies XX</i>
    (pp. 975018-975018–8). San Francisco, USA: SPIE. <a href="https://doi.org/10.1117/12.2214331">https://doi.org/10.1117/12.2214331</a>'
  bibtex: '@inproceedings{Hammer_2016, title={Wave interaction in photonic integrated
    circuits: Hybrid analytical / numerical coupled mode modeling}, DOI={<a href="https://doi.org/10.1117/12.2214331">10.1117/12.2214331</a>},
    number={9750}, booktitle={Integrated Optics: Devices, Materials, and Technologies
    XX}, publisher={SPIE}, author={Hammer, Manfred}, editor={Broquin, Jean-Emmanuel
    and Nunzi Conti, GualtieroEditors}, year={2016}, pages={975018-975018–8} }'
  chicago: 'Hammer, Manfred. “Wave Interaction in Photonic Integrated Circuits: Hybrid
    Analytical / Numerical Coupled Mode Modeling.” In <i>Integrated Optics: Devices,
    Materials, and Technologies XX</i>, edited by Jean-Emmanuel Broquin and Gualtiero
    Nunzi Conti, 975018-975018–8. SPIE, 2016. <a href="https://doi.org/10.1117/12.2214331">https://doi.org/10.1117/12.2214331</a>.'
  ieee: 'M. Hammer, “Wave interaction in photonic integrated circuits: Hybrid analytical
    / numerical coupled mode modeling,” in <i>Integrated Optics: Devices, Materials,
    and Technologies XX</i>, San Francisco, USA, 2016, no. 9750, pp. 975018-975018–8.'
  mla: 'Hammer, Manfred. “Wave Interaction in Photonic Integrated Circuits: Hybrid
    Analytical / Numerical Coupled Mode Modeling.” <i>Integrated Optics: Devices,
    Materials, and Technologies XX</i>, edited by Jean-Emmanuel Broquin and Gualtiero
    Nunzi Conti, no. 9750, SPIE, 2016, pp. 975018-975018–8, doi:<a href="https://doi.org/10.1117/12.2214331">10.1117/12.2214331</a>.'
  short: 'M. Hammer, in: J.-E. Broquin, G. Nunzi Conti (Eds.), Integrated Optics:
    Devices, Materials, and Technologies XX, SPIE, 2016, pp. 975018-975018–8.'
conference:
  location: San Francisco, USA
  name: Photonics West 2016/OPTO 2016
date_created: 2018-08-20T09:25:13Z
date_updated: 2022-01-06T06:59:56Z
department:
- _id: '61'
doi: 10.1117/12.2214331
editor:
- first_name: Jean-Emmanuel
  full_name: Broquin, Jean-Emmanuel
  last_name: Broquin
- first_name: Gualtiero
  full_name: Nunzi Conti, Gualtiero
  last_name: Nunzi Conti
issue: '9750'
keyword:
- tet_topic_waveguide
- tet_topic_numerics
language:
- iso: eng
page: '975018-975018-8 '
publication: 'Integrated Optics: Devices, Materials, and Technologies XX'
publication_status: published
publisher: SPIE
status: public
title: 'Wave interaction in photonic integrated circuits: Hybrid analytical / numerical
  coupled mode modeling'
type: conference
user_id: '55706'
year: '2016'
...
---
_id: '3890'
abstract:
- lang: eng
  text: "The incidenceofthin-film-guided, in-planeunguidedwavesatobliqueanglesonstraightdiscontinuities
    of dielectricslabwaveguides,anearlyproblemofintegratedoptics,isbeingre-considered.The3-D
    frequencydomainMaxwellequationsreducetoaparametrizedinhomogeneousvectorialproblemona\r\n2-D
    computationaldomain,withtransparent-influx boundaryconditions.Weproposearigorousvec-\r\ntorial
    solverbasedonsimultaneousexpansionsintopolarizedlocalslabeigenmodesalongthetwo\r\northogonal
    crosssectioncoordinates(quadridirectionaleigenmodepropagationQUEP).Thequasi-ana-\r\nlytical
    schemeisapplicabletoconfigurations with — in principle — arbitrary crosssectiongeometries.\r\nExamples
    forahigh-contrastfacetofanasymmetricslabwaveguide,forthelateralexcitationofa\r\nchannel
    waveguide,andforastepdiscontinuitybetweenslabwaveguidesofdifferentthicknessesare\r\ndiscussed."
article_type: original
author:
- first_name: Manfred
  full_name: Hammer, Manfred
  id: '48077'
  last_name: Hammer
  orcid: 0000-0002-6331-9348
citation:
  ama: 'Hammer M. Oblique incidence of semi-guided waves on rectangular slab waveguide
    discontinuities: A vectorial QUEP solver. <i>Optics Communications</i>. 2014;338:447-456.
