一维光学格子孤子的传输特性及控制研究

利用解析和数值方法研究了在具有横向折射率周期性调制的克尔型非线性介质中光学格子孤子的传输，得到了孤子参数的演化方程以及格子孤子的形成和稳定传输的条件.结果表明：当光束的入射角小于某临界角度时，光束可被类似波导形式的路径俘获而稳定传输，该临界角随折射率调制周期、调制深度的增加而增大，且光束越窄临界值越大.此外，线性空间啁啾虽然对光束传输的中心位置没有任何影响，但会导致光束发散从而破坏格子孤子的形成和稳定传输，对此提出了采用特定功率取值来补偿啁啾作用从而形成格子孤子的方案. 关键词： 光孤子 光学格子 光传输 矩方法     

Break up of bound-N-spatial-soliton in a ramp waveguide

We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the particle theory shows that the soliton beam follows a parabolic curve in the region where the linear refractive index increases and a straight line outside the waveguide. The acceleration of the soliton depends on the beam intensity: higher amplitude solitons experience higher acceleration. Numerical calculations using an implicit Crank–Nicolson scheme confirm the result of the particle theory. Combining these propagation properties with the theory about bound-N-soliton, we study the break up of such a bound-N-soliton in a ramp waveguide. In a ramp waveguide, a bound-N-soliton will always be splitted into N independent solitons with the higher amplitude soliton emitted first. The amplitude of the separated solitons after break up are calculated using the soliton theory as if the solitons are independent. Numerical simulations show that the results agree quite well with this theoretical prediction, indicating that the interaction during break up has only little influence.     

Break up of bound-N-spatial-soliton in a ramp waveguide

We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the particle theory shows that the soliton beam follows a parabolic curve in the region where the linear refractive index increases and a straight line outside the waveguide. The acceleration of the soliton depends on the beam intensity: higher amplitude solitons experience higher acceleration. Numerical calculations using an implicit Crank-Nicolson scheme confirm the result of the particle theory. Combining these propagation properties with the theory about bound-N-soliton, we study the break up of such a bound-N-soliton in a ramp waveguide. In a ramp waveguide, a bound-N-soliton will always be splitted intoN independent solitons with the higher amplitude soliton emitted first. The amplitude of the separated solitons after break up are calculated using the soliton theory as if the solitons are independent. Numerical simulations show that the results agree quite well with this theoretical prediction, indicating that the interaction during break up has only little influence. On Leave from Jurusan Matematika, Universitas Brawijaya, Jl. MT Haryono 167 Malang Indonesia.     

非局域高次非线性介质中的多极暗孤子

研究一维非局域三-五次非线性模型下,暗孤子和多极暗孤子的新解和传输特性.发现非局域程度和非线性参量变化对暗孤子的峰值和束宽产生影响,并且在特定的竞争非局域非线性参数下存在稳定基态暗孤子和多极暗孤子的束缚态.另外,讨论了在局域自聚焦三次和非局域自散焦五次非线性介质中暗孤子和两极暗孤子的传输特性,发现孤子比在自散焦三次和自聚焦五次的非线性介质中传输更加稳定.进一步研究了单暗孤子和三极暗孤子的功率与传播常数和非局域程度的关系,并讨论了不同类型暗孤子的线性稳定性问题.     

梯度折射率非局域介质中空间孤子振荡行为研究

应用等效粒子近似方法研究了光学空间孤子在带有局域和非局域非线性横向非均匀介质中的传输动力学行为.发现孤子在传播过程中横向的周期性振荡.折射率调制幅度和波导的归一化宽度决定了振荡周期的大小.介质的非局域对振荡振幅有着较小的影响.模拟了孤子传输过程,所得数值结果与理论分析符合很好.此外,模拟传输还发现多孤子束缚态能够在这个模型中稳定传播.这种振荡特性或许可以应用于光学路由器、转换器、开关等.     

强非局域光晶格中空间孤子的脉动传播

根据强非局域结构中空间孤子的演化方程——非局域非线性薛定谔方程,采用分步傅里叶方法,对一维强非局域光晶格结构中空间孤子的脉动传播进行数值研究.分析了孤子的初始光束能量、非局域程度、光晶格调制强度、光晶格周期以及线性折射率的纵向调制率与空间孤子的脉动传播周期之间的关系,并对影响脉动传播的内在物理机制进行了讨论.同时,还研究了在线性折射率纵向调制情况下强非局域光晶格结构中空间孤子传输的开关行为. 关键词： 非局域非线性薛定谔方程 光晶格 空间孤子 光开关     

Bragg solitons in quantum-well structures

Soliton pulse propagation in a periodic quantum-well structure with a period close to one-half the light wavelength corresponding to the exciton resonance frequency was studied. The various kinds of exciton nonlinearity characteristic of a quantum well (P³-and EP²-type nonlinearities, biexciton nonlinearity) were included. The characteristic features of the soliton were studied in each of the cases considered. The effect of refractive index mismatch between the barrier and quantum-well materials on the soliton parameters was analyzed. Soliton solutions to the Maxwell-Bloch nonlinear equations are compared with their plane-wave solutions.     

