Journal article
Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities
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.
Language: | English |
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Publisher: | IEEE |
Year: | 2011 |
Pages: | 143-146 |
ISSN: | 15485757 and 15361225 |
Types: | Journal article |
DOI: | 10.1109/LAWP.2011.2114319 |
ORCIDs: | Lavrinenko, Andrei |
Finite-difference time domain (FDTD) Four-wave mixing (FWM) Nonlinearity Optical Kerr effect
CPU time Electric fields Equations FDTD-adopted numerical algorithms Finite difference methods Kerr nonlinearities Mathematical model Nonlinear optics Optical pulses Time domain analysis auxiliary differential equation techniques differential equations electric field finite difference time-domain analysis finite-difference time-domain modeling four-wave mixing (FWM) full-vectorial 3D ADE FDTD modeling iterative methods iterative solution light propagation noniterative explicit schemes nonlinear algebraic equations nonlinear equations nonlinear media nonlinearity optical Kerr effect optical media optical pulse propagation two-photon absorption