IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p2069-d448019.html
   My bibliography  Save this article

Non-Spiking Laser Controlled by a Delayed Feedback

Author

Listed:
  • Anton V. Kovalev

    (Birzhevaya Liniya 14, ITMO University, 199034 Saint Petersburg, Russia
    These authors contributed equally to this work.)

  • Evgeny A. Viktorov

    (Birzhevaya Liniya 14, ITMO University, 199034 Saint Petersburg, Russia
    These authors contributed equally to this work.)

  • Thomas Erneux

    (Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine C.P. 231, 1050 Bruxelles, Belgium
    These authors contributed equally to this work.)

Abstract

In 1965, Statz et al. (J. Appl. Phys. 30, 1510 (1965)) investigated theoretically and experimentally the conditions under which spiking in the laser output can be completely suppressed by using a delayed optical feedback. In order to explore its effects, they formulate a delay differential equation model within the framework of laser rate equations. From their numerical simulations, they concluded that the feedback is effective in controlling the intensity laser pulses provided the delay is short enough. Ten years later, Krivoshchekov et al. (Sov. J. Quant. Electron. 5394 (1975)) reconsidered the Statz et al. delay differential equation and analyzed the limit of small delays. The stability conditions for arbitrary delays, however, were not determined. In this paper, we revisit Statz et al.’s delay differential equation model by using modern mathematical tools. We determine an asymptotic approximation of both the domains of stable steady states as well as a sub-domain of purely exponential transients.

Suggested Citation

  • Anton V. Kovalev & Evgeny A. Viktorov & Thomas Erneux, 2020. "Non-Spiking Laser Controlled by a Delayed Feedback," Mathematics, MDPI, vol. 8(11), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2069-:d:448019
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/2069/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/2069/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2069-:d:448019. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.