Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti- PT -symmetry

Can Nth order Born approximation be exact?

“…Unlike adiabatic and semiclassical approximations, the task of finding conditions for the exactness of the Born approximation has eluded several generations of physicists. Recently, we used the dynamical formulation of stationary scattering of [14,19] to identify scattering problems in two and three dimensions that are exactly solvable by the first-order Born approximation [14,15]. In the case of EM scattering, this relied on the technical assumption pertaining the existence of a coordinate system where the detectors are placed on the planes x 3 = ±∞, and ε33 (x) and μ33 (x) do not vanish, [15].…”

“…The results of [13][14][15] make extensive use of a recently developed dynamical formulation of stationary scattering [14,[17][18][19] which relies on a fundamental notion of transfer matrix. In one dimension this coincides with the standard transfer matrix used to conduct scattering calculations since the 1940's [20][21][22][23][24].…”