    doi:<a href="https://doi.org/10.1016/j.optcom.2014.09.087">10.1016/j.optcom.2014.09.087</a>'
  apa: 'Hammer, M. (2014). Oblique incidence of semi-guided waves on rectangular slab
    waveguide discontinuities: A vectorial QUEP solver. <i>Optics Communications</i>,
    <i>338</i>, 447–456. <a href="https://doi.org/10.1016/j.optcom.2014.09.087">https://doi.org/10.1016/j.optcom.2014.09.087</a>'
  bibtex: '@article{Hammer_2014, title={Oblique incidence of semi-guided waves on
    rectangular slab waveguide discontinuities: A vectorial QUEP solver}, volume={338},
    DOI={<a href="https://doi.org/10.1016/j.optcom.2014.09.087">10.1016/j.optcom.2014.09.087</a>},
    journal={Optics Communications}, publisher={Elsevier BV}, author={Hammer, Manfred},
    year={2014}, pages={447–456} }'
  chicago: 'Hammer, Manfred. “Oblique Incidence of Semi-Guided Waves on Rectangular
    Slab Waveguide Discontinuities: A Vectorial QUEP Solver.” <i>Optics Communications</i>
    338 (2014): 447–56. <a href="https://doi.org/10.1016/j.optcom.2014.09.087">https://doi.org/10.1016/j.optcom.2014.09.087</a>.'
  ieee: 'M. Hammer, “Oblique incidence of semi-guided waves on rectangular slab waveguide
    discontinuities: A vectorial QUEP solver,” <i>Optics Communications</i>, vol.
    338, pp. 447–456, 2014.'
  mla: 'Hammer, Manfred. “Oblique Incidence of Semi-Guided Waves on Rectangular Slab
    Waveguide Discontinuities: A Vectorial QUEP Solver.” <i>Optics Communications</i>,
    vol. 338, Elsevier BV, 2014, pp. 447–56, doi:<a href="https://doi.org/10.1016/j.optcom.2014.09.087">10.1016/j.optcom.2014.09.087</a>.'
  short: M. Hammer, Optics Communications 338 (2014) 447–456.
date_created: 2018-08-13T09:28:01Z
date_updated: 2022-01-06T06:59:50Z
ddc:
- '530'
department:
- _id: '61'
doi: 10.1016/j.optcom.2014.09.087
file:
- access_level: closed
  content_type: application/pdf
  creator: hclaudia
  date_created: 2018-08-13T09:29:14Z
  date_updated: 2018-08-13T09:29:14Z
  file_id: '3891'
  file_name: 2015 Hammer_Oblique incidence of semi-guided waves on rectangular slab
    waveguide discontinuities_A vectorial QUEP solver_Optics communications.pdf
  file_size: 1872449
  relation: main_file
  success: 1
file_date_updated: 2018-08-13T09:29:14Z
has_accepted_license: '1'
intvolume: '       338'
keyword:
- tet_topic_waveguide
- tet_topic_numerics
language:
- iso: eng
page: 447-456
publication: Optics Communications
publication_identifier:
  issn:
  - 0030-4018
publication_status: published
publisher: Elsevier BV
status: public
title: 'Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities:
  A vectorial QUEP solver'
type: journal_article
user_id: '55706'
volume: 338
year: '2014'
...
---
_id: '4044'
abstract:
- lang: eng
  text: A simulation environment for metallic nanostructures based on the Discontinuous
    Galerkin Time Domain method is presented. The model is used to compute the linear
    and nonlinear optical response of split ring resonators and to study physical
    mechanisms that contribute to second harmonic generation.
article_number: C1V89S1P041
article_type: original
author:
- first_name: Yevgen
  full_name: Grynko, Yevgen
  id: '26059'
  last_name: Grynko
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
citation:
  ama: Grynko Y, Förstner J, Meier T. Application of the discontinous Galerkin time
    domain method to the optics of metallic nanostructures. <i>AAPP | Atti della Accademia
    Peloritana dei Pericolanti</i>. 2011;89(1). doi:<a href="https://doi.org/10.1478/C1V89S1P041">10.1478/C1V89S1P041</a>
  apa: Grynko, Y., Förstner, J., &#38; Meier, T. (2011). Application of the discontinous
    Galerkin time domain method to the optics of metallic nanostructures. <i>AAPP
    | Atti Della Accademia Peloritana Dei Pericolanti</i>, <i>89</i>(1), Article C1V89S1P041.
