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The numerical simulation method for accurately solving the coupled generalized nonlinear Schrödinger equations (C-GNLSE) is essential for describing the dynamic behavior of ultrashort pulse propagating in optical fiber and developing the corresponding nonlinear fiber-optic devices. C-GNLSE in the normal picture is first mapped into the interaction picture by the representation transformation, and then, the two coupled nonlinear partial differential equations in the interaction picture are solved in frequency domain, with synchronous data updating in each iteration step, by using the vector form of Hult’s fourth-order Runge-Kutta iterative scheme. The proposed vector form algorithm of fourth-order Runge-Kutta in interaction picture (V-JH-RK4IP) is verified by using it in simulating the supercontinuum generation in high birefringence photonic crystal fiber. Moreover, the V-JH-RK4IP algorithm also exhibits the highest accuracy and computational efficiency as compared to other classical algorithms.
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Keywords:
- coupled generalized nonlinear Schrö /
- dinger equations (C-GNLSE) /
- interaction picture /
- four-order Runge-Kutta
[1] Dudley J M, Taylor J R 2010 Supercontinuum Generation in Optical Fibers (Cambridge University Press)
[2] Agrawal G P 2007 Nonlinear Fiber Optics (Academic Press)
[3] Povazay B, Bizheva K, Unterhuber A, Hermann B, Sattmann H, Fercher A F, Drexler W, Apolonski A, Wadsworth W J, Knight J C, Russell P S,Vetterlein M, Scherzer E 2002 Opt. Lett. 27 1800
[4] Paulsen H N, Hilligse K M, Thogersen J, Keiding S R, Larsen J J 2003 Opt. Lett. 28 1123
[5] Dudley M, Coen S 2006 Rev. Mod. Phys. 78 1135
[6] Zakharov V E, Shabat A B 1972 Sov. Phys. JETP 34 62
[7] Fermann M E, Kruglov V I, Thomsen B C, Dudley J M, Harvey J D 2000 Phys. Rev. Lett. 84 6010
[8] Hohage T, Schmidt F, Konrad-Zuse-Zentrum fr Informationstechnik, Berlin, Germany, 2002 Tech. Rep. ZIB-Report Jan 02-04, 2002
[9] Zhao L, Sui Z, Zhu Q H, Zhang Y, Zuo Y L 2009 Acta Phys. Sin. 58 4731 (in Chinese) [赵磊, 隋展, 朱启华, 张颖, 左言磊 2009 58 4731]
[10] Reeves W H, Skyabin D V, Biancalana F, Knight J C, Omenetto F G, Efimov A, Taylor A J 2003 Nature 424 511
[11] Hillingsoe K M, Paulsen H Thogersen N J, Keiding S R, Larsen J J 2003 J. Opt. Soc. Am. B 20 1887
[12] Siederdissen T H Z, Nielsen N C, Kuhl J, Giessen H 2006 J. Opt. Soc. Am. B 23 1360
[13] Cristiani I, Tediosi R, Tartara L, Degiorgio V 2003 Opt. Express 12 124
[14] Liu X M, Byoungho L 2003 IEEE Photon. Technol. Lett. 15 1549
[15] Blow K J, D Wood 1989 IEEE J. Quantum Electron 25 2665
[16] Hult J 2007 J. Lightw. Technol 25 3770
[17] Sinkin O V, Holzlöhner R, Zweck J, Menyuk C R 2003 J. Lightw. Technol 21 61
[18] Heidt A 2009 J. Lightwave Technol 27 3984
[19] Rieznik A A, Heidt A M, Konig P G, Bettachini V A, Grosz D F 2012 IEEE Photonics Journal 4 552
[20] Lu F, Lin Q, Knox W H, Agrawal G P 2004 Phys. Rev. Lett. 93 183901
[21] TU H H, Liu Y, Liu X M, Turchinovich D, Laegsgaard J, Stephen A B 2012 Opt. Express 20 1113
