The Nth-order Darboux transformation,vector dark solitons and breathers for the coupled defocusing Hirota system in a birefringent nonlinear fiber

Under investigation in this paper is the coupled defocusing Hirota system, which describes the propagation of ultra-short pulses in a birefringent nonlinear fiber. With respect to the amplitudes of the pulse envelopes, we construct the Nth-order Darboux transformation, which is different from those in the existing literatures, where N is a positive integer. The first- and second-order solutions are obtained via the Darboux transformation. Pulse envelopes including the gray-gray/antidark-gray/dark-bright solitons, vector Akhmediev breathers, temporal cavity solitons and (time, space)-periodic breathers are acquired. As the relative width of the spectrum that arises due to the quasi monochromocity decreases, we find that: the velocity and width of the dark-bright solitons increase; the width of the temporal cavity soliton decreases; the temporal period of the vector (time, space)-periodic breather becomes longer while its spacial period becomes shorter. Relative width of the spectrum that arises due to the quasi monochromocity does not affect the amplitudes of the pulse envelopes obtained. Elastic interactions between the breathers and solitons, and inelastic interactions between the two gray-gray solitons are obtained.     

Dark and composite rogue waves in the coupled Hirota equations

The intriguing dark and composite rogue wave dynamics in a coupled Hirota system are unveiled, based on the exact explicit rational solutions obtained under the assumption of equal background height. It is found that a dark rogue wave state would occur as a result of the strong coupling between two field components with large wavenumber difference, and there would appear plenty of composite structures that are attributed to the specific wavenumber difference and the free choice of three independent structural parameters. The coexistence of different fundamental rogue waves in such a coupled system is also demonstrated.     

Rogue-wave pair and dark-bright-rogue wave solutions of the coupled Hirota equations

Novel explicit rogue wave solutions of the coupled Hirota equations are obtained by using the Darboux transformation.In contrast to the fundamental Peregrine solitons and dark rogue waves, we present an interesting rogue-wave pair that involves four zero-amplitude holes for the coupled Hirota equations. It is significant that the corresponding expressions of the rogue-wave pair solutions contain polynomials of the fourth order rather than the second order. Moreover, dark-brightrogue wave solutions of the coupled Hirota equations are given, and interactions between Peregrine solitons and dark-bright solitons are analyzed. The results further reveal the dynamical properties of rogue waves for the coupled Hirota equations.     

Parametric analysis of four wave mixing in DWDM systems

The developments made over the years in WDM (Wavelength Division Multiplexing), on one side, produced compensation of increasing traffic and channel capacity, but on other side, pertinently caused WDM systems to undergo different linear and non-linear effects thereby degrading the performance as such. To overcome linear effects is relatively convenient and manageable, however, the non-linear effects including four wave mixing (FWM) is not only difficult to eliminate but also highly incompatible from system point of view. In this research, valid parameters which lead to generation and enhancement of FWM, are discussed, simulated and based on exhaustive sets of obtained results, a detailed analysis has been carried out to reduce the FWM. The simulated results obtained by exploiting nine important parameters using Optisys simulator, divulge very incisive information for the removal of nonlinear effects in WDM. The authors are reasonably confident to extend their results as a contribution in the subject area.     

Matter wave solitons in coupled system with external potentials

We present Lax-pair corresponding to the coupled Gross-Pitaevskii equation (CGPE) which governs the evolution of the macroscopic wave function of two components Bose-Einstein condensates trapped in time-dependent harmonic potential. Kinds of soliton solutions can be derived from the Lax-pair through Darboux transformation conveniently. Furthermore, soliton management in two-component Bose-Einstein condensate would be realized base on that the shape and motion of soliton in both components are investigated analytically. Moreover, it is found that there is a transformation existed between the nonautonomous coupled system and Manakov model.     

Investigation of four wave mixing effect with different number of input channels at various channel spacing

In this paper the design, implementation and performance analysis of four wave mixing (FWM) in optical communication system for different number of input channels is presented using various values of channel spacing. Here, all the input channels have been spaced evenly at various values like 6.25 GHz, 12.5 GHz, 25 GHz, 40 GHz, 50 GHz with the different number of channels at the input i.e. with 2, 4, 6, 8, 12 input channels. The simulation results reveal that the four wave mixing is minimum when the channel spacing is maximum i.e. 50 GHz with minimum number of channels i.e. 2 input channels. It is observed that on increasing the channel spacing, the interference between the input frequencies decreases and hence the four wave mixing also decreases. Also, on increasing the number of input channels/users, the interference between the input frequencies increases and thus, the four wave mixing also increases.     

Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber

We reported the generation of visible red light through degenerate four wave mixing (FWM) in an all solid photonic bandgap fiber (PBGF), which was achieved by pumping the fiber with a 800 nm Ti:sapphire-based femtosecond pulse laser. At a fiber length of 30 m, a broadband anti-Stokes spectrum range from 620 nm to 740 nm was obtained at the highest pump power, the spectrum evolution as a function of pump power and propagation distance had been measured. Furthermore, the intensity-dependent parametric gain characteristic is also calculated, which accords well with the experimental results.     

New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems

In this Letter, to further understand the role of nonlinear dispersion in coupled nonlinear wave systems in both real and complex fields, we study the coupled Klein–Gordon equations with nonlinear dispersion in real field (called CKG(m,n,k)$\mathrm{CKG}(m,n,k)$ equation) and (2+1)$(2+1)$-dimensional generalization of coupled nonlinear Schrödinger equation with nonlinear dispersion in complex field (called GCNLS(m,n,k)$\mathrm{GCNLS}(m,n,k)$ equation) via some transformations. As a consequence, some types of solutions are obtained, which contain compactons, solitary pattern solutions, envelope compacton solutions, envelope solitary pattern solutions, solitary wave solutions and rational solutions.     

A novel frequency encoded all optical logic gates exploiting polarization insesensitive four wave mixing in semiconductor optical amplifier, filtering property of ADD/DROP multiplexer and non-linearity of reflective semiconductor amplifier

All optical logic gates exploiting polarization independent four wave mixing in semiconductor optical amplifier (SOA), filtering property of ADD/DROP multiplexer (ADM) and non-linearity in reflective semiconductor optical amplifier (RSOA) have been proposed. The logic gates proposed are polarization independent which ensures hardware simplicity and greater speed. The all optical frequency encoded logic gates NOT, OR, NOR, AND, NAND, X-OR, X-NOR are implemented which are very useful in optical computing ad signal processing, cryptography, etc. The logic gates proposed have the advantages that there is no intensity loss dependent problem, and are polarization and temperature insensitive.     

Evolution and stability of spatial solitons in a photorefractive two-wave mixing system

The dynamical evolution and stability of bright dissipative holographic solitons in biased photorefractive materials in which the self-trapping beam obtains a gain from the pump beam via two-wave mixing has been investigated numerically. Results show that these solitons are stable relative to small perturbations. Adjusting some system parameters, such as the bias field and the angle between beams, can easily control the generation of such solitons. Potential applications in optical switches or repeaters are discussed.     

On the polarisation sensitivity and performance optimisation of a dual pump four wave mixing based wavelength converter

This paper presents a detailed investigation of the performance of a wavelength conversion scheme. The converter is based on four wave mixing in semiconductor optical amplifiers using two parallel polarised pumps. Measurements of the conversion efficiency and the signal to background noise ratio of the two replicas of the signal, for the cases of the signal polarisation being either parallel or orthogonal relative to the pump waves have been carried out. These measurements will reveal the polarisation sensitivity of this scheme which appears to be less than 1 dB when the wavelength spacing between the signal and its closest spaced pump is larger than 12 nm. The experimental results are supported in a satisfactory way by theoretical considerations. A simple theoretical expression describing the polarisation sensitivity have been derived and the theoretical results are in good agreement with those experimentally obtained. A performance comparison of the conversion scheme using semiconductor optical amplifiers with different lengths but the same structure is also performed. Through the following study the optimum operational conditions for this wavelength conversion scheme will be determined.     

