Bistability in nonlinear optical structures involving photonic crystals

Periodic inhomogeneities of linear dielectric materials are known to give rise to highly complex transmission spectra, widely adjustable by tuning geometric parameters. In this work, the theory of optical periodic structures is extended to materials exhibiting the nonlinear Kerr effect. A new computational scheme, based on the transfer-matrix method, is introduced in order to perform, in a selfconsistent way, the simultaneous adjustment of the refractive index and transisting electric field and compute the intensity-dependent transmittance of nonlinear films. For adequate geometries and with a suitably adjusted frequency, hysteresis loops can appear in the transmittance vs. intensity diagrams, signaling bistability. We observe that a bistable behavior can appear without the construction of a Fabry-Perot structure. For a nonlinear film structured by a periodic side variation of the refractive index, we provide evidence that bistability can also take place for frequencies corresponding to Fano resonances. Depending on the geometry of the film, we observe a wide variety of shapes for the transmittance hysteresis loops.