Multipole-free fast multilevel algorithm for layered media

A purely plane-wave based fast algorithm is presented for layered media problems. As long as the steepest descent path for the 2-D translator is well defined, the accuracy can be maintained under the MFLMA paradigm, and ultimately achieves the same computational complexity as the mixed form fast inhomogeneous plane-wave algorithm (FIPWA). The advantage is that multipoles are not needed, which makes this new form of FIPWA more easily adaptable to problems that must exploit a mixture of propagating and evanescent plane-waves