  Highly directional radiation from photonic structures is important for many
applications, including high power photonic crystal surface emitting lasers,
grating couplers, and light detection and ranging devices. However, previous
dielectric, few-layer designs only achieved moderate asymmetry ratios, and a
fundamental understanding of bounds on asymmetric radiation from arbitrary
structures is still lacking. Here, we show that breaking the 180$^\circ$
rotational symmetry of the structure is crucial for achieving highly asymmetric
radiation. We develop a general temporal coupled-mode theory formalism to
derive bounds on the asymmetric decay rates to the top and bottom of a photonic
crystal slab for a resonance with arbitrary in-plane wavevector. Guided by this
formalism, we show that infinite asymmetry is still achievable even without the
need of back-reflection mirrors, and we provide numerical examples of designs
that achieve asymmetry ratios exceeding $10^4$. The emission direction can also
be rapidly switched from top to bottom by tuning the wavevector or frequency.
Furthermore, we show that with the addition of weak material absorption loss,
such structures can be used to achieve perfect absorption with single-sided
illumination, even for single-pass absorption rates less than $0.5\%$ and
without back-reflection mirrors. Our work provides new design principles for
achieving highly directional radiation and perfect absorption in photonics.
