Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra

In this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized into two two-dimensional wave equations with first-order time derivatives. Then, using suitable approximations, not only Engquist and Majda ABCs can be obtained, but also generalized ABCs proposed by Trefethen and Halpern, which are applicable to simulations of radiation problems.