[22] Nishizawa N, Goto T 2003 Opt. Express 11 359
[23] Voronin A A, Fedotov I V, Kobelke J, Jager M, Schuster K, Fedotov A B, Bartelt H, Zheltikov A M 2012 Opt. Lett. 37 5163
[24] Liu X M 2011 Phys. Rev. A 84 053828
[25] Liu X M 2011 Phys. Rev. A 84 023835
[26] Trillo S, Wabnitz S 1992 J. Opt. Soc. Am. B 9 1061
[27] Martins E R, Spadoti D H, Romero M A, B V Borges 2007 Opt. Express 15 14335
[28] Lin Q, Agrawal G P 2006 Opt. Lett. 31 3086
[29] Menyuk C R, Islam M N, Gordon J P 1991 Opt. Lett. 16 566
[30] Chick B J, Chon J W M, Gu M 2007 Opt. Express 16 20099
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[1] Dudley J M, Taylor J R 2010 Supercontinuum Generation in Optical Fibers (Cambridge University Press)
[2] Agrawal G P 2007 Nonlinear Fiber Optics (Academic Press)
[3] Povazay B, Bizheva K, Unterhuber A, Hermann B, Sattmann H, Fercher A F, Drexler W, Apolonski A, Wadsworth W J, Knight J C, Russell P S,Vetterlein M, Scherzer E 2002 Opt. Lett. 27 1800
[4] Paulsen H N, Hilligse K M, Thogersen J, Keiding S R, Larsen J J 2003 Opt. Lett. 28 1123
[5] Dudley M, Coen S 2006 Rev. Mod. Phys. 78 1135
[6] Zakharov V E, Shabat A B 1972 Sov. Phys. JETP 34 62
[7] Fermann M E, Kruglov V I, Thomsen B C, Dudley J M, Harvey J D 2000 Phys. Rev. Lett. 84 6010
[8] Hohage T, Schmidt F, Konrad-Zuse-Zentrum fr Informationstechnik, Berlin, Germany, 2002 Tech. Rep. ZIB-Report Jan 02-04, 2002
[9] Zhao L, Sui Z, Zhu Q H, Zhang Y, Zuo Y L 2009 Acta Phys. Sin. 58 4731 (in Chinese) [赵磊, 隋展, 朱启华, 张颖, 左言磊 2009 58 4731]
[10] Reeves W H, Skyabin D V, Biancalana F, Knight J C, Omenetto F G, Efimov A, Taylor A J 2003 Nature 424 511
[11] Hillingsoe K M, Paulsen H Thogersen N J, Keiding S R, Larsen J J 2003 J. Opt. Soc. Am. B 20 1887
[12] Siederdissen T H Z, Nielsen N C, Kuhl J, Giessen H 2006 J. Opt. Soc. Am. B 23 1360
[13] Cristiani I, Tediosi R, Tartara L, Degiorgio V 2003 Opt. Express 12 124
[14] Liu X M, Byoungho L 2003 IEEE Photon. Technol. Lett. 15 1549
[15] Blow K J, D Wood 1989 IEEE J. Quantum Electron 25 2665
[16] Hult J 2007 J. Lightw. Technol 25 3770
[17] Sinkin O V, Holzlöhner R, Zweck J, Menyuk C R 2003 J. Lightw. Technol 21 61
[18] Heidt A 2009 J. Lightwave Technol 27 3984
[19] Rieznik A A, Heidt A M, Konig P G, Bettachini V A, Grosz D F 2012 IEEE Photonics Journal 4 552
[20] Lu F, Lin Q, Knox W H, Agrawal G P 2004 Phys. Rev. Lett. 93 183901
[21] TU H H, Liu Y, Liu X M, Turchinovich D, Laegsgaard J, Stephen A B 2012 Opt. Express 20 1113
[22] Nishizawa N, Goto T 2003 Opt. Express 11 359
[23] Voronin A A, Fedotov I V, Kobelke J, Jager M, Schuster K, Fedotov A B, Bartelt H, Zheltikov A M 2012 Opt. Lett. 37 5163
[24] Liu X M 2011 Phys. Rev. A 84 053828
[25] Liu X M 2011 Phys. Rev. A 84 023835
[26] Trillo S, Wabnitz S 1992 J. Opt. Soc. Am. B 9 1061
[27] Martins E R, Spadoti D H, Romero M A, B V Borges 2007 Opt. Express 15 14335
[28] Lin Q, Agrawal G P 2006 Opt. Lett. 31 3086
[29] Menyuk C R, Islam M N, Gordon J P 1991 Opt. Lett. 16 566
[30] Chick B J, Chon J W M, Gu M 2007 Opt. Express 16 20099
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