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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