High-Dimensional Nonlinear Envelope Equations and Nonlinear Localized Excitations in Photonic Crystals

We investigate the nonlinear localized structures of optical pulses propagating in a one-dimensional photonic crystal with a quadratic nonlinearity. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and long-wavelength mean fields, generated by the self-interaction of the wave packet, are governed by a set of coupled high-dimenslonal nonlinear envelope equations, which can be reduced to Davey-Stewartson equations and thus support dromionlike high-dimensional nonlinear excitations in the system.     

High-Dimensional Nonlinear Envelope Equations and Nonlinear Localized Excitations in Photonic Crystals

We investigate the nonlinear localized structures of optical pulses propagating in a one-dimensional photonic crystal with a quadratic nonlinearity. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and long-wavelength mean fields, generated by the self-interaction of the wave packet, are governed by a set of coupled high-dimensional nonlinear envelope equations, which can be reduced to Davey-Stewartson equations and thus support dromionlike high-dimensional nonlinear excitations in the system.     

激子-声子相互作用对三阶非线性光学性质的影响

在对激子不作任何近似的条件下,对强耦合激子声子系统中非线性光学性质在理论上进行了研究,结果表明当信号光场频率与激子频率的失谐量等于光学声子的频率时,系统的非线性光学吸收和克尔系数显著增大,从而证明了激子声子的强相互作用对介质的非线性光学性质的影响相当大。并且,与对激子作代松马利夫(Dyson-Maleev)变换近似和玻色近似的结果进行仔细的比较,发现对激子不作近似时,这种影响将进一步增大。     

Nonlinear frequency conversion in coupled ring cavities

The steady-state distribution of circulating power in coupled, unidirectional ring resonators containing a diode-pumped laser crystal and nonlinear optical elements is computed. The full set of transcendental nonlinear equations describing the interactions between the circulating power and the optical elements is solved by a numerical root find function of a commercial mathematics software. The method allows computation of the output of sequential nonlinear processes such as laser gain, second harmonic generation and optical parametric amplification as a function of the input diode pump power. It is also possible to optimize the nonlinear interaction by selecting the optimum interaction cross-section or crystal length. The circulating power may thereby be re-distributed to obtain the lowest possible passive loss.     

强耦合激子-声子系统中的三阶非线性光学系数的理论计算

应用Dyson-Maleev变换,对强耦合激子—声子系统中非线性光学性质进行了理论研究.结果表明,当信号光场频率与激子频率的失谐量等于光学声子的频率时,系统的非线性光学吸收和克尔（Kerr）系数显著增大,从而证明了激子-声子的强相互作用对介质的非线性光学性质的影响相当大,并且当考虑激子偏离玻色子模型时,这种影响将进一步增大.     

Darboux Transformation and Soliton Solutions for Inhomogeneous Coupled Nonlinear Schrodinger Equations with Symbolic Computation

With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems （i.e. Lax pair）, we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.     

Nonlinear localized modes at phase-slip defects in waveguide arrays

We study light localization at a phase-slip defect created by two semi-infinite mismatched identical arrays of coupled optical waveguides. We demonstrate that the nonlinear defect modes possess the specific properties of both nonlinear surface modes and discrete solitons. We analyze the stability of the localized modes and their generation in both linear and nonlinear regimes.     

All Optical Light Deflection and Displacement Using Nonlinear Slab Waveguide

The possibility of all optical control of light deflection and displacement through a planar nonlinear waveguide has been discussed in this article. In this scheme a strong command beam controls the propagation characteristics of a weak signal beam in a nonlinear waveguide. Employing variational approach, we have established a set of coupled nonlinear equations for the displacement of the center of gravity, beam size, deflection angle, and beam divergence of the signal beam. These equations have been solved numerically to confirm the possibility of all optical control of deflection and displacement of a signal beam by a command beam.     

Nonlinear three-wave interaction in photonic crystals

We present a multi-scale analysis of nonlinear three-wave-interaction processes in photonic crystals. Based on photonic Bloch functions as carrier waves, we derive the effective nonlinear coupled wave equations that govern pulse propagation in these systems and obtain the corresponding effective photonic crystal parameters directly from photonic band-structure computations. As an illustration, we show how hitherto inaccessible radiation-conversion processes such as wave-front reversal of optical pulses can be realized. Furthermore, we describe a novel regime of nonlinear three-wave interaction in photonic crystals associated with the nearly degenerate case and show how these results may be utilized to study experimentally certain problems from plasma physics and hydrodynamics in the context of nonlinear photonic crystals.     

Nonlinear optical responses due to exciton-phonon interactions in strongly coupled exciton-phonon systems

The excitonic nonlinear optical responses due to exciton-phonon interactions in strongly coupled exciton-phonon systems are investigated theoretically. It is shown that the influence of exciton-phonon interactions on the nonlinear optical absorptions and Kerr nonlinear coefficients is significant as the signal field frequency detuning from the exciton frequency approaches to the optical phonon frequency. How to manipulate the nonlinear optical responses by using the control fields is also presented.Received: 16 March 2004, Published online: 4 May 2004PACS: 42.50.Gy Effects of atomic coherence on propagation, absorption, and amplification of light; electromagnetically induced transparency and absorption - 42.50.Hz Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift - 42.25.Bs Wave propagation, transmission and absorption - 72.80.Le Polymers; organic compounds (including organic semiconductors)     

Nonlinear theory of polarization-mode dispersion for fiber solitons

We consider the evolution of optical solitons inside a nonlinear dispersive fiber with random birefringence, causing polarization-mode dispersion. We convert the pair of coupled nonlinear Schr?dinger equations satisfied by the orthogonally polarized components into a Fokker-Planck equation using the collective-variable approach. We solve this equation and derive expressions for the probability density functions associated with the differential group delay and the pulse width in the limit of large propagation distances.     

