The contrast between defect solitons in parity-time symmetric superlattice and simple-lattice complex potentials

The existence and stability of defect superlattice solitons in parity-time (PT) symmetric superlattice and simplelattice complex potentials are reported.Compared with defect simple-lattice solitons in similar potentials,the defect soliton in superlattice has a wider stable range than that in simple-lattice.The solitons’ power increases with increasing propagation constant.For the positive defect,the solitons are stable in the whole region where solitons exist in the semi-infinite gap.For the zero defect,the solitons are unstable at the edge of the band.For the negative defect,the solitons propagate with the shape of Y at low propagation constant and propagate stably at the large one.     

Gap solitons in parity time complex superlattice with dual periods

A theory is presented to investigate the existence and propagation stability of gap solitons in a parity-time （PT） com- plex superlattice with dual periods. In this superlattice, the real and imaginary parts are both in the form of superlattices with dual periods. In the self-focusing nonlinearity, PT solitons can exist in the semi-infinite gap. However, only those gap solitons with low powers can propagate stably, whereas the high-power solitons present periodic oscillation and simultane- ously suffer energy decay. In the self-defocusing nonlinearity, PT solitons only exist in the first gap and all these solitons are stable.     

Defect solitons supported by parity-time symmetric defects in superlattices

The existence and stability of defect solitons supported by parity-time (PT) symmetric defects in superlattices are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive defects, zero defects, and negative defects. In the first gap, out-of-phase solitons are stable for positive defects or zero defects, whereas in-phase solitons are stable for negative defects. For both the in-phase and out-of-phase solitons with the positive defect and in-phase solitons with negative defect in the first gap, there exists a cutoff point of the propagation constant below which the defect solitons vanish. The value of the cutoff point depends on the depth of defect and the imaginary parts of the PT symmetric defect potentials. The influence of the imaginary part of the PT symmetric defect potentials on soliton stability is revealed.     

Surface superlattice solitons in nonlocal nonlinear media

We analyse surface solitons at the interface between a one-dimensional photonic superlattice and a uniform medium with weak nonlocal nonlinearity. We demonstrate that in deep lattices there exist three kinds of surface solitons when the propagation constant exceeds a critical value, including two on-site solitons and one off-site soliton. These three kinds of surface solitons have unique dynamical properties. If the relative depth of the superlattice is low, there is only one kind of off-site soliton; however, the solitons of this kind can propagate stably, unlike their deep superlattice counterparts. Dipole surface solitons are also investigated, and the stable domain is given.     

局域单PT对称势中多级孤子的传输特性研究

具有Parity-Time(PT)对称性的光学系统是近年提出的一种新型光学结构,在光开关、光子信息处理器件等方面具有潜在的应用。研究了局域单PT对称光学系统中双级孤子和三级孤子的存在范围与稳定特性。研究结果表明:多级孤子存在一临界传播常数,传播常数对应了线性模下的本征值。双级孤子和三级孤子仅能在较深的PT对称势中才能稳定地传输。多级孤子的稳定性的范围随着PT对称势的深度增加而扩大;孤子的能量随着传播常数的增大而增加,但随着PT对称势的调制深度的增加而减少。     

亮孤子在宇称时间对称波导中的传输和控制

基于光波在宇称-时间(PT)对称波导中传输的理论模型, 数值研究了亮孤子在呈高斯分布的PT对称克尔非线性平板波导中的传输和控制. PT对称波导, 要求波导的折射率分布呈偶对称, 而增益/损耗分布呈奇对称. 结果表明: 当波导的折射率分布强度为正时, PT对称波导的中心折射率最大, 即使没有自聚焦克尔非线性效应, PT对称波导也可以束缚光波, 形成波浪形光束且长距离传输; 当折射率分布强度为负时, PT对称波导的中心折射率最小, 光波的传输方向发生偏移. 而增益/损耗分布可控制光波的偏移方向: 增益/损耗分布强度为正, 光波向左偏移; 强度为负, 光波向右偏移; 强度为零时, 光波被分为两束. 且当折射率分布强度为负时, 可以很好地抑制相邻亮孤子间的相互作用. 该研究结果可为未来PT对称波导在全光控制方面的应用提供一定的理论依据.     

Surface defect gap solitons in one-dimensional dual-frequency lattices

We study the surface defect gap solitons in an interface between a defect of one-dimensional dual-frequency lattices and the uniform media. Some unique properties are revealed that such lattices can broaden the region of semi-finite gap, and the semi-finite gap exists not only in the positive and zero defects but also in the negative defect; unlike in the regular lattices, the semi-finite gap exists in the positive and zero defects but does not exist in the negative defect. In particular, stable solitons exist almost in the whole semi-finite gap for the positive and zero defects. These properties are different from other lattices with defects. In addition, it is found that the existence of surface dual-frequency lattice solitons does not need a threshold power.     