Propagation characteristics of chirped soliton in periodic distributed amplification systems with variable coefficients

Propagation characteristics of chirped soliton in periodic distributed amplification systems with variable coefficients are investigated by using the split-step Fourier method. The soliton pulse still maintains soliton characteristics after propagation in the system. The shape of output spectrum is still with a single peak. The temporal FWHM of an unchirped soliton performs a slight oscillation with the increase of propagation distance. The oscillation amplitude is slightly increased with the increase of the gain or loss parameter σ. The chirped soliton is obviously and periodically compressed and broadened with the increase of propagation distance in the system. The lager the value of chirp parameter |C| and σ is, the greater the variation of temporal width with the distance is. The effect of chirp on temporal width of soliton in a amplification system is greater than that in a loss system. Three types of numerical experiments show that the soliton with different perturbations can stably propagate along the fiber. In practical applications, one can obtain a suitable soliton pulse by controlling the parameters of the fiber system.     

Theoretical description of low divergence Gaussian fields in self-defocusing photorefractive media

Experimental evidence is presented that shows that low intensity optical fields preserve their Gaussian transverse amplitude distribution as they propagate through self-defocusing Ce:BaTiO₃ photorefractive media. The Gaussian nature of the field is used in a theoretical treatment to derive conditions under which bright solitons are formed in photorefractive media that have a light induced refractive index that is approximately quadratic. This analysis shows that while it is not possible to produce a single bright soliton in self-defocusing media that it is possible to minimize the field’s divergence such that the change in beam radius is small (<1%) over large propagation distances (∼1 m). An imaginary light induced refractive index component is necessary to generate the low divergence fields in both self-focusing and self-defocusing media when illuminated with Gaussian fields that have a non-planar wavefront.     

Solitary waves in a nonlinear oppositely directed coupler

The propagation of pulses in the system of two tunnel-coupled optical waveguides from optically nonlinear materials one of which has a negative refractive index, while the other one, positive, is investigated theoretically. The propagation of nonlinear waves in this structure is studied based on the model of coupled modes. For linear waves, this pair of coupled waveguides behaves as a mirror resulting in the change of direction of the energy flow upon penetration of radiation from one waveguide to the other. The solutions to the system of nonlinear equations describing the stationary propagation of the solitary wave, the gap soliton, in a particular direction are found. This soliton is formed by the coupled pair of wave packets each localized in the corresponding waveguide.     

光折变有机聚合物中的双色光空间孤子

对光折变有机聚合物中的双色光空间孤子进行了理论分析,证明双色信号光的两个频率成分相互作用可以在折射率改变为正的光折变有机聚合物中形成暗暗和亮暗空间孤子,在折射率改变为负的光折变有机聚合物中形成亮亮和亮暗空间孤子。与单色光孤子的情况不同,对于双色光孤子情况,通过与一形成暗孤子的频率成分相互作用,另一频率成分在折射率改变为正的有机聚合物中也可形成亮孤子;通过与一形成亮孤子的频率成分相互作用,另一频率成分在折射率改变为负的材料中也可形成暗孤子。     

Light propagation and reflection-refraction event in absorbing media

The light propagation within an absorbing medium and the reflection and refraction at the interface of two absorbing media are studied. By using the unit vectors denoting the planes of constant field amplitude and constant phase respectively, the light propagation and attenuation are described by the effective refractive indices which depend on both the complex refractive index of the medium and the angle between the unit vectors. With the expression for the light propagation, the corresponding Snell＇s law and the expression of Fresnel coefficients are obtained, which can be applied to describe the reflection-refraction event at the interface between an arbitrary combination of transparent and absorbing media.     

过冷水溶液中的空间光孤子

建立了在过冷水溶液中传播的光束的非局域非线性模型.过冷水的热致折射率扰动在温度扰动较小的情况下随温度增大,但在温度扰动达到一定程度后随温度减小.在求出该模型的数值孤子解后,对孤子的性态进行了研究.研究表明,在光功率较小时,过冷水表现出自聚焦的特性,而在光功率较大时,在孤子的中心区域的过冷水表现出自散焦的特性,而在孤子的外围仍表现为自聚焦.在总功率较大的情况下,孤子间的相互作用也表现出这种部分自散焦,部分自聚焦的现象.     