    <a href="https://doi.org/10.1478/C1V89S1P041">https://doi.org/10.1478/C1V89S1P041</a>
  bibtex: '@article{Grynko_Förstner_Meier_2011, title={Application of the discontinous
    Galerkin time domain method to the optics of metallic nanostructures}, volume={89},
    DOI={<a href="https://doi.org/10.1478/C1V89S1P041">10.1478/C1V89S1P041</a>}, number={1C1V89S1P041},
    journal={AAPP | Atti della Accademia Peloritana dei Pericolanti}, author={Grynko,
    Yevgen and Förstner, Jens and Meier, Torsten}, year={2011} }'
  chicago: Grynko, Yevgen, Jens Förstner, and Torsten Meier. “Application of the Discontinous
    Galerkin Time Domain Method to the Optics of Metallic Nanostructures.” <i>AAPP
    | Atti Della Accademia Peloritana Dei Pericolanti</i> 89, no. 1 (2011). <a href="https://doi.org/10.1478/C1V89S1P041">https://doi.org/10.1478/C1V89S1P041</a>.
  ieee: 'Y. Grynko, J. Förstner, and T. Meier, “Application of the discontinous Galerkin
    time domain method to the optics of metallic nanostructures,” <i>AAPP | Atti della
    Accademia Peloritana dei Pericolanti</i>, vol. 89, no. 1, Art. no. C1V89S1P041,
    2011, doi: <a href="https://doi.org/10.1478/C1V89S1P041">10.1478/C1V89S1P041</a>.'
  mla: Grynko, Yevgen, et al. “Application of the Discontinous Galerkin Time Domain
    Method to the Optics of Metallic Nanostructures.” <i>AAPP | Atti Della Accademia
    Peloritana Dei Pericolanti</i>, vol. 89, no. 1, C1V89S1P041, 2011, doi:<a href="https://doi.org/10.1478/C1V89S1P041">10.1478/C1V89S1P041</a>.
  short: Y. Grynko, J. Förstner, T. Meier, AAPP | Atti Della Accademia Peloritana
    Dei Pericolanti 89 (2011).
date_created: 2018-08-22T10:18:44Z
date_updated: 2025-12-16T11:21:11Z
ddc:
- '530'
department:
- _id: '15'
- _id: '293'
- _id: '170'
- _id: '230'
- _id: '35'
- _id: '34'
- _id: '61'
doi: 10.1478/C1V89S1P041
file:
- access_level: open_access
  content_type: application/pdf
  creator: hclaudia
  date_created: 2018-08-22T10:17:27Z
  date_updated: 2018-09-04T19:11:52Z
  file_id: '4045'
  file_name: 2011 Grynko,Förstner,Meier_Application of the discontinous Galerkin time
    domain method to the optics of metallic nanostructures.pdf
  file_size: 258268
  relation: main_file
file_date_updated: 2018-09-04T19:11:52Z
has_accepted_license: '1'
intvolume: '        89'
issue: '1'
keyword:
- tet_topic_numerics
- tet_topic_shg
- tet_topic_meta
language:
- iso: eng
oa: '1'
publication: AAPP | Atti della Accademia Peloritana dei Pericolanti
publication_identifier:
  issn:
  - 1825-1242
publication_status: published
status: public
title: Application of the discontinous Galerkin time domain method to the optics of
  metallic nanostructures
type: journal_article
urn: '40448'
user_id: '16199'
volume: 89
year: '2011'
...
---
_id: '4167'
abstract:
- lang: eng
  text: "The electromagnetic field in the vicinity of sharp edges needs a special
    treatment in numeric calculation whenever accurate, fast converging results are
    necessary. One of the fundamental works concerning field singularities has been
    proposed in 1972 [1] and states that the electromagnetic energy density must be
    integrable over any finite\r\ndomain, even if this domain contains singularities.
    It is shown, that the magnetic field \x02H(\x03, ϕ) and electric field \x02E(\x03,
    ϕ) are proportional to ∝ \x03(t−1) for \x03 → 0. The variable \x03 is the distance
    to the edge and t has to fulfill the integrability condition and thus is restricted
    to 0 < t < 1. This result is often used to reduce the error corresponding to the
    singularity without increasing the numerical effort [2 - 5]. For this purpose,
    a correction factor K is estimated by inserting the proportionality into the wave
    equation. It is shown, that this method improves the accuracy of the result significantly,
    however the order of convergence is often not studied. In [4] a method to modify
    the material parameters in order to use analytic results to improve the numeric
    calculation is presented. In this contribution we will - inspired by the scheme
    given in [4] - develop a new method to estimate a correction factor for perfect
    conducting materials (PEC) and demonstrate the improvement of the results compared
    to the standard edge correction. Therefore analytic results (comparable to [1])
    are consequently merged with the scheme in [4]. The main goal of this work is
    the calculation of the second harmonic generation (SHG) in the wave response of
    so-called metamaterials [6]. Frequently these structures\r\ncontain sharp metallic
    edges with field singularities at the interfaces which have a strong impact on
    the SHG signals. Thus, an accurate simulation of singularities is highly important.
