A time domain beam propagation method based on a finite element scheme

Efficient time-domain finite-difference beam propagation methods for the analysis of slab and circularly symmetric waveguides

“…For TE-mode propagation, (5) can be written as follows [4]- [9]: (6) Here, we discretize (6) using the alternating-direction implicit method (ADIM) as was shown in [12]. The first half-step in ADIM factorization for (6) can be separated into (7) (8) The GD scheme can directly be applied to the second derivatives with respect to both the and directions.…”