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Based on the theoretical model of optical wave propagation in parity-time (PT) symmetric waveguide, the transmission and control of bright solitons in PT symmetric Kerr nonlinear planar waveguide with Gaussian distribution are studied numerically. The PT symmetric waveguide requires that the refractive index distribution of waveguide should have to be an even symmetry, whereas the gain/loss distribution should be odd. The results show that when the strength of refractive index distribution of waveguide is positive, the refractive index has a maximum value in the center of the PT symmetric waveguide. Without the self-focusing Kerr nonlinear effect, the waveguide can also restrict optical wave to form the wavy light beam and transmit with long distance. When the strength of refractive index distribution is negative, the refractive index has a minimum value in the center of the PT symmetric waveguide. The transmission direction of optical wave is shifted. The gain/loss distribution can control the transmission direction of optical wave: if the strength of gain/loss distribution is positive, the optical wave is shifted toward the left; if the strength is negative, the optical wave is shifted toward the right; if the strength equals zero, the optical wave is divided into two beams. And when the refractive index distribution is negative, the interaction between adjacent bright solitons can be suppressed very well. The results of this research can provide a theoretical basis for the application of PT symmetric waveguide in all-optical control in the future.
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Keywords:
- bright solitons /
- parity-time symmetric /
- complex refractive index /
- transmission of optical wave
[1] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243
[2] El-Ganainy R, Makris K G, Christodoulides D N, Musslimani Z H 2007 Opt. Lett. 32 2632
[3] Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2008 Phys. Rev. Lett. 100 103904
[4] Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2010 Phys. Rev. A 81 063807
[5] Rter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192
[6] Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V, Siviloglou G A, Christodoulides D N 2009 Phys. Rev. Lett. 103 093902
[7] Chiao R Y, Garmire E, Townes C H 1964 Phys. Rev. Lett. 13 479
[8] Kelley P L 1965 Phys. Rev. Lett. 15 1005
[9] Stegeman G I, Segev M 1999 Science 286 1518
[10] Gao X H, Zhang C Y, Tang D, Zheng H, Lu D Q, Hu W 2013 Acta Phys. Sin. 62 044214 (in Chinese) [高星辉, 张承云, 唐冬, 郑晖, 陆大全, 胡巍 2013 62 044214]
[11] Li Q, Zhai Y H, Liang G, Guo Q 2013 Acta Phys. Sin. 62 024202 (in Chinese) [李琼, 翟永惠, 梁果, 郭旗 2013 62 024202]
[12] Ouyang S G 2013 Acta Phys. Sin. 62 040504 (in Chinese) [欧阳世根 2013 62 040504]
[13] Hu S, Ma X, Lu D, Yang Z, Zheng Y, Hu W 2011 Phys. Rev. A 84 043818
[14] Musslimani Z H, Makris K G, El-Ganainy R, Christodoulides D N 2008 Phys. Rev. Lett. 100 030402
[15] Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2010 Phys. Rev. A 81 063807
[16] Nixon S, Ge L, Yang J 2012 Phys. Rev. A 85 023822
[17] Abdullaev F K, Kartashov Y V, Konotop V V, Zezyulin D A 2011 Phys. Rev. A 83 041805
[18] Miri M A, Aceves A B, Kottos T, Kovanis V, Christodoulides D N 2012 Phys. Rev. A 86 033801
[19] Shi Z, Jiang X, Zhu X, Li H 2011 Phys. Rev. A 84 053855
[20] Khare A, Al-Marzoug S M, Bahlouli H 2012 Phys. Lett. A 376 2880
[21] Midya B, Roychoudhury R 2014 Ann. Phys. 341 12
[22] Al Khawaja U, Al-Marzoug S M, Bahlouli H, Kivshar Y S 2013 Phys. Rev. A 88 023830
