While an omnidirectional bandgap is necessary to reflect arbitrary polarized light with a planar periodic reflector at any angle of radiation incidence, we demonstrate that omnidirectionality is not at all necessary for efficient antiguiding of modes of any polarization in low-index core photonic bandgap (PBG) fibers and waveguides. For a given radiation decay rate into the reflector and multilayer bandgap size we characterize the phase space of fiber materials leading to the same effective guiding conditions. We demonstrate that low- and high-index-contrast PBG waveguides can antiguide problematic TM-like modes equally effectively. Finally, the possibility of TE-like guidance of a TM-polarized mode is described.
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