单通道与多通道多极格子孤子及其动力学行为
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摘要
基于非线性薛定谔方程,研究了具有光格子的局域非线性介质中存在的单通道和多通道多极格子孤子的光场分布、稳定性和动力学行为。研究发现,系统中存在同相和反相2种类型的多通道多极格子孤子;在单通道情形下,只存在反相多极格子孤子,同相的多极格子孤子不存在;在3种类型的格子中,同相多极格子孤子的稳定性最差,而多通道反相多极格子孤子的稳定性最高。在撤去光格子的情况下,3类格子孤子呈现出不同的动力学行为。同相多极格子孤子分裂成相应数目的光束后,或合并成1个光束、或能量重新分配、或周期性碰撞。而反相多极格子孤子分裂后,光束相互排斥,2个边带光束沿直线路径向前传输,且轨迹与原传播方向的夹角相等;在传播常数较小时,可能会出现光束弥散。这些性质对全光路由、全光开关等全光控制技术的研究有一定的参考作用。
Based on nonlinear Schr9 dinger equation,we research the light field properties,including the distribution and the stability,and dynamical behaviors of multi-polar lattice solitons,distributed on a single channel or across different channels in nonlinear media with optical lattices.These survey results indicate that there are two kinds of multi-polar solitons such as in-phase soliton and out-of-phase soliton in such systems.Significantly,multi-polar lattice soliton distributed on a single channel can only be out-of-phase,but an in-phase multi-polar lattice soliton is not allowed.Among three kinds of multi-polar lattice solitons,stability of in-phase multi-polar lattice soliton is the worst,and that of out-of-phase multi-polar lattice soliton distributed across different channels is the best.If optical lattice is removed,three kinds of multi-polar lattice solitons present different dynamical behaviors.After the optical lattice is removed,an in-phase multi-polar lattice soliton first splits into a corresponding number of light beams,and then they merge into one beam,or their energy is redistributed,or they collide periodically.Nevertheless,the outof-phase multi-polar lattice soliton splits into several light beams,and then the beams repel each other,in which two side light beams transmit forwards along their respective straight trajectories,and the angle between any of their straight trajectories and its original direction of propagation is equal;especially,light beams,generated from the fission of out-of-phase multi-polar lattice soliton with a small propagation constant,may diffuse when the optical lattice is withdrawn.These results may have certain value to all-optical controlling techniques such as all-optical routing and all-optical switching.
Based on nonlinear Schr9 dinger equation,we research the light field properties,including the distribution and the stability,and dynamical behaviors of multi-polar lattice solitons,distributed on a single channel or across different channels in nonlinear media with optical lattices.These survey results indicate that there are two kinds of multi-polar solitons such as in-phase soliton and out-of-phase soliton in such systems.Significantly,multi-polar lattice soliton distributed on a single channel can only be out-of-phase,but an in-phase multi-polar lattice soliton is not allowed.Among three kinds of multi-polar lattice solitons,stability of in-phase multi-polar lattice soliton is the worst,and that of out-of-phase multi-polar lattice soliton distributed across different channels is the best.If optical lattice is removed,three kinds of multi-polar lattice solitons present different dynamical behaviors.After the optical lattice is removed,an in-phase multi-polar lattice soliton first splits into a corresponding number of light beams,and then they merge into one beam,or their energy is redistributed,or they collide periodically.Nevertheless,the outof-phase multi-polar lattice soliton splits into several light beams,and then the beams repel each other,in which two side light beams transmit forwards along their respective straight trajectories,and the angle between any of their straight trajectories and its original direction of propagation is equal;especially,light beams,generated from the fission of out-of-phase multi-polar lattice soliton with a small propagation constant,may diffuse when the optical lattice is withdrawn.These results may have certain value to all-optical controlling techniques such as all-optical routing and all-optical switching.
引文
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[26] Xu Z Y,Kartashov Y V,Torner L.Upper thresholdfor stability of multipole-mode solitons in nonlocalnonlinear media[J].Optics Letters,2005,30(23):3171-3173.
