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

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.

[1]  S. B. Cavalcanti,et al.  Modulation instability of ultrashort pulses via a generalized nonlinear Schrödinger equation with deviating argument , 1996 .

[2]  A. Buryak,et al.  Soliton states and bifurcation phenomena in three-core nonlinear fiber couplers , 1994 .

[3]  N. Trivunac-Vukovic.  Realization of All-optical Ultrafast Logic Gates using Triple Core Asymmetric Nonlinear Directional Coupler , 2001 .

[4]  Hongzhi Sun,et al.  High speed all optical logic gates based on quantum dot semiconductor optical amplifiers. , 2010, Optics express.

[5]  Nicolas K Fontaine,et al.  Optical Arbitrary Waveform Generation-Based Packet Generation and All-Optical Separation for Optical-Label Switching , 2010, IEEE Photonics Technology Letters.

[6]  Chinlon Lin,et al.  Self-phase modulation in silica optical fibers (A) , 1978 .

[7]  Keith J. Blow,et al.  Theoretical description of transient stimulated Raman scattering in optical fibers , 1989 .

[8]  W. Deering,et al.  Controlling all-optical switching in multicore nonlinear couplers , 2003 .

[9]  A. Rostami,et al.  Tb/s Optical Logic Gates Based on Quantum-Dot Semiconductor Optical Amplifiers , 2010, IEEE Journal of Quantum Electronics.

[10]  T. Taha,et al.  Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation , 1984 .

[11]  Y. Chen.  Asymmetric triple-core couplers , 1992 .

[12]  K. Nakkeeran,et al.  Modeling Self-Similar Optical Pulse Compression in Nonlinear Fiber Bragg Grating Using Coupled-Mode Equations , 2011, Journal of Lightwave Technology.

[13]  A. R. Blythe,et al.  Electrical properties of polymers , 1979 .

[14]  R. W. Hellwarth,et al.  Third-order optical susceptibilities of liquids and solids , 1977 .

[15]  P. Chu,et al.  Logic operations in dispersion-mismatched nonlinear fibre couplers , 1996 .

[16]  Asymmetric nonlinear coupling and its applications to logic functions , 1992 .

[17]  G. Agrawal.  Chapter 5 – Fiber Lasers , 2001 .

[18]  A. Buryak,et al.  Stationary pulse propagation in n-core nonlinear fiber arrays , 1995 .

[19]  M. Nurhuda,et al.  Effects of delayed Kerr nonlinearity and ionization on the filamentary ultrashort laser pulses in air. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  É. Lantz,et al.  Spatiotemporal dynamics of soliton arrays generated from spatial noise in a planar waveguide with relaxing Kerr nonlinearity. , 2002, Optics express.

[21]  M. R. Uddin,et al.  All-Optical Wavelength Conversion by the Modulation of Self-Locking State of a Single-Mode FP-LD , 2010, IEEE Photonics Technology Letters.

[22]  George I. Stegeman,et al.  Parametric amplification and modulational instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity , 1989 .

[23]  Partha Pratim Sahu.  All-optical switch using optically controlled two mode interference coupler. , 2012, Applied optics.

[24]  I. Gleria,et al.  Modulational instability in lossless fibers with saturable delayed nonlinear response , 2008 .

[25]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[26]  N. Akhmediev,et al.  Novel soliton states and bifurcation phenomena in nonlinear fiber couplers. , 1993, Physical review letters.

[27]  J. W. M. Menezes,et al.  Periodic Modulation of Nonlinearity in a Fiber Bragg Grating: A Numerical Investigation , 2012 .

[28]  A. Sombra,et al.  SOLITON SWITCHING IN THREE-CORE NONLINEAR DIRECTIONAL FIBER COUPLERS , 1998 .

[29]  M. Potasek,et al.  Modulation instability in an extended nonlinear Schrödinger equation. , 1987, Optics letters.

[30]  Mathieu Chauvet,et al.  Spatiotemporal behavior of periodic arrays of spatial solitons in a planar waveguide with relaxing Kerr nonlinearity , 2002 .

[31]  Yong Liu,et al.  All-optical signal processing based on semiconductor optical amplifiers , 2011 .

[32]  E. A. Golovchenko,et al.  Unified analysis of four-photon mixing, modulational instability, and stimulated Raman scattering under various polarization conditions in fibers , 1994 .

[33]  Xue Liu,et al.  Modulation instability for a relaxational Kerr medium , 2008 .