Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities

Ivan S. Maksymov, Andrey A. Sukhorukov, Andrei Lavrinenko, Yuri S. Kivshar

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon absorption in optical media is proceeded conventionally through the iterative solution of nonlinear algebraic equations. Here, we study three approaches for the field update including simple noniterative explicit schemes. By comparing them to the analytical results for optical pulse propagation in long nonlinear media (nonlinear phase incursion for the pump wave of about $\pi$ radians), we demonstrate convincingly that simple noniterative FDTD updating schemes, which are commonly believed to be inaccurate and unstable, produce accurate results and drastically speed up the computation as compared to ADE approaches. Such schemes can significantly reduce the CPU time for nonlinear computations, especially in 3-D models.
    Original languageEnglish
    JournalI E E E Antennas and Wireless Propagation Letters
    Volume10
    Pages (from-to)143-146
    ISSN1536-1225
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Finite-difference time domain (FDTD)
    • Optical Kerr effect
    • Four-wave mixing (FWM)
    • Nonlinearity

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