Optical waveguides using segmented periodically-spaced high contrast gratings bounding a hollow core propagation region on at least two sides. Incident light is received in a hollow waveguide (HW) region (core) between opposing HCG faces which provide lateral confinement in response to glancing reflections of the incident light beam from high refractive index segments of the HCG as it traverses the core. Embodiments are described for planar waveguides (1D) having a planar core between two planar HCGs, as well as 2D waveguides, such as having rectangular segments of the HCG through which light is propagated. Additionally, other configurations of HCG-HW, including those having arbitrary incidence and azimuth, angled HCG segments, propagation in a direction which is transverse, or alternatively parallel, to the segments of the HCG.