Generalized Darboux Transformations,Rogue Waves,and Modulation Instability for the Coherently Coupled Nonlinear Schrödinger Equations in Nonlinear Optics

Nonlinear optics plays a central role in the advancement of optical science and laser‐based technologies. The second‐order rogue‐wave solutions and modulation instability for the coherently coupled nonlinear Schrödinger equations with the positive coherent coupling in nonlinear optics are reported in this paper. Generalized Darboux transformations for such coupled equations are derived, with which the second‐order rational solutions for the purpose of modelling the rogue waves are obtained. With respect to the slowly‐varying complex amplitudes of two interacting optical modes, it is observed that 1) number of valleys of the second‐order rogue waves increases and peak value of the second‐order rogue wave decreases first and then increases; 2) single‐hump second‐order rogue wave turns into the double‐hump second‐order rogue wave; 3) single‐hump bright second‐order rogue wave turns into the dark second‐order rogue wave and finally becomes the three‐hump bright second‐order rogue wave. Meanwhile, baseband modulation instability through the linear stability analysis is seen.     

Darboux Transformation and Soliton Solutions for InhomogeneousCoupled Nonlinear Schrödinger Equations with Symbolic Computation

With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrödinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e. Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features ofpicosecond solitons in inhomogeneous optical fibers.     

Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

We investigated the soliton solution for N$N$ coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management.     

Nonlinear interactions and quantum entanglement for collective fields in near-resonantly driven systems

This paper proposes a novel form of multimode nonlinear interactions by using a near-resonantly dressed atomic ensemble in an optical cavity.Due to quantum interference,a pair of collective fields come into the bilinear interactions,whose strengths are proportional to the population difference between dressed states which are coupled to the collective fields.By such an interaction,it is possible to obtain perfect multimode squeezing and collective Einstein-Podolsky-Rosen(EPR) entanglement in the cavity output.     

高非线性光纤中受激布里渊散射快光提前及脉冲形变

基于受激布里渊散射三波耦合方程组,应用小信号分析,研究了高非线性光纤的信号光脉冲提前及形变。结果表明,光纤中信号光脉冲的时间提前量在一定范围内随着输入信号光功率和传输距离的增长而近似线性增长,同时脉冲压缩程度加强;在相同条件下,非线性光纤比普通单模光纤的时间提前量更大,在50 m长的高非线性光纤中,信号光能量在50 m W时实现了203 ns的时间提前量和较小的脉冲形变。高非线性光纤的快光提前效率显著提高,脉冲形变显著减小。研究结果对快光的实现和应用具有参考意义。     

非线性光学材料倍频效应测试系统研究

开展了一种红外和可见波段非线性光学性能测试研究。该研究基于二阶非线性光学原理, 结合光电信号探测技术, 提出了一种采用红外OPO激光以及把倍频光及其他光效应产生的光通过谱仪分光并结合CCD阵列探测器加以区分探测的新检测方案。主要解决了测试使用1 064 nm光源时, 材料的倍频信号532 nm被样品吸收后而探测不到倍频信号的缺点, 以及准确测量了倍频信号强度, 排除了其他光学效应产生的噪声干扰。其特点是采用1 064和1 905 nm的双波长激光替代单一波长的激光源, 该方案能适用于可见和红外非线性材料光学性能的测试。研究工作包括测试系统组成, 工作原理和测试方法, 并给出了采用本方法测试KTP, KDP, AGS以及几种新的红外非线性材料的实验结果, 并且发现了几种有前途的非线性光学晶体材料。研究结果表明本方法具有稳定可靠、判别精度高、操作简单等优点, 可以有效地定性或半定量测试材料的可见-红外非线性光学性能, 为研究可见、红外乃至紫外二阶非线性光学材料提供重要的测试手段。     

非线性一维光子晶体波导光双稳

利用非线性折射率系数较大且非线性时间响应较快的CdS_xSe_1-x玻璃为材料,设计并制备了非线性一维光子晶体波导光双稳器件,该器件的折射率空间分布呈正弦形式。实验测得双稳开关的阈值功率密度为1.60×10⁵W/cm²,开关时间为63ps。采用时域有限差分方法讨论了光子晶体带隙随入射光强变化而移动的情况,随着入射光功率密度的增加,光子晶体的带隙中心向短波方向移动。同时计算了该器件的双稳特性,理论计算得到双稳开关的阈值功率密度为1.40×10⁵W/cm²,开关时间约为50ps。获得了理论与实验基本一致的结果。     

A Nonlinear Landau-Zener Formula

We consider a system of two coupled ordinary differential equations which appears as an envelope equation in Bose–Einstein Condensation. This system can be viewed as a nonlinear extension of the celebrated model introduced by Landau and Zener. We show how the nonlinear system may appear from different physical models. We focus our attention on the large time behavior of the solution. We show the existence of a nonlinear scattering operator, which is reminiscent of long range scattering for the nonlinear Schrödinger equation, and which can be compared with its linear counterpart.     

非线性光学超构表面

在线性光学范畴内,人们已经通过亚波长尺度的超薄超构表面成功实现了对光的众多新颖特性的调控功能.其主要理念是通过对具有亚波长尺度且空间方向变化的超构功能基元进行特定的排列,从而实现对光的偏振、相位和振幅的有效控制.近来,超构表面上的非线性光学特性也引起了大家的广泛关注.在本综述中,我们对非线性光学超构表面的设计、超构功能单元的材料和对称性选择、非线性手性光学、非线性贝里几何相位和非线性波前整形等内容进行了总结;最后对非线性光学超构表面在调控光与物质的相互作用中面临的挑战和前景进行了展望.