[27] Kartashov Y V, Malomed B A,Kivshar Y S.Solitons in nonlinear lattices[J].Review of ModernPhysics,2011,83(1):247-305.
[28] Birnbaum Z, Malomed B A.Families of spatialsolitons in a two-channel waveguide with the cubic-quintic nonlinearity[J].Physica D,2008,237(24):3252-3262.
[29] Dong L W,Ye F W.Shaping solitons by latticedefects[J].Physical Review A,2010,82(5):053829.
[30] Ablowitz M J,Antar N,Bakirtas I,et al.Vortexand dipole solitons in complex two-dimensionalnonlinear lattices[J].Physical Review A,2012,86(3):033804.
[31] He Y J,Wang H Z.(1+1)-dimensional dipolesolitons supported by optical lattice[J].OpticsExpress,2006,14(21):9832-9837.
[32] Press W H,Teukolsky S A,Vetterling W T,et al.Numerical recipes in Fortran 77:the art of scientificcomputing[M].New York:Cambridge UniversityPress,2001:753-764.
[33] Louis P J Y,Ostrovskaya E A,Savage C M,et al.Bose-Einstein condensates in optical lattices:band-gap structure and solitons[J].Physical Review A,2003,67(1):013602.
[2] Agrawal G P.Nonlinear fiber optics[M].Berlin,Heidelberg:Springer,2000:195-211.
[3] Agrawal G P.Applications ofnonlinear fiber optics[M].Cambridge:Academic Press,2010.
[4] Liu S M,Guo R,Xu J J.Photorefractive nonlinearoptics and its applications[M].Beijing:SciencePress,2004.刘思敏,郭儒,许京军.光折变非线性光学及其应用[M].北京:科学出版社,2004.
[5] Efremidis N K,Sears S,Christodoulides D N,et al.Discrete solitons in photorefractive optically inducedphotonic lattices[J].Physical Review E,2002,66(4):046602.
[6] Fleischer J W, Carmon T,Segev M,et al.Observation of discrete solitons in optically inducedreal time waveguide arrays[J].Physical ReviewLetters,2003,90(2):023902.
[7] Fleischer J W,Segev M,Efremidis N K,et al.Observation of two-dimensional discrete solitons inoptically induced nonlinear photonic lattices[J].Nature,2003,422(6928):147-150.
[8] Neshev D,Sukhorukov A A, Hanna B,et al.Controlled generation and steering of spatial gap solitons[J].Physical Review Letters,2004,93(8):083905.
[9] Cao Z,Li X J,Tan Q G,eta l.Trajectory variations ofoptical Bloch oscillations for Airy beams in transverselyand longitudinally modulated photonic lattices[J].Applied Optics,2017,56(12):3484-3490.
[10] Yang J K,Musslimani Z H.Fundamental and vortexsolitons in a two-dimensional optical lattice[J].Optics Letters,2003,28(21):2094-2096.
[11] Neshev D N,Alexander T J,Ostrovskaya E A,etal.Observation of discrete vortex solitons in opticallyinduced photonic lattices[J]. Physical ReviewLetters,2004,92(12):123903.
[12] Musslimani Z H,Yang J K.Self-trapping of light ina two-dimensional photonic lattice[J].Journal of theOptical Society of America B,2004,21(5):973-981.
[13] Fleischer J W, Bartal G, Cohen O,et al.Observation of vortex-ring “discrete”solitons in 2Dphotonic lattices[J].Physical Review Letters,2004,92(12):123904.
[14] Wang X S,Chen Z G,Kevrekidis P G.Observationof discrete solitons and soliton rotation in opticallyinduced periodic ring lattices[J].Physical ReviewLetters,2006,96(8):083904.
[15] Kartashov Y V,Vysloukh V A,Torner L.Rotarysolitons in Bessel optical lattices[J].Physical ReviewLetters,2004,93(9):093904.
