We have theoretically investigated the general properties of photonic crystals without time-reversal and space-inversion symmetries by examining the case of one-dimensional periodic, lossless dielectric helical media (HM) with magneto-optic (MO) activity. We show that photonic bandgap formation in the absence of these two symmetry elements leads to a remarkable set of properties: indirect photonic bandgaps (edges not aligned in k space), backward wave propagating eigenmodes (which allow for negative refraction), unusual nonpropagating modes in the gap (their complex-valued wave vectors have frequency-dependent, nonzero real parts, which do not change sign for opposite decay directions), anomalous propagation, and group-velocity-based unidirectional superprism effects. Particular properties of MO HM are discussed in detail.
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