  We analyze the resonant transmission of light through a photonic-crystal
waveguide side coupled to a Kerr nonlinear cavity, and demonstrate how to
design the structure geometry for achieving bistability and all-optical
switching at ultra-low powers in the slow-light regime. We show that the
resonance quality factor in such structures scales inversely proportional to
the group velocity of light at the resonant frequency and thus grows
indefinitely in the slow-light regime. Accordingly, the power threshold
required for all-optical switching in such structures scales as a square of the
group velocity, rapidly vanishing in the slow-light regime.