[16] Suntsov S,Makris K G,Christodoulides D N,et al.Observation of discrete surface solitons[J].PhysicalReview Letters,2006,96(6):063901.
[17] Makris K G,Suntsov S,Christodoulides D N,et al.Discrete surface solitons[J].Optics Letters,2005,30(18):2466-2468.
[18] Xu S L,Beli'c M R,Cai D P,et al.Vortex solitonsproduced in spatially modulated linear and nonlinearrefractive index waveguides[J].Journal of the OpticalSociety of America B,2018,35(2):410-416.
[19] Xie K,Boardman A D,Li Q,et al.Spatial algebraicsolitons at the Dirac point in optically inducednonlinear photonic lattices[J]. Optics Express,2017,25(24):30349-30364.
[20] Kartashov Y V, Vysloukh V A, Torner L.Asymmetric soliton mobility in competing linear-nonlinear parity-time-symmetric lattices[J].OpticsLetters,2016,41(18):4348-4351.
[21] Zhou K Y,Wei TT,Sun H P,et al.Solitondynamics in a PT-symmetric optical lattice with alongitudinal potential barrier[J].Optics Express,2015,23(13):16903-16911.
[22] Lopez-Aguayo S,Ruelas-Valdez C,Perez-Garcia B,et al. Quasi-one-dimensional optical lattices forsoliton manipulation[J].Optics Letters,2014,39(22):6545-6548.
[23] Li Y L,Qin Y L,Mao S Y,et al.Propagationcharacteristics of optical solitons in parity-timesymmetric potentials with longitudinal barriers[J].Laser &Optoelectronics Progress,2017,54(8):081901.李屹磊,覃亚丽,毛盛益,等.宇称-时间对称纵向势垒中光孤子的传播特性[J].激光与光电子学进展,2017,54(8):081901.
[24] Chen S F,Xu S L.Transmission characteristics oftwo-dimensional optical soliton throughphotoisomerization[J].Laser &OptoelectronicsProgress,2018,55(5):050601.陈顺芳,徐四六.二维光致异构光孤子传输特性的研究[J].激光与光电子学进展,2018,55(5):050601.
[25] Wang Y,Zhang P, Li X Y,et al. Opticalcommunication performance of solitonic pulses inweak oceanic turbulence[J].Chinese Journal ofLasers,2018,45(5):0506004.王阳,张鹏,李晓燕,等.海洋弱湍流条件下光孤子脉冲通信性能[J].中国激光,2018,45(5):0506004.
[26] Xu Z Y,Kartashov Y V,Torner L.Upper thresholdfor stability of multipole-mode solitons in nonlocalnonlinear media[J].Optics Letters,2005,30(23):3171-3173.
[27] Kartashov Y V, Malomed B A,Kivshar Y S.Solitons in nonlinear lattices[J].Review of ModernPhysics,2011,83(1):247-305.
[28] Birnbaum Z, Malomed B A.Families of spatialsolitons in a two-channel waveguide with the cubic-quintic nonlinearity[J].Physica D,2008,237(24):3252-3262.
[29] Dong L W,Ye F W.Shaping solitons by latticedefects[J].Physical Review A,2010,82(5):053829.
[30] Ablowitz M J,Antar N,Bakirtas I,et al.Vortexand dipole solitons in complex two-dimensionalnonlinear lattices[J].Physical Review A,2012,86(3):033804.
[31] He Y J,Wang H Z.(1+1)-dimensional dipolesolitons supported by optical lattice[J].OpticsExpress,2006,14(21):9832-9837.
[32] Press W H,Teukolsky S A,Vetterling W T,et al.Numerical recipes in Fortran 77:the art of scientificcomputing[M].New York:Cambridge UniversityPress,2001:753-764.
[33] Louis P J Y,Ostrovskaya E A,Savage C M,et al.Bose-Einstein condensates in optical lattices:band-gap structure and solitons[J].Physical Review A,2003,67(1):013602.
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