NUMERICAL ANALYSIS OF THE INSTANTANEOUS AND RELAXED KERR MODEL FOR GENERATION OF THE ALL-OPTICAL LOGIC GATES WITH TRIANGULAR FIBER COUPLER (TFC)

Abstract

All-optical logic gates can enable many advanced functions such as all-optical bit-pattern recognition, all-optical bit-error rate monitoring, all-optical packet address and payload separation, all-optical label swapping and all-optical packet drop in optical time domain multiplexing (OTDM) networks. Recently, much attention has been given to the influence of the relaxation process (sometimes called the Debye relaxation model) of the nonlinear response because the usual assumption of instantaneous nonlinear response fails for ultrashort pulses and additional contributions coming from nonlinear dispersion and relaxed nonlinearity have to be taken into account. The Kerr–Debye model is a relaxation of the nonlinear Kerr model in which the relaxation coefficient is a finite response time of the nonlinear material. In this paper, we have presented a numerical analysis of the triangular fiber coupler (TFC) for generation of the all-optical logic gates with nonlinear optical (NLO) properties, where we consider the nonlinear effects Kerr group velocity dispersion (GVD) and self-phase modulation (SPM) instantaneous and relaxed (Kerr–Debye model). To implement all-optical logic gates we used TFC of three symmetric configurations [Instantaneous (III), Relaxed (RRR-5 and RRR-9)]. In the instantaneous condition, the TFC is made up of silica optical fibers (with instantaneous response time — indicated by III) and in the relaxed conditions (RRR-5 and RRR-9) the TFC is made up of fibers with delayed response time of around 25 ps (for example, the polymer optical fibers). In our paper, we are interested in the transmission characteristics, the XRatio level (XR (dB)) as a function of the ΔΦ parameter, the normalized time duration (NTD) and the pulse evolution along the TFC and finally to compare the performance of all-optical logic gates, we will use the figure-of-merit of the logic gates (FOMELG (dB)) defined as a function of the extinction ratio of the gate outputs. All results were obtained numerically, considering a very simple model for generation of a optical logic gates.