---
_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: '61932'
abstract:
- lang: eng
  text: <jats:p>Substantial improvements in the performance of optical interconnects
    based on multi-mode fibers are required to support emerging single-channel data
    transmission rates of 200 Gb/s and 400 Gb/s. Future optical components must combine
    very high modulation bandwidths—supporting signaling at 100 Gbaud and 200 Gbaud—with
    reduced spectral width to mitigate chromatic-dispersion-induced pulse broadening
    and increased brightness to further restrict flux-confining area in multi-mode
    fibers and thereby increase the effective modal bandwidth (EMB). A particularly
    promising route to improved performance within standard oxide-confined VCSEL technology
    is the introduction of multiple isolated or optically coupled oxide-confined apertures,
    which we refer to collectively as multi-aperture (MA) VCSEL arrays. We show that
    properly designed MA VCSELs exhibit narrow emission spectra, narrow far-field
    profiles and extended intrinsic modulation bandwidths, enabling longer-reach data
    transmission over both multi-mode (MMF) and single-mode fibers (SMF). One approach
    uses optically isolated apertures with lateral dimensions of approximately 2–3
    µm arranged with a pitch of 10–12 µm or less. Such devices demonstrate relaxation
    oscillation frequencies of around 30 GHz in continuous-wave operation and intrinsic
    modulation bandwidths approaching 50 GHz. Compared with a conventional single-aperture
    VCSELs of equivalent oxide-confined area, MA designs can reduce the spectral width
    (root mean square values &lt; 0.15 nm), lower series resistance (≈50 Ω) and limit
    junction overheating through more efficient multi-spot heat dissipation at the
    same total current. As each aperture lases in a single transverse mode, these
    devices exhibit narrow far-field patterns. In combination with well-defined spacing
    between emitting spots, they permit tailored restricted launch conditions in MMFs,
    enhancing effective modal bandwidth. In another MA approach, the apertures are
    optically coupled such that self-injection locking (SIL) leads to lasing in a
    single supermode. One may regard one of the supermodes as acting as a master mode
    controlling the other one. Streak-camera studies reveal post-pulse oscillations
    in the SIL regime at frequencies up to 100 GHz. MA VCSELs enable a favorable combination
    of wavelength chirp and chromatic dispersion, extending transmission distances
    over MMFs beyond those expected for zero-chirp sources and supporting transfer
    bandwidths up to 60 GHz over kilometer-length SMF links.</jats:p>
article_number: '1037'
author:
- first_name: Nikolay N.
  full_name: Ledentsov, Nikolay N.
  last_name: Ledentsov
- first_name: Nikolay
  full_name: Ledentsov, Nikolay
  last_name: Ledentsov
- first_name: Vitaly A.
  full_name: Shchukin, Vitaly A.
  last_name: Shchukin
- first_name: Alexander N.
  full_name: Ledentsov, Alexander N.
  last_name: Ledentsov
- first_name: Oleg Yu.
  full_name: Makarov, Oleg Yu.
  last_name: Makarov
- first_name: Ilya E.
  full_name: Titkov, Ilya E.
  last_name: Titkov
- first_name: Markus
  full_name: Lindemann, Markus
  last_name: Lindemann
- first_name: Thomas
  full_name: de Adelsburg Ettmayer, Thomas
  last_name: de Adelsburg Ettmayer
- first_name: Nils Christopher
  full_name: Gerhardt, Nils Christopher
  id: '115298'
  last_name: Gerhardt
  orcid: 0009-0002-5538-231X
- first_name: Martin R.
  full_name: Hofmann, Martin R.
  last_name: Hofmann
- first_name: Xin
  full_name: Chen, Xin
  last_name: Chen
- first_name: Jason E.
  full_name: Hurley, Jason E.
  last_name: Hurley
- first_name: Hao
  full_name: Dong, Hao
  last_name: Dong
- first_name: Ming-Jun
  full_name: Li, Ming-Jun
  last_name: Li
citation:
  ama: 'Ledentsov NN, Ledentsov N, Shchukin VA, et al. VCSELs: Influence of Design
    on Performance and Data Transmission over Multi-Mode and Single-Mode Fibers. <i>Photonics</i>.
