Compact 2D stencils for inhomogeneous Helmholtz equation based on method of connected local fields

We extend the numerical theory of the method of connected local fields (CLFs) for obtaining semi-analytical solutions of Helmholtz equation with dielectric discontinuities. Using two sets of local plane waves we match the tangential fields along the dielectric interface. We are able to obtain 2D compact FD-like stencil for CLF cell with a straight interface. The results are then compared with other high-accuracy frequency-domain finite-difference (FD-FD) methods with ours. At five points per wavelength spatial sampling, compact CLF-LPW derived coefficients achieve less than .01% relative local error near a planar interface subjecting to an arbitrary incident plane wave.