Experimental study of coupled vibration in a finite periodic dual-layered structure with transverse connection

The analytical equations of the transfer matrix method are further derived for the multi-coupled vibration of flexural and longitudinal waves in a periodic dual-layered beam structure with connection branches, with full consideration given to the flexural and longitudinal motions that are tri-coupled at each connection. Measurements of mobilities at the junctions on the uni-layered beam and the cross-layered beam are made. The numerical results agree well with the experimental results at all frequencies from 10 to 2000 Hz, which verifies the theoretical methodology for the multi-coupled vibration in a finite dual-layered beam. The cross-layer energy transmission is calculated, which reveals that the transmitted longitudinal energy is enhanced not only at the longitudinal resonant modes but also at the flexural resonant modes of the connection branches due to the structural wave coupling. The flexural energy is excited by wave coupling and becomes stronger at the longitudinal resonant modes and the flexural resonant modes of the connection branches. The cross-layer vibration motions from coupled waves in the branches can be effectively controlled by the attached cantilevers with mass at the resonance modes. This method can be used to control the structure-borne sound transmission in multi-layer beam structures.     

半导体激光器激活层中的四波混频和相位共轭光的发生

本文提出了一种从半导体激光器中发生和检测相位共轭光的新方法,并用1.3μm分布反馈半导体激光器作了实验验证。本方法不仅可以用来发生相位共轭光,还可以用来研究振荡运转中的激光激活介质的非线性光学特性。     

亚10 fs激光脉冲产生中的受激拉曼散射与四波混频效应

自行搭建的自锁模钛宝石激光器工作在下稳区的上边界附近,采用熔融石英棱镜对在激光器谐振腔的腔内和腔外同时进行群速度色散补偿.随着腔内棱镜对提供色散补偿的变化,输出激光脉冲的频谱会突然展宽至664—840nm,其空间模式也由基横模变化至衍射环状结构,这是受激拉曼散射和四波混频效应导致锁模激光脉冲频谱进一步展宽的结果.在此状态下自锁模钛宝石激光器可实现670—865nm范围的波长调谐.如此宽的频谱为钛宝石激光器产生亚10fs激光脉冲提供了必要的条件. 关键词： 飞秒激光脉冲 受激拉曼散射 四波混频 群速度色散     

Characteristics of degenerated four wave mixing in ZnS/CdSe/ZnS quantum dot quantum well with multi-shell structure

The wave functions and eigenenergies of electrons in ZnS/CdSe/ZnS cylindrical quantum dot quantum well (QDQW) have been calculated by solving a three-dimensional nonlinear Schrödinger equation, in the framework of the effective-mass envelope-function theory. The third-order susceptibilities of the degenerated four waves mixing (DFWM) have been calculated theoretically by means of compact density matrix. The third-order susceptibilities as the function of the shell radius R₂, R₃ have been analyzed. The results show that the magnitude of nonlinear susceptibility is increased with the increasing of well radius. The resonance frequency of the photon have a shift when R₂ or R₃ is increasing and the relation between nonlinear susceptibility and relaxation time has also been studied.     

Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices

We present an algorithm for polarized radiative transfer in a vertically stratified system consisting of two plane-parallel media with different refractive indices. It is based on the discrete ordinate method and includes multiple elastic scattering, thermal radiation, Fresnel reflection and transmission, incident parallel-beam or isotropic radiation at the top of the upper medium and bidirectional reflection at the bottom of the lower medium. Comparisons with results from Monte Carlo simulations show that the discrete-ordinate code provides accurate results for all four elements of the Stokes vector (I, Q, U, and V) at a speed that is orders of magnitude faster.     

Computational studies of steady-state sound field and reverberant sound decay in a system of two coupled rooms

The acoustical properties of an irregularly shaped room consisting of two connected rectangular subrooms were studied. An eigenmode method supported by a numerical implementation has been used to predict acoustic characteristics of the coupled system, such as the distribution of the sound pressure in steady-state and the reverberation time. In the theoretical model a low-frequency limit was considered. In this case the eigenmodes are lightly damped, thusthey were approximated by normal acoustic modes of a hard-walled room. The eigenfunctions and eigenfrequencies were computed numerically via application of a forced oscillator method with a finite difference algorithm. The influence of coupling between subrooms on acoustic parameters of the enclosure was demonstrated in numerical simulations where different distributions of absorbing materials on the walls of the subrooms and various positions of the sound source were assumed. Calculation results have shown that for large differences in the absorption coefficient in the subrooms the effect of modal localization contributes to peaks of RMS pressure in steady-state and