    However, the following approach can also be applied to many other setups, and
    one of them is shown in the example below."
article_number: '11515155 '
author:
- first_name: C
  full_name: Classen, C
  last_name: Classen
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: R
  full_name: Schuhmann, R
  last_name: Schuhmann
citation:
  ama: 'Classen C, Förstner J, Meier T, Schuhmann R. Enhanced FDTD edge correction
    for nonlinear effects calculation. In: <i>2010 IEEE Antennas and Propagation Society
    International Symposium</i>. IEEE; 2010. doi:<a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>'
  apa: Classen, C., Förstner, J., Meier, T., &#38; Schuhmann, R. (2010). Enhanced
    FDTD edge correction for nonlinear effects calculation. <i>2010 IEEE Antennas
    and Propagation Society International Symposium</i>, Article 11515155. 2010 IEEE
    international Symposium Antennas, Toronto, ON, Canada. <a href="https://doi.org/10.1109/aps.2010.5562017">https://doi.org/10.1109/aps.2010.5562017</a>
  bibtex: '@inproceedings{Classen_Förstner_Meier_Schuhmann_2010, title={Enhanced FDTD
    edge correction for nonlinear effects calculation}, DOI={<a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>},
    number={11515155}, booktitle={2010 IEEE Antennas and Propagation Society International
    Symposium}, publisher={IEEE}, author={Classen, C and Förstner, Jens and Meier,
    Torsten and Schuhmann, R}, year={2010} }'
  chicago: Classen, C, Jens Förstner, Torsten Meier, and R Schuhmann. “Enhanced FDTD
    Edge Correction for Nonlinear Effects Calculation.” In <i>2010 IEEE Antennas and
    Propagation Society International Symposium</i>. IEEE, 2010. <a href="https://doi.org/10.1109/aps.2010.5562017">https://doi.org/10.1109/aps.2010.5562017</a>.
  ieee: 'C. Classen, J. Förstner, T. Meier, and R. Schuhmann, “Enhanced FDTD edge
    correction for nonlinear effects calculation,” presented at the 2010 IEEE international
    Symposium Antennas, Toronto, ON, Canada, 2010, doi: <a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>.'
  mla: Classen, C., et al. “Enhanced FDTD Edge Correction for Nonlinear Effects Calculation.”
    <i>2010 IEEE Antennas and Propagation Society International Symposium</i>, 11515155,
    IEEE, 2010, doi:<a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>.
  short: 'C. Classen, J. Förstner, T. Meier, R. Schuhmann, in: 2010 IEEE Antennas
    and Propagation Society International Symposium, IEEE, 2010.'
conference:
  end_date: 2010-07-17
  location: Toronto, ON, Canada
  name: 2010 IEEE international Symposium Antennas
  start_date: 2010-07-11
date_created: 2018-08-28T08:34:52Z
date_updated: 2025-12-16T12:35:39Z
ddc:
- '530'
department:
- _id: '61'
- _id: '15'
- _id: '293'
- _id: '170'
- _id: '230'
- _id: '35'
- _id: '34'
doi: 10.1109/aps.2010.5562017
file:
- access_level: open_access
  content_type: application/pdf
  creator: hclaudia
  date_created: 2018-08-28T08:36:44Z
  date_updated: 2018-09-04T19:31:42Z
  file_id: '4168'
  file_name: 2010 Classen,Förstner, Meier T,Schuhmann_Enhanced FDTD edge correction
    for nonlinear effects calculation.pdf
  file_size: 209412
  relation: main_file
file_date_updated: 2018-09-04T19:31:42Z
has_accepted_license: '1'
keyword:
- tet_topic_numerics
language:
- iso: eng
oa: '1'
publication: 2010 IEEE Antennas and Propagation Society International Symposium
publication_identifier:
  isbn:
  - '9781424449675'
  - '9781424449682'
publication_status: published
publisher: IEEE
status: public
title: Enhanced FDTD edge correction for nonlinear effects calculation
type: conference
urn: '41677'
user_id: '16199'
year: '2010'
...