    2025;12(10). doi:<a href="https://doi.org/10.3390/photonics12101037">10.3390/photonics12101037</a>'
  apa: 'Ledentsov, N. N., Ledentsov, N., Shchukin, V. A., Ledentsov, A. N., Makarov,
    O. Yu., Titkov, I. E., Lindemann, M., de Adelsburg Ettmayer, T., Gerhardt, N.
    C., Hofmann, M. R., Chen, X., Hurley, J. E., Dong, H., &#38; Li, M.-J. (2025).
    VCSELs: Influence of Design on Performance and Data Transmission over Multi-Mode
    and Single-Mode Fibers. <i>Photonics</i>, <i>12</i>(10), Article 1037. <a href="https://doi.org/10.3390/photonics12101037">https://doi.org/10.3390/photonics12101037</a>'
  bibtex: '@article{Ledentsov_Ledentsov_Shchukin_Ledentsov_Makarov_Titkov_Lindemann_de
    Adelsburg Ettmayer_Gerhardt_Hofmann_et al._2025, title={VCSELs: Influence of Design
    on Performance and Data Transmission over Multi-Mode and Single-Mode Fibers},
    volume={12}, DOI={<a href="https://doi.org/10.3390/photonics12101037">10.3390/photonics12101037</a>},
    number={101037}, journal={Photonics}, publisher={MDPI AG}, author={Ledentsov,
    Nikolay N. and Ledentsov, Nikolay and Shchukin, Vitaly A. and Ledentsov, Alexander
    N. and Makarov, Oleg Yu. and Titkov, Ilya E. and Lindemann, Markus and de Adelsburg
    Ettmayer, Thomas and Gerhardt, Nils Christopher and Hofmann, Martin R. and et
    al.}, year={2025} }'
  chicago: 'Ledentsov, Nikolay N., Nikolay Ledentsov, Vitaly A. Shchukin, Alexander
    N. Ledentsov, Oleg Yu. Makarov, Ilya E. Titkov, Markus Lindemann, et al. “VCSELs:
    Influence of Design on Performance and Data Transmission over Multi-Mode and Single-Mode
    Fibers.” <i>Photonics</i> 12, no. 10 (2025). <a href="https://doi.org/10.3390/photonics12101037">https://doi.org/10.3390/photonics12101037</a>.'
  ieee: 'N. N. Ledentsov <i>et al.</i>, “VCSELs: Influence of Design on Performance
    and Data Transmission over Multi-Mode and Single-Mode Fibers,” <i>Photonics</i>,
    vol. 12, no. 10, Art. no. 1037, 2025, doi: <a href="https://doi.org/10.3390/photonics12101037">10.3390/photonics12101037</a>.'
  mla: 'Ledentsov, Nikolay N., et al. “VCSELs: Influence of Design on Performance
    and Data Transmission over Multi-Mode and Single-Mode Fibers.” <i>Photonics</i>,
    vol. 12, no. 10, 1037, MDPI AG, 2025, doi:<a href="https://doi.org/10.3390/photonics12101037">10.3390/photonics12101037</a>.'
  short: N.N. Ledentsov, N. Ledentsov, V.A. Shchukin, A.N. Ledentsov, O.Yu. Makarov,
    I.E. Titkov, M. Lindemann, T. de Adelsburg Ettmayer, N.C. Gerhardt, M.R. Hofmann,
    X. Chen, J.E. Hurley, H. Dong, M.-J. Li, Photonics 12 (2025).
date_created: 2025-10-23T10:59:59Z
date_updated: 2026-02-19T12:39:12Z
department:
- _id: '977'
doi: 10.3390/photonics12101037
intvolume: '        12'
issue: '10'
language:
- iso: eng
publication: Photonics
publication_identifier:
  issn:
  - 2304-6732
publication_status: published
publisher: MDPI AG
status: public
title: 'VCSELs: Influence of Design on Performance and Data Transmission over Multi-Mode
  and Single-Mode Fibers'
type: journal_article
user_id: '15911'
volume: 12
year: '2025'
...