Internal oscillation of vector solitons and necklace solitons

Internal modes and internal oscillation of vector solitons associated with photoisomerization and necklace solitons in Bessel lattices are researched. While white noise gives rise to the unsmoothness of the vector solitons, the perturbation of internal modes results in the long-distance quasi-periodic oscillation of soliton shape. Internal modes of two-dimensional necklace solitons in Bessel lattices have both real and imaginary parts, which is different with the internal modes of one-dimensional solitons which have only real part.     

光子晶格中新颖的空间带隙孤子——饶毓泰基础光学二等奖介绍

光子晶格作为一种光学周期性离散体系,具有通常均匀介质所无法比拟的独特性质,它为空间离散孤子、表面波以及衍射操控等一系列线性和非线性离散动力学行为的实验观测提供了便利条件,同时在全光路由、全光开关和光子计算机等方面具有重要的应用前景.文章简要回顾了南开大学的研究小组近期在二维光子晶格中有关空间带隙孤子的一系列研究工作,包括二维基本带隙孤子、类偶极带隙孤子、带隙孤子串以及涡旋带隙孤子等.在有的实验过程中,文章作者清晰地观测到探测光束的频谱整形,波常数从具有反常衍射的导带底部演化到光子禁带中,并且通过干涉图反映     

Dipole solitons in an optical lattice with longitudinal modulation

In this paper, we numerically demonstrate the (1+1)-dimensional dipole solitons can exist in a new Kerr-type optical lattice with longitudinal modulation that fades away and boosts up alternately. The solitons whose two dipoles simultaneously located at one lattice site and at two adjacent lattice sites are investigated, respectively. The results show that, in the two cases, the dipole solitons can be stably trapped in this kind of lattice by properly adjusting lattice parameters and soliton parameters when the repulsive force of dipoles balances the centripetal force resulting from the lattice potential effect on dipole solitons. In addition, the trapping of dipole solitons with an incident angle or the initial center position is discussed.     

Vectorial coupled—mode solitons in one—dimensional photonic crystals

We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-mode equations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.      

Dynamics of surface dipole and tripole solitons in nonlocal nonlinear media with optical lattice field

We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.     

Polarization vortex spatial optical solitons in Bessel optical lattices

We investigate the formation of polarization vortex spatial optical solitons in optical lattice induced by a non-diffracting Bessel beam. The properties of these solitons in zeroth-order and first-order Bessel lattices with focusing and defocusing Kerr nonlinearity are discussed. It is found that these solitons have some analogies with phase vortex solitons carrying single positive or negative topological charge in these lattices. Besides, these polarization vortex solitons have complicated dynamical characteristic and can be stabilized in some parameter region.     

Band gap extension in honeycomb lattice two-dimensional plasma photonic crystals in the presence of dissipation

We investigate two types of honeycomb lattice two-dimensional plasma photonic crystals that possess large photonic band gaps in the presence of dissipation. We obtain a clear insight into the band structures and find imaginary parts of the eigenvalue band structure at the symmetry points display discontinuous behaviour when the filling factor of plasma in type-1 structure is low. Further more, we show how the photonic band gaps are affected by the normalized plasma frequency, radius of cylinder, dielectric constant and collision frequency. Our results demonstrate the band gap extension by increasing normalized plasma frequency in both type structures and radius of plasma cylinders in type-1 structure. The width of band gaps could also be enlarged by decreasing dielectric cylinder's radius. The bands shift toward lower frequencies when relative dielectric constant increases in both two types. These results may provide theoretical instructions to design new optoelectronic devices.     

Effects of three-body atomic interaction and optical lattice on solitons in quasi-one-dimensional Bose-Einstein condensate

We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of √1 − bg ₃ with g ₃ the coupling constant of the lattice potential and b = 0.7301.      

Interface kink solitons in defocusing saturable nonlinear media

We report on the dynamics of semi-localized nonlinear optical modes supported by an interface separating a uniform defocusing saturable medium and an imprinted semi-infinite photonic lattice. Out-of-phase and in-phase kink solitons composed by dark-soliton-like pedestals and oscillatory tails are found. Two branches of out-of-phase kink solitons exist in shallow lattices. Saturable nonlinearity enhances the pedestal height and renormalized energy flow of kink solitons evidently. While in-phase kink solitons are always unstable, out-of-phase kink solitons will be completely stable provided that lattice depth exceeds a critical value. Furthermore, stable kink solitons in the higher band gaps are also possible. Our results may give a helpful hint for understanding the dynamics of kink solitons with high pedestals in other fields.     

