Theory of the nonlinear all-optical logical gates based on PBG structures

In our work, we show that photonic bandgap (PBG) systems containing nonlinear insertions are of interest for possible applications as the all-optical adders and logical gates. Two principal schemes of an all-optical adder based on the combined 1D-3D PBG materials containing optically nonlinear layers are discussed. Due to the electromagnetic spectra nonlinear dependence on the light signal intensity, the reflection properties of the system change significantly for chosen operation frequencies. The photonic structure behavior with changing intensity is investigated for a few systems consisting of a periodically layered structure covered with an optically nonlinear material and a 3D opal PBG structure. The latter plays the role of a motherboard controlling and directing the signals after the logical transformation. Theoretical estimations of the adder cell parameters are made for Si/SiO₂ and GaAs/AlAs photonic crystals covered with layers made from nonlinear doped glasses. The ideology of angular signal processing is developed. It is shown that the angular-frequency diagram contains extremely sensitive areas inside the total reflection range, where the weak nonlinearity leads to dramatic change in light reflection and transmission. Both solitary local modes and pure band modes are considered. For 256-digit capacity the adder body has to consist of 32768 cells connecting by optical channels in the both schemes. In summary, we discuss some general problems of "all-optical" signal processing, mechanisms of nonlinear signal transformation and the optical negative differential resistance areas existence, heating, energy losses and energy redistribution channels and geometry factors.