Nonlinear switching and solitons in PT‐symmetric photonic systems

One of the challenges of the modern photonics is to develop all‐optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity‐Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non‐conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT‐symmetric photonic systems with an intensity‐dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly‐induced PT‐symmetry breaking, and all‐optical switching. Nonlinear PT‐symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

     

Disorder in parity-time symmetric quantum walks

We experimentally investigate the impact of static disorder and dynamic disorder on the non-unitary dynamics of parity-time(PT)-symmetric quantum walks.Via temporally alternating photon losses in an interferometric network,we realize the passive PT-symmetric quantum dynamics for single photons.Controllable coin operations allow us to simulate different environmental influences,which result in three different behaviors of quantum walkers:a standard ballistic spread,a diffusive behavior,and a localization,respectively,in a PT-symmetric quantum walk architecture.     

A lattice of electromagnetic solitons in a superlattice formed by a system of quantum dots

Considering the Maxwell equations for the electromagnetic-field propagation in a solid with a three-dimensional superlattice of quantum dots linked by strong tunneling along one axis, we obtained a phenomenological equation in the form of the classical 2+1-dimensional sine-Gordon equation. Electrons were considered classically in the formalism of the Boltzmann kinetic equation for the distribution function. Solutions were obtained as a soliton lattice for the vector potential of the electric field. These lattices emerge as a consequence of the coherent change of the classical distribution function and the electric field generated by tunneling electrons in a system of quantum wells.     

Surface defect solitons at interfaces between dual-frequency and simple lattices

We reveal theoretically the existence and stability of surface defect solitons (SDSs) at interfaces between dual-frequency and simple lattices with focusing saturable nonlinearity. Solitons with some unique properties exist in such composite structures with the change of defect intensity. For zero defect or positive defect, the surface solitons exist at the semi-infinite gap and cannot exist in the first gap, and solitons are stable at lower power but unstable at high power. For the case of negative defect, the surface solitons exist not only in the semi-infinite gap, but also in the first gap. With increasing the defect depth, the stable region of surface solitons becomes narrower in the semi-infinite gap, these solitons are stable within a moderate power region in the first gap within unstable solitons in the entire semi-infinite gap.     

Multi-peak solitons in PT-symmetric Bessel optical lattices with defects

This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity–time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μ _c for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ > μ _c . In the self-defocusing case, solitons exist only when μ < μ _c . Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.     

Extraordinary solitons in non-centrally symmetric photorefractive crystals

The directions of the phase normals for which extraordinary bright screened solitons can be formed are described analytically. Formulas are derived for the directions in which extraordinary solitons can exist in lithium niobate for arbitrary orientations of the external electric field. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 403–410, May–June, 2009.     

Spatial solitons in photonic lattices with large-scale defects

We address the existence,stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium.Several families of soliton solutions,including flat-topped,dipole-like,and multipole-like solitons,can be supported by the defected lattices with different heights of defects.The width of existence domain of solitons is determined solely by the saturable parameter.The existence domains of various types of solitons can be shifted by the variations of defect size,lattice depth and soliton order.Solitons in the model are stable in a wide parameter window,provided that the propagation constant exceeds a critical value,which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium.We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.     

Bright ordinary solitons in non-centrally symmetric photorefractive crystals

The directions of the phase normal such that bright ordinary screening solitons can exist in non-centrally symmetric crystals are determined analytically. The results are used to calculate the directions of solitons in lithium niobate. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 152–160, January–February, 2009.     

Interactions between bright solitons in different species of Bose—Einstein condensates

The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied.The interaction between bright solitons in different species with small separation is derived.Unlike the interaction between solitons of the same species,it is independent of the phase difference between solitons.It may be of attraction or repulsion.In the former case,each soliton will oscillate about and pass through each other around the mass-center of the system,which will also oscillate harmonically due to the harmonic trapping potential.     

玻色-爱因斯坦凝聚体中的双孤子相互作用操控

考虑周期性驱动线性势, 利用Darboux变换法解析地研究了玻色-爱因斯坦凝聚体(BEC)中的双孤子相互作用, 得到了S-波散射长度的临界值. 结果表明: 当S-波散射长度高于临界值时, BEC中的两个亮孤子相互吸引并融合; 而当S-波散射长度低于临界值时, 两个亮孤子保持局域稳定. 此外, 在外部势阱的驱动下, 两个稳定的亮孤子产生周期性振荡行为.     

(2+1)维Boiti-Leon-Pempinelli系统的混沌行为及孤子间的相互作用

利用改进的变系数的Riccati方程映射法，得到了(2+1)维Boiti-Leon-Pempinelli系统(BLP)的新显式精确解.根据得到的解，研究了BLP系统的混沌行为及孤子间的相互作用. 关键词： 改进的映射法 Boiti-Leon-Pempinelli系统 混沌行为 相互作用     

三元合金缺陷层对有限超晶格中局域界面光学声子模的影响

在宏观介电连续近似下，采用转移距阵方法，研究了三元合金缺陷层对有限超晶格中局域界面光学声子模的影响.在这种有限超晶格结构中，可以清楚地看到所有界面模的演化轨迹.结果表明：存在两类局域模，它们的宏观静电势波函数分别局域在缺陷层和表面层附近，且这些模随着超晶格组分层和缺陷层的相对厚度和介电常数的改变，其局域位置和特性发生显著变化.此外，发现虽然能隙中局域模的数目不守恒，但所有界面模的总数守恒.