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We investigate optical bistability in a multilayer one-dimensional photoniccrystal where the central layer is doped with $\Lambda$-type three level atoms.We take into account the influence of spontaneously generated coherence whenthe lower atomic levels are sufficiently close to each other, in which caseKerr-type nonlinear response of the atoms is enhanced. We calculate thepropagation of a probe beam in the defect mode window using numerical nonlineartransfer matrix method. We find that Rabi frequency of a control field actingon the defect layer and the detuning of the probe field from the atomicresonance can be used to control the size and contrast of the hysteresis loopand the threshold of the optical bistability. In particular we find that, atthe optimal spontaneously generated coherence, three orders of magnitude lowerthreshold can be achieved relative to the case without the coherence.

Optical bistability in one dimensional doped photonic crystals with spontaneously generated coherence