AN EFFICIENT ALGORITHM FOR TRUNCATING SPATIAL DOMAIN IN MODELING LIGHT-SCATTERING BY FINITE-DIFFERENCE TECHNIQUE

The finite-difference time domain technique is one of the the most rob ust and accurate numerical methods for the solution of light scatterin g by small particles with arbitrary composition and geometry. In pract ice, this method requires that the spatial domain for the computation of near-field be truncated, An absorbing boundary condition must be im posed in conjunction with this truncation. The performance of this bou ndary condition is essential to the stability of numerical computation s and the reliability of results. In the present study, a new boundary condition, referred to as the mixed T algorithm has been developed, w hich is a generalization of the transmitting boundary condition origin ally developed by Liao and co-workers. The present algorithm does not require spatial interpolation far wave values at interior grid points. In addition, it produces two minima of spurious reflections at small and large incident angles, allowing efficient absorption of the scatte red waves at the boundary for large incident angles, When the third-or der mixed T algorithm is used, the reflection coefficient of the bound ary is less than 1% for incident angles from 0 degrees to about 70 deg rees, We find that the numerical instability associated with the trans mitting boundary condition is caused by the location-dependent amplitu de of outgoing waves in the vicinity of the boundary, For this reason, the mixed T algorithm is stabilized by consistently introducing diffu sive coefficients into the boundary equation. When the stabilized algo rithm is applied, the near-field within the truncated domain can be co mputed by using single-precision arithmetic without overflows for more than 10(5) steps in the time-marching iteration. Finally, the new abs orbing boundary condition is validated by carrying out numerical exper iments involving the propagation of a TM wave excited by a sinusoidal point source, simultaneous simulation of the wave propagation in small and large domains, and the scattering of a TM wave by an infinite cir cular cylinder. (C) 1998 Academic Press.