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Not only the interaction between optical pulse and orbital electron but also the interaction between optical pulse and optical phonon needs to be considered when input pulse energy is large. The latter induces the simulated Raman scattering, thus generating the Raman gain. We analyze the effect of Raman gain, especially parallel Raman gain, on dark soliton trapping in high birefringence fiber by analytical method and numerical method. In the first part, we introduce some research results of soliton trapping obtained in recent years. In the second part, the coupled nonlinear Schrödinger equation including Raman gain is utilized for high birefringence fiber. The trapping threshold of dark soliton with considering the Raman gain is deduced by the Lagrangian approach when input pulse is the dark soliton pulse that the amplitude of two polarized components of the dark soliton are the same (see formula (26)). Fig. 1. shows the relation between threshold and parallel Raman gain according to formula (26) when group velocity mismatching coefficient values are 0.15, 0.3, and 0.5 (vertical Raman gains are all 0.1). In the third part, the propagation of the two orthogonal polarization components of dark soliton is simulated by the fractional Fourier transform method. Figures 2-4 show respectively dark soliton trapping with group velocity mismatching coefficient values of 0.15, 0.3 and 0.5. We consider three situations in which Raman gain is not included and the parallel Raman gains are 0.4 and 0.6 when vertical Raman gains are both 0.1 in different group velocity mismatching coefficient values. We obtain the threshold of dark soliton by numerical method under different conditions and analyze the figures. At the same time, we compare the analytical solution with the numerical solution and discuss the effect of Raman gain on dark soliton trapping. The last part focuses on our conclusion. It is found that the threshold which is obtained by analytical method is smaller than that from the numerical solution. The difference between the analytical and numerical dependences decreases with group velocity mismatching coefficient decreases. As a result, formula (26) is in good agreement with numerical data for small group velocity mismatching. The larger the group velocity mismatching, the larger the amplitude threshold of dark soliton is. It also shows that the amplitude threshold of dark soliton can be reduced due to Raman gain and the threshold is reduced faster with the increasing of Raman gain.
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Keywords:
- Raman gain /
- dark soliton /
- trapping /
- high birefringence fiber
[1] Agrawal G P 2010 Nonlinear Fiber Optics (2rd Ed.) (Boston: Academic Press) pp134-165
[2] Islam M N, Poole C D, Gordon J P 1989 Opt. Lett. 14 1011
[3] Skryabin D V, Gorbach A V 2007 Phys. Rev. A 76 053803
[4] Gorbach A V, Skryabin D V 2007 Nat. Photon. 1 653
[5] Travers J C, Taylor J R 2009 Opt. Lett. 34 115
[6] He Y J, Mihalache D, Hu B 2010 Opt. Lett. 35 1716
[7] Liu H Y, Dai Y T, Xu C, Wu J, Xu K, Li Y, Hong X B, Lin J T 2010 Opt. Lett. 35 4042
[8] Wang W B, Yang H, Tang P H, Han F 2013 Opt. Ecpress 21 11215
[9] Cheng C, Wang X, Fang Z, Shen B 2005 Appl. Phys. B 80 291
[10] Zheng L, Tang Y 2010 Chin. Phys. B 19 044209
[11] Zheng L, Tang Y 2009 J. Nonlinear Opt. Phys. 18 457
[12] Liu B L, Jia W G, Wang Y P, Qiao H L, Wang X D, Menke N M L 2014 Acta Phys. Sin. 63 214207(in Chinese) [刘宝林, 贾维国, 王玉平, 乔海龙, 王旭东, 门克内木乐 2014 63 214207]
[13] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Acta Phys. Sin. 64 054207(in Chinese) [于宇, 贾维国, 闫青, 门克内木乐, 张俊萍 2015 64 054207]
[14] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Chin. Phys. B 24 084210
[15] Lin Q, Agrawal G P 2006 Opt. Lett. 31 3086
[16] Agrawal G P 2010 Nonlinear Fiber Optics (2rd Ed.) (Boston: Academic Press) pp105-107
[17] Satsuma J, Yajima N 1974 Progr. Theor. Phys. Suppl. 55 284
[18] Kivshar Y S 1990 J. Opt. Soc. Am. B 7 2204
[19] Anderson D, Lisak M 1985 Phys. Rev. A 32 2270
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[1] Agrawal G P 2010 Nonlinear Fiber Optics (2rd Ed.) (Boston: Academic Press) pp134-165
[2] Islam M N, Poole C D, Gordon J P 1989 Opt. Lett. 14 1011
[3] Skryabin D V, Gorbach A V 2007 Phys. Rev. A 76 053803
[4] Gorbach A V, Skryabin D V 2007 Nat. Photon. 1 653
[5] Travers J C, Taylor J R 2009 Opt. Lett. 34 115
[6] He Y J, Mihalache D, Hu B 2010 Opt. Lett. 35 1716
[7] Liu H Y, Dai Y T, Xu C, Wu J, Xu K, Li Y, Hong X B, Lin J T 2010 Opt. Lett. 35 4042
[8] Wang W B, Yang H, Tang P H, Han F 2013 Opt. Ecpress 21 11215
[9] Cheng C, Wang X, Fang Z, Shen B 2005 Appl. Phys. B 80 291
[10] Zheng L, Tang Y 2010 Chin. Phys. B 19 044209
[11] Zheng L, Tang Y 2009 J. Nonlinear Opt. Phys. 18 457
[12] Liu B L, Jia W G, Wang Y P, Qiao H L, Wang X D, Menke N M L 2014 Acta Phys. Sin. 63 214207(in Chinese) [刘宝林, 贾维国, 王玉平, 乔海龙, 王旭东, 门克内木乐 2014 63 214207]
[13] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Acta Phys. Sin. 64 054207(in Chinese) [于宇, 贾维国, 闫青, 门克内木乐, 张俊萍 2015 64 054207]
[14] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Chin. Phys. B 24 084210
[15] Lin Q, Agrawal G P 2006 Opt. Lett. 31 3086
[16] Agrawal G P 2010 Nonlinear Fiber Optics (2rd Ed.) (Boston: Academic Press) pp105-107
[17] Satsuma J, Yajima N 1974 Progr. Theor. Phys. Suppl. 55 284
[18] Kivshar Y S 1990 J. Opt. Soc. Am. B 7 2204
[19] Anderson D, Lisak M 1985 Phys. Rev. A 32 2270
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