  Photonic bandgap design is one of the most basic ways to effectively control
the interaction between light and matter. However, the traditional photonic
bandgap is always dispersive (blueshift with the increase of the incident
angle), which is disadvantageous to the construction of wide-angle optical
devices. Hypercrystal, that the photonic crystal with layered hyperbolic
metamaterials (HMMs), can strongly modify the bandgap properties based on the
anomalous wavevector dispersion of the HMM. Here, based on phase variation
compensation between HMM and isotropic dielectric layers, we propose for the
first time to design nonreciprocal and flexible photonic bandgaps using
magneto-optical HMMs in one-dimensional photonic crystals. Especially for the
forward and backward incident light, the blueshift and dispersionless of the
forward and backward cavity modes are designed respectively to realize the
interesting omnidirectional nonreciprocal absorber. Our results show high (low)
absorption about 0.99 (0.25) in an angle range of 20-75 degrees for the forward
(backward) incident light at the wavelength of 367 nm. The nonreciprocal
omnidirectional cavity mode not only facilitates the design of perfect
unidirectional optical absorbers working in a wide-angle range, but also
possesses significant applications for all-angle reflectors and filters.
