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A hollow core fiber (HCF) has a cross section with a substantially-circular hollow core in a cladding lattice, an axial center and a reference direction that extends radially in one direction from the axial center. The HCF comprises modified holes that are located along linear paths that extend radially outward from the axial center. The modified holes, which are located at various radial distances from the axial center and at various azimuthal angles from the reference direction, have non-uniform modified properties. These non-uniform modified properties include radially-varying properties, azimuthally-varying properties, or a combination of radially-varying and azimuthally-varying properties.