Exact analysis of cascaded second-order nonlinearity in rotated Ti:LiNbO3 Couplers

The effects of anisotropic coupling on the nonlinear behavior of different LiNbO₃ waveguides and couplers employing cascaded second-order nonlinearity are analyzed and the importance of leaky mode effect is shown. A set of practical coupling structures made of both symmetric and asymmetric waveguides is investigated and their performance is compared. The home-made computer-code, based on coupled wave theory and anisotropic mode propagation in the complex domain, allows an exact electromagnetic investigation of devices, taking into account both guided and leaky propagation in structures which exhibit losses, the generated second harmonic wave having leaky nature. As an example, for the well-investigated slab three layer waveguide, by taking into account the leaky nature of the generated second harmonic, the modal mismatch = 333 m^–1 is obtained at the azimuthal angle _m 61.9 (between the crystal optical c-axis and the propagation direction) while the angle found via the conventional approach is _m 63.5. Moreover, the calculated second harmonic wave exhibits an attenuation equal to 7.44 × 10^–1dB/cm that strongly influences the whole cascaded second-order phenomenon. The simulation results, for those structures in which it is possible to neglect the hybrid and leaky nature of the propagation modes, are compared with the literature data and an excellent agreement is found.     

Irrational rotation numbers and unboundedness of solutions of the second order differential equations with asymmetric nonlinearities

In this paper, we study the dynamics of the mappings

where is a irrational rotation number. We prove the existence of orbits that go to infinity in the future or in the past by using the well-known Birkhoff Ergodic Theorem. Applying this conclusion, we deal with the unboundedness of solutions of Liénard equations with asymmetric nonlinearities.

     

应用"逐差法"处理实验数据

本详尽地讨论了“逐差法”处理实验数据的理论方法并结合实例说明：如何记录数据,如何处理数据。     

Study of the third order nonlinear optical properties of Zn<Subscript>1−x</Subscript>Mg<Subscript>x</Subscript>Se and Cd<Subscript>1−x</Subscript>Mg<Subscript>x</Subscript>Se crystals

Third order nonlinear optical susceptibilities χ^<3> of ternary Zn_1−xMg_xSe and Cd_1−xMg_xSe crystals have been measured using standard degenerate four-wave mixing (DFWM) method at 532 nm. The nonlinear transmission technique has been applied to check if our crystals exhibit two-photon absorption. The studied Zn_1−xMg_xSe and Cd_1−xMg_xSe solid solutions were grown from the melt by the modified high-pressure Bridgman method. For both crystals the energy gap increases with increasing Mg content. In the case of Zn_1−xMg_xSe, it was found that the value of third order nonlinear optical susceptibility χ^<3> decreases with increasing Mg content. An explanation of this behaviour results from the dependence of optical nonlinearities on the energy band gap E_g of the studied crystals. In the case of Cd_1txMg_xSe with low content of Mg, no response was observed for the studied wavelength since the energy gap in such crystals is smaller than the photon energy of the used laser radiation. It was also found that the value of third order nonlinear optical susceptibility χ^<3> for Cd_0.70Mg_0.30Se is higher than for Zn_0.67Mg_0.33Se. This behaviour can be understood if one take into consideration that the free carrier concentration in Cd_1−xMg_xSe samples is about four orders of magnitude higher than that in Zn_1txMg_xSe ones with comparable Mg content respectively. It is commonly known that when the electric conductivity increases, the values of nonlinear optical properties increase. From the performed measurements one can conclude that the incorporation of Mg as constituent into ZnSe and CdSe crystals leads to a change of the third order nonlinear optical susceptibilities.     

LN晶体自散焦到自聚焦转换的耦合理论分析

对铌酸锂晶体进行了三阶非线性折射系数测量的Z扫描实验和光折变非线性系数测量的时间扫描实验。为了分析时间分辨扫描曲线的特点，基于非线性介质中光折变非线性与三阶非线性光学效应的耦合作用，引入非线性折射率随时间变化的表达式，分析了空间亮孤子的形成过程，进而揭示了其在一定条件下从自散焦到自聚焦转换的动态行为的物理机制,得到了与实验现象相一致的结论，并说明了自聚焦光折变晶体中可能存在稳定的暗空间孤子。     

副热带圈和赤道太平洋年代际变更的海-气振子模型解的同伦映射方法

研究了一类海-气振子时滞方程.目的是构建一个非线性海-气振子模型的近似求解方法，利用同伦映射理论讨论了对应的问题的近似解.这是一个近似的解析方法，它能够进一步分析海-气振子模型海表温度异常的其他性态.     

Noether-Symmetry Analysis using Alternative Lagrangian Representations

We have sought to work with an approach to Noether symmetry analysis which uses the properties of infinitesimal point transformations in the space-time (q, t) variable to establish the association between symmetries and conservation laws of a dynamical system. In this approach symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of two uncoupled Harmonic oscillators and two such oscillators coupled by an interaction. Both these systems can have alternative Lagrangian representations. We have studied in detail how the association between symmetries and conservation laws changes as one alters the analytic or Lagrangian representation. This analysis is carried out with a view to explicitly demonstrate that the correlation between symmetry transformation and corresponding invariant quantity depends crucially on the choice of the analytic representation. PACS 45.20.Jj, 45.20.df, 45.20.dh     

Enhancement of Kerr nonlinearity and its application to entangled state discrimination

In this paper, the recent research on the enhanced Kerr nonlinearity and its application in entangled state discrimination is reported. Two kinds of dynamics, including interacting double dark resonances and spontaneously generated coherence, are presented to enhance the Kerr nonlinearity. The application of Kerr nonlinearity in quantum state discrimination is also discussed. An arbitrary Greenberger-Horne-Zeilinger state can be discriminated using two-photon polarization parity detection which resorts to cross-Kerr nonlinearity between a single-photon qubit and probe field. In addition, a scheme for Greenberger-Horne-Zeilinger state discrimination of matter qubits is also proposed using the dipole induced transparency in a cavity-dipole system.      

Difference in the Nonlinearity of Absorption in Natural and Synthetic Coals

It is established that on an increase in the SHF radiation power for powder anthracite, a more rapid increase in the amplitude of the EPR line is observed in comparison to the case of linear absorption, whereas for carbon obtained by deposition of the products of pyrolysis of deuterobenzene (C₆D₆) on the surface of -Al₂O₃ there occurs saturation of absorption. At an air pressure of 10^–3 mm Hg, saturation of resonance absorption is observed in both samples. The linear effects observed can be understood within the framework of the formalism of a three-level scheme possible in the case of the triplet ground state of the paramagnetic centers of powder anthracite.     

对称线布载荷作用下圆底扁球壳的大挠度问题

本文研究对称线布载荷作用下圆底扁球壳的轴对称非线性弯曲和稳定性,讨论了当几何参数固定而载荷位置发生变化吋壳体的屈曲行为,以及当载荷作用位置固定而几何参数发生变化时壳体的屈曲行为,分析了屈曲模式对临界载荷的影响,并就ν=0.3的情形给出了数值结果。