Periodic Modulation of Nonlinearity in a Two-Core Photonic Crystal Fiber: A Numerical Investigation

Abstract

We present a numerical investigation of the propagation and the switching of ultra-short pulses (100 fs) in a two-core nonlinear coupler of photonic crystal fibers constructed with periodically modulated the non-linearity fiber (PMNL-PFC). Our simulations are taking into account different amplitude and frequency modulations of the PMNL-PFC. A coupler for coupling whose length is Lc = 1.8 cm, the transmission characteristics, the compression factor, the crosstalk (Xtalk) and extinction ratio (Xratio) levels of the first order solitons were studied for low to high pump energies considering 2Lc. By an analysis on the reference channel (channel 2), it is observed that at low modulation frequencies an increase occurs in the switching power increasing transmission efficiency. For high modulation frequencies, the transmitted energy efficiency loses. The switching pulses are stronger for low frequency and high amplitude modulation. The Xtalk is a function of the measurement made on the secondary channel (channel 1). It was observed that this unwanted high-frequency energy increases to lessen the measure of the amplitude modulation. In summary, we have demonstrated that introduction of a non-linearity profile takes the periodically modulated PMNL-PFC to strong variations at transmission efficiency, Xtalk, Xratio a function of frequency and modulation amplitude and the input power.

Share and Cite:

Filho, A. , Mendes, A. , Sousa, J. , Batista, G. , Bastos, A. , Sobrinho, C. , Lyra, M. and Sombra, A. (2015) Periodic Modulation of Nonlinearity in a Two-Core Photonic Crystal Fiber: A Numerical Investigation. Journal of Electromagnetic Analysis and Applications, 7, 41-51. doi: 10.4236/jemaa.2015.72005.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Knight, J.C. (2003) Review Article Photonic Crystal Fibres. Nature, 424, 847-851.
http://dx.doi.org/10.1038/nature01940
[2] Skryabin, D.V., Luan, F., Knight, J.C. and Russell, P.St.J. (2003) Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers. Science, 301, 1705-1708.
http://dx.doi.org/10.1126/science.1088516
[3] Liu, M. and Chiang, K.S. (2010) Propagation of Ultrashort Pulses in a Nonlinear Two-Core Photonic Crystal Fiber. Applied Physics B, 98, 815-820.
http://dx.doi.org/10.1007/s00340-009-3870-8
[4] Jensen, S.M. (1982) The Nonlinear Coherent Coupler. IEEE Journal of Quantum Electronics, 18, 1580-1583.
http://dx.doi.org/10.1109/JQE.1982.1071438
[5] Trillo, S., Wabnitz, S., Wright, E.M. and Stegman, G.I. (1988) Soliton Switching in Fiber Nonlinear Directional Coupler. Optics Letters, 13, 672-674.
http://dx.doi.org/10.1364/OL.13.000672
[6] Peng, G.D. and Ankiewicz, A. (1992) Fundamental and Second Order Soliton Transmission in Nonlinear Directional Fiber Couplers. Journal of Nonlinear Optical Physics & Materials, 1, 135.
http://dx.doi.org/10.1142/S021819919200008X
[7] da Silva, M.G., Teles, A.F. and Sombra, A.S.B. (1998) Soliton Switching in Three-Core Nonlinear Directional Fiber Couplers. Journal of Applied Physics, 84, 1834-1842.
http://dx.doi.org/10.1063/1.368615
[8] Powelson, J.C., Feng, W., Lin, S., Feuerstein, R.J. and Tomic, D. (1998) Crosstalk of Passive Directional Couplers. Journal of Lightwave Technology, 16, 2020-2027.
http://dx.doi.org/10.1109/50.730365
[9] da Silva, M.G., Bastos, A.M., Sobrinho, C.S., Lima, J.L.S., de Almeida, E.F. and Sombra, A.S.B. (2005) Optical Crosstalk in a Periodically Inhomogeneous Nonlinear Dispersion Directional Fiber Coupler. Optical Fiber Technology, 11, 180-192.
http://dx.doi.org/10.1016/j.yofte.2004.09.005
[10] Coelho, A.G., Costa, M.B.C., Ferreira, A.C., da Silva, M.G., Lyra, M.L. and Sombra, A.S.B. (2013) Realization of All-Optical Logic Gates in a Triangular Triple-Core Photonic Crystal Fiber. Journal of Lightwave Technology, 31, 731-739.
http://dx.doi.org/10.1109/JLT.2012.2232641
[11] Agrawal, G.P. (2001) Applications of Nonlinear Fiber Optics. Academic Press, San Diego.
[12] Khan, K.R., Wu, T.X., Christodoulides, D.N. and Stegeman, G.I. (2008) Soliton Switching and Multi-Frequency Generation in a Nonlinear Photonic Crystal Fiber Coupler. Optics Express, 16, 9417-9428.
http://dx.doi.org/10.1364/OE.16.009417
[13] Chiang, K.S. (1997) Coupled-Mode Equations for Pulse Switching in Parallel Waveguides. IEEE Journal of Quantum Electronics, 33, 950-954.
http://dx.doi.org/10.1109/3.585482
[14] Chiang, K.S. (1997) Propagation of Short Optical Pulses in Directional Couplers with Kerr Nonlinearity. Journal of the Optical Society of America B, 14, 1437-1443.
http://dx.doi.org/10.1364/JOSAB.14.001437
[15] Chiang, K.S. (1995) Intermodal Dispersion in Two-Core Optical Fibers. Optics Letters, 20, 997-999.
http://dx.doi.org/10.1364/OL.20.000997
[16] Gear, C.W. (1971) Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs.
[17] Acton, F.S. (1990) Numerical Methods That Work. Corrected Edition, Mathematical Association of America, Washington DC, Chapter 5.
[18] Stoer, J. and Bulirsch, R. (1980) Introduction to Numerical Analysis. Springer-Verlag, New York, Chapter 7.
http://dx.doi.org/10.1007/978-1-4757-5592-3
[19] Lambert, J. (1973) Computational Methods in Ordinary Differential Equations. Wiley, New York.
[20] Lapidus, L. and Seinfeld, J. (1971) Numerical Solution of Ordinary Differential Equations. Academic Press, New York.
[21] Hanza, H.H., Chu, P.L., Malomed, B.A. and Peng, G.D. (1997) Soliton Compression and Splitting in Double-Core Nonlinear Optical Fibers. Optics Communications, 134, 59-65.
http://dx.doi.org/10.1016/S0030-4018(96)00587-1
[22] Pelusi, M.D. and Liu, H.F. (1997) Higher Order Soliton Pulse Compression in Dispersion-Decreasing Optical Fibers. IEEE Journal of Quantum Electronics, 33, 1430-1439.
http://dx.doi.org/10.1109/3.605567

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.