Based on the Padé approximation and multistep method, we propose an implicit high-order unconditionally stable complex envelope algorithm to solve the time-dependent Maxwell’s equations. Unconditional numerical stability can be achieved simultaneously with a high-order accuracy in time. As we adopt the complex envelope Maxwell’s equations, numerical dispersion and dissipation are very small even at comparatively large time steps. To verify the capability of our algorithm, we compare the results of the proposed method with the exact solutions.
© 2008 Optical Society of America
Original Manuscript: August 26, 2008
Revised Manuscript: October 17, 2008
Manuscript Accepted: October 18, 2008
Published: November 19, 2008
Shuqi Chen, Weiping Zang, Axel Schülzgen, Jinjie Liu, Lin Han, Yong Zeng, Jianguo Tian, Feng Song, Jerome V. Moloney, and Nasser Peyghambarian, "Implicit high-order unconditionally stable complex envelope algorithm for solving the time-dependent Maxwell's equations," Opt. Lett. 33, 2755-2757 (2008)