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.     

Band structure of photonic crystal fibers with silica rings in triangular lattice

The characteristics of the cladding band structure of air-core photonic crystal fibers with silica rings in triangular lattice are investigated by using a standard plane wave method. The numerical results show that light can be localized in the air core by the photonic band gaps of the fiber. By increasing the air-filling fraction, the band gap edges of the low frequency photonic band gaps shift to shorter wavelength, whereas the band gap width decreases linearly. In order to make a specified light fall in the low frequency band gaps of the fiber, the interplay of the silica ring spacing and the air-filling fraction is also analyzed. It shows that the silica ring spacing increases monotonously when the air-filling fraction is increased, and the spacing range increases exponentially. This type fiber might have potential in infrared light transmission.     

光诱导光子晶格结构中新型的离散空间光孤子

离散孤子标志着从线性到非线性，从连续到非连续，从相干到非相干，人们对孤子认识的一个飞越．文章简要回顾了近期在二维光致光子晶格结构中有关空间离散光孤子的研究，包括基模离散孤子、类矢量离散孤子、离散偶极孤子、离散涡旋孤子和离散孤子串等．在非线性光折变晶体里用部分相干光诱导的波导阵列中，对每一种离散孤子，都清楚地观测到光从二维的离散衍射状态到自囚禁形成离散孤子的转变过程，获得的结果将对其他离散非线性系统中类似现象的研究有所启发．     

格子气的声振荡衰减

采用格子气数值方法模拟了共振腔中气体声振荡衰减过程．计算结果表明：格子气中声振荡衰减的规律和经典理论结果一致;衰减系数随频率增加而减小,并且随密度增加而减小．该结果可以用来说明一些大学统计物理教科书中的一个经典例子存在不完善之处．本中采用了一种新的扭转9-bit格子气模型和并行计算方法,这些结果对今后研究格子气中的热声问题有参考价值．     

Properties of nano-scale soliton-like excitations in two-dimensional lattice layers

Nano-scale soliton-like supersonic, intrinsic localized excitations in two-dimensional atomic anharmonic lattice layers are here considered. We study the propagation, the velocity and other soliton-like features at head-on collisions of such lattice excitations created by using suitable initial mechanical and thermal conditions. Noteworthy is that narrow, highly-energetic solitons moving along one lattice row are very robust, accompanied by weak anti-phase oscillations in the lateral direction.     

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.     

Microcavity filters based on hexagonal lattice 2-D photonic crystal structures embedded in ridge waveguides

Two-dimensionally periodic photonic crystal microcavity filters in a ridge waveguide format have been designed and fabricated. Transition mode-matching features were added to increase the optical throughput by more than a factor of two. An increase of Q-factor (more than 100%) was achieved by the addition of two further rows of photonic crystal holes to the microcavity filters. Attempts have also been made to tailor the filter response by applying design concepts used in other Bragg-grating optical filter technologies.     

The appearance of gap solitons in a nonlinear Schrödinger lattice

We study the appearance of discrete gap solitons in a nonlinear Schrödinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase (q=π/2) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this “nonlinear gap boundary” are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose-Einstein condensates in periodic potentials. For lattices whose gap edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.     

Bistability and stationary gap solitons in quasiperiodic photonic crystals based on Thue–Morse sequence

The nonlinear properties of quasiperiodic photonic crystals based on the Thue–Morse sequence are investigated. The intrinsic asymmetry of these one-dimensional structures for odd generation numbers results in bistability thresholds which are sensitive to propagation direction. Along with resonances of perfect transmission, this feature allows to obtain strongly nonreciprocal propagation and to create an all-optical diode. The efficiency of two schemes is compared: passive and active when an additional short pump signal is applied to the system. The existence of stationary gap solitons in quasiperiodic photonic crystals is shown numerically, and their difference from the Bragg case is emphasized.     

Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals

The frequency bands for self-collimation at both TE and TM polarizations in square lattice annular photonic crystals are studied systematically by plane-wave expansion and finite difference time domain methods. By increasing the inner ring radius or reducing the outer ring radius, the self-collimation band will be moved to a lower frequency. Compared with the TM modes, TE ones have different frequency sensitivities to both the inner ring radius and outer ring radius tuning. Using these features, a polarization insensitive self-collimation waveguide in a high dielectric contrast system with bandwidth up to 102.9 nm is demonstrated as an example of the implementation of photonic integration circuits.