光孤子对的振幅比与相位差对传输的影响

利用分步傅里叶变换法分别求解含三阶色散效应和不考虑三阶色散情况下的光孤子非线性薛定谔（NLS）方程,通过数值求解发现三阶色散效应会使孤子对脉冲发生单边振荡,并在振荡侧逐级产生次脉冲。讨论孤子对的两束孤子脉冲之间的振幅比与相位差对传输的影响,发现在不考虑三阶色散的情况下,振幅比与相位差均对孤子对的传输有显著影响,在考虑三阶色散效应时,只有相位差对孤子对的传输产生影响,并可以导致脉冲能量转移。     

Bragg optical solitons beyond the coupled mode approximation

Properties of conservative and dissipative Bragg solitons formed in single-mode optical fibers with induced longitudinal modulation of the refractive index are analyzed beyond the standard approximation of coupled modes, or of slowly varying amplitudes. It is shown that, if the initial velocity of a Bragg soliton is smaller than a critical value, the soliton stops in the process of propagation.     

Mode Structure and the Envelope of a Short Pulse in a Graded-Index Optical Fiber with a Longitudinal Inhomogeneity and a Spatial Bending

We consider propagation of a short optical pulse in an optical fiber whose refractive index is strongly dependent on the radial coordinate and is weakly dependent on the longitudinal coordinate with allowance for the possible weak spatial bending of the fiber axis. The three-dimensional nonlinear wave equation modelling the pulse propagation is solved asymptotically with respect to a small parameter specifying the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of the singular Sturm-Liouville problem is established. The pulse propagation is shown to have three scales: the high-frequency carrier is modulated by the envelope which evolves in a two-scale manner and is described by a nonlinear Schrödinger equation whose coefficients depend on the longitudinal coordinate. The transverse distribution of the wave field and the envelope soliton are obtained in terms of elementary functions for several types of transverse and longitudinal inhomogeneities of the fiber. The possibility of controlling the pulse parameters by varying the transverse and longitudinal inhomogeneities of the fiber is pointed out.     

Non linear analysis of obliquely propagating spin electron acoustic wave in a partially spin polarized degenerate plasma

By employing the separated spin evolution quantum hydrodynamic model, non-linear evolution of obliquely propagating spin electron acoustic wave (SEAW) is presented. The solitary structures of SEAW is investigated through the Korteweg–de Vries (KdV) equation derived using reductive perturbation method. From the first order perturbations we derive the dispersion relation of SEAW and find that both the spin polarization and the propagation angle reduce the phase velocity while the electron streaming enhances it. Using small amplitude approximation, the solitary structure of SEAW is analyzed and the effects of spin polarization, propagation angle and electron streaming on the SEA soliton are studied. Our numerical results demonstrate that the spin polarization and the propagation angle play a balancing act on the soliton structures. The possible applications of our investigation to the astrophysical environments like white dwarfs is also discussed.     

小入射角条件下气动光学成像偏移

针对超声速飞行器在大气中飞行时由于气动光学效应产生的成像偏移,推导了光线偏折角和流场折射率梯度之间的关系,给出了小入射角情况下,离散折射率场光线偏折角的一种计算方法;利用不同流场的计算流体力学数据计算出对应的折射率场;使用光线追迹法得到光线通过不同流场后的偏折角和传播路径上的折射率梯度分布。仿真结果表明,新的偏折角计算方法所得结果在入射角小于30°时与Runge-Kutta和Snell光线追迹法具有很好的一致性;同一高度下小入射角时,光线的偏折角并不随着飞行速度的增加而增加,而是基本保持稳定;光线通过流场的偏折是正负折射率梯度区域共同作用的结果,负的折射率梯度区域可以减少光线偏折,起到部分"校正"作用。     

Investigation of refractive index modifications in CW CO2 laser written planar optical waveguides

This paper presents the measurement of the refractive index profile of buried channel waveguides fabricated by a CW CO₂ direct writing technique. A reflectance method is used to assess the refractive index distribution n(x,y) in these structures as it is a key parameter determining the propagation properties of guided wave devices. Beam propagation method (BMP) is used with experimentally determined cross-sectional data and refractive index profile to model the waveguides. The spatial resolution is 1.3 μm and, 5.10⁻⁴ for the refractive index.     

Kerr类非线性介质周期结构中的慢Bragg孤子

在耦合模理论的基础上,给出了一维无限大Kerr类非线性介质周期结构中的孤波解,并且指出,孤波的振幅依赖于入射频率以及脉宽两个参量.同时也证明,在布拉格共振极限条件下,孤波解可以简化成所谓的“隙孤子”解或是“慢布拉格孤子”解 关键词： 孤波 慢布拉格孤子 隙孤子 耦合模理论