[23] Yuan D Z, Li L 2013 Acta Sin. Quant. Opt. 19 155 (in Chinese) [原大洲, 李禄 2013 量子光学学报 19 155]
[24] Xu Y J, Dai C Q 2014 Opt. Commun. 318 112
[25] Chen Y X, Dai C Q, Wang X G 2014 Opt. Commun. 324 10
[26] Hu S, Hu W 2012 J. Phys. B: At. Mol. Opt. Phys. 45 225401
[27] Zezyulin D A, Konotop V V 2012 Phys. Rev. A 85 043840
[28] He Y, Zhu X, Mihalache D, Liu J, Chen Z 2012 Phys. Rev. A 85 013831
[29] Li C Y, Huang C M, Dong L W 2013 Chin. Phys. B 22 074209
[30] Hu S M, Hu W 2013 Chin. Phys. B 22 074201
[31] Agrawal G P (Translated by Jia D F, Yu Z H) 2002 Nonlinear Fiber Optics & Applications of Nonlinear Optics (Beijing: Publishing House of Electronics Industry) pp26, 34 (in Chinese) [阿戈沃 著(贾东红, 余震虹 译) 2002非线性光纤学原理及应用(北京: 电子工业出版社)第26, 34页]
[32] Kovsh D I, Yang S, Hagan D J, van Stryland E W 1999 Appl. Opt. 38 5168
[33] Ahmed Z 2001 Phys. Lett. A 287 295
-
[1] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243
[2] El-Ganainy R, Makris K G, Christodoulides D N, Musslimani Z H 2007 Opt. Lett. 32 2632
[3] Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2008 Phys. Rev. Lett. 100 103904
[4] Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2010 Phys. Rev. A 81 063807
[5] Rter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192
[6] Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V, Siviloglou G A, Christodoulides D N 2009 Phys. Rev. Lett. 103 093902
[7] Chiao R Y, Garmire E, Townes C H 1964 Phys. Rev. Lett. 13 479
[8] Kelley P L 1965 Phys. Rev. Lett. 15 1005
[9] Stegeman G I, Segev M 1999 Science 286 1518
[10] Gao X H, Zhang C Y, Tang D, Zheng H, Lu D Q, Hu W 2013 Acta Phys. Sin. 62 044214 (in Chinese) [高星辉, 张承云, 唐冬, 郑晖, 陆大全, 胡巍 2013 62 044214]
[11] Li Q, Zhai Y H, Liang G, Guo Q 2013 Acta Phys. Sin. 62 024202 (in Chinese) [李琼, 翟永惠, 梁果, 郭旗 2013 62 024202]
[12] Ouyang S G 2013 Acta Phys. Sin. 62 040504 (in Chinese) [欧阳世根 2013 62 040504]
[13] Hu S, Ma X, Lu D, Yang Z, Zheng Y, Hu W 2011 Phys. Rev. A 84 043818
[14] Musslimani Z H, Makris K G, El-Ganainy R, Christodoulides D N 2008 Phys. Rev. Lett. 100 030402
[15] Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2010 Phys. Rev. A 81 063807
[16] Nixon S, Ge L, Yang J 2012 Phys. Rev. A 85 023822
[17] Abdullaev F K, Kartashov Y V, Konotop V V, Zezyulin D A 2011 Phys. Rev. A 83 041805
[18] Miri M A, Aceves A B, Kottos T, Kovanis V, Christodoulides D N 2012 Phys. Rev. A 86 033801
[19] Shi Z, Jiang X, Zhu X, Li H 2011 Phys. Rev. A 84 053855
[20] Khare A, Al-Marzoug S M, Bahlouli H 2012 Phys. Lett. A 376 2880
[21] Midya B, Roychoudhury R 2014 Ann. Phys. 341 12
[22] Al Khawaja U, Al-Marzoug S M, Bahlouli H, Kivshar Y S 2013 Phys. Rev. A 88 023830
[23] Yuan D Z, Li L 2013 Acta Sin. Quant. Opt. 19 155 (in Chinese) [原大洲, 李禄 2013 量子光学学报 19 155]
[24] Xu Y J, Dai C Q 2014 Opt. Commun. 318 112
[25] Chen Y X, Dai C Q, Wang X G 2014 Opt. Commun. 324 10
[26] Hu S, Hu W 2012 J. Phys. B: At. Mol. Opt. Phys. 45 225401
[27] Zezyulin D A, Konotop V V 2012 Phys. Rev. A 85 043840
[28] He Y, Zhu X, Mihalache D, Liu J, Chen Z 2012 Phys. Rev. A 85 013831
[29] Li C Y, Huang C M, Dong L W 2013 Chin. Phys. B 22 074209
[30] Hu S M, Hu W 2013 Chin. Phys. B 22 074201
[31] Agrawal G P (Translated by Jia D F, Yu Z H) 2002 Nonlinear Fiber Optics & Applications of Nonlinear Optics (Beijing: Publishing House of Electronics Industry) pp26, 34 (in Chinese) [阿戈沃 著(贾东红, 余震虹 译) 2002非线性光纤学原理及应用(北京: 电子工业出版社)第26, 34页]
[32] Kovsh D I, Yang S, Hagan D J, van Stryland E W 1999 Appl. Opt. 38 5168
[33] Ahmed Z 2001 Phys. Lett. A 287 295
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