Abstract
This paper presents an unconditionally stable Split-Step Finite-Difference Time-Domain (SS-FDTD) method with 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order accuracy in time. Analytical proof of its unconditional stability is provided and numerical dispersion results are shown. Compared to the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order SS-FDTD, the 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order SS-FDTD yields a lower phase velocity error. Compared further to the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order SS-FDTD with three iterations (for the same number of time marching steps), the 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order SS-FDTD still achieves better numerical dispersion performance with sufficiently fine mesh.
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