A multilayer optical polarizing film has optical layers whose refractive indices substantially match along orthogonal in-plane x- and y-axes, and that mismatch along a z-axis by at least 0.1 and in some cases by at least 0.15. The film has substantially no reflection bands at normal incidence, and for obliquely incident light has at least one reflection band, for p-polarized light only, that monotonically increases and that shifts to shorter wavelengths as the incidence angle increases.