---
_id: '4579'
abstract:
- lang: eng
  text: Semi-guided waves confined in dielectric slab waveguides are being considered
    for oblique angles of propagation. If the waves encounter a linear discontinuity
    of (mostly) arbitrary shape and extension, a variant of Snell's law applies, separately
    for each pair of incoming and outgoing modes. Depending on the effective indices
    involved, and on the angle of incidence, power transfer to specific outgoing waves
    can be allowed or forbidden. In particular, critical angles of incidence can be
    identified, beyond which any power transfer to non-guided waves is forbidden,
    i.e. all radiative losses are suppressed. In that case the input power is carried
    away from the discontinuity exclusively by reflected semi-guided waves in the
    input slab, or by semi-guided waves that are transmitted into other outgoing slab
    waveguides. Vectorial equations on a 2-D cross sectional domain apply. These are
    formally identical to the equations that govern the eigenmodes of 3-D channel
    waveguides. Here, however, these need to be solved not as an eigenvalue problem,
    but as an inhomogeneous problem with a right-hand-side that is given by the incoming
    semi-guided wave, and subject to transparent boundary conditions. The equations
    resemble a standard 2-D Helmholtz problem, with an effective permittivity in place
    of the actual relative permittivity. Depending on the properties of the incoming
    wave, including the angle of incidence, this effective permittivity can become
    locally negative, causing the suppression of propagating outgoing waves. A series
    of high-contrast example configurations are discussed, where these effects lead
    to - in some respects - quite surprising transmission characteristics.
author:
- first_name: Manfred
  full_name: Hammer, Manfred
  id: '48077'
  last_name: Hammer
  orcid: 0000-0002-6331-9348
- first_name: Lena
  full_name: Ebers, Lena
  id: '40428'
  last_name: Ebers
- first_name: Andre
  full_name: Hildebrandt, Andre
  last_name: Hildebrandt
- first_name: Samer
  full_name: Alhaddad, Samer
  id: '42456'
  last_name: Alhaddad
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
citation:
  ama: 'Hammer M, Ebers L, Hildebrandt A, Alhaddad S, Förstner J. Oblique Semi-Guided
    Waves: 2-D Integrated Photonics with Negative Effective Permittivity. 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.2018.8460455">10.1109/mmet.2018.8460455</a>'
  apa: 'Hammer, M., Ebers, L., Hildebrandt, A., Alhaddad, S., &#38; Förstner, J. (2018).
    Oblique Semi-Guided Waves: 2-D Integrated Photonics with Negative Effective Permittivity.
    In <i>2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic
    Theory (MMET)</i>. IEEE. <a href="https://doi.org/10.1109/mmet.2018.8460455">https://doi.org/10.1109/mmet.2018.8460455</a>'
  bibtex: '@inproceedings{Hammer_Ebers_Hildebrandt_Alhaddad_Förstner_2018, title={Oblique
    Semi-Guided Waves: 2-D Integrated Photonics with Negative Effective Permittivity},
    DOI={<a href="https://doi.org/10.1109/mmet.2018.8460455">10.1109/mmet.2018.8460455</a>},
    booktitle={2018 IEEE 17th International Conference on Mathematical Methods in
    Electromagnetic Theory (MMET)}, publisher={IEEE}, author={Hammer, Manfred and
    Ebers, Lena and Hildebrandt, Andre and Alhaddad, Samer and Förstner, Jens}, year={2018}
    }'
  chicago: 'Hammer, Manfred, Lena Ebers, Andre Hildebrandt, Samer Alhaddad, and Jens
    Förstner. “Oblique Semi-Guided Waves: 2-D Integrated Photonics with Negative Effective
    Permittivity.” 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.2018.8460455">https://doi.org/10.1109/mmet.2018.8460455</a>.'
  ieee: 'M. Hammer, L. Ebers, A. Hildebrandt, S. Alhaddad, and J. Förstner, “Oblique
    Semi-Guided Waves: 2-D Integrated Photonics with Negative Effective Permittivity,”
    in <i>2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic
    Theory (MMET)</i>, 2018.'
  mla: 'Hammer, Manfred, et al. “Oblique Semi-Guided Waves: 2-D Integrated Photonics
    with Negative Effective Permittivity.” <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.2018.8460455">10.1109/mmet.2018.8460455</a>.'
  short: 'M. Hammer, L. Ebers, A. Hildebrandt, S. Alhaddad, J. Förstner, in: 2018
    IEEE 17th International Conference on Mathematical Methods in Electromagnetic
    Theory (MMET), IEEE, 2018.'
date_created: 2018-10-02T17:11:59Z
date_updated: 2022-01-06T07:01:13Z
ddc:
- '530'
department:
- _id: '61'
- _id: '230'
- _id: '429'
doi: 10.1109/mmet.2018.8460455
file:
- access_level: closed
  content_type: application/pdf
  creator: fossie
  date_created: 2018-10-02T17:13:55Z
  date_updated: 2018-10-02T17:13:55Z
  file_id: '4580'
  file_name: 2018-09 Hammer - MMET (final draft).pdf
  file_size: 242956
  relation: main_file
  success: 1
file_date_updated: 2018-10-02T17:13:55Z
has_accepted_license: '1'
keyword:
- tet_topic_waveguides
project:
- _id: '53'
  name: TRR 142
- _id: '56'
  name: TRR 142 - Project Area C
- _id: '75'
  name: TRR 142 - Subproject C5
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: 'Oblique Semi-Guided Waves: 2-D Integrated Photonics with Negative Effective
  Permittivity'
type: conference
user_id: '158'
year: '2018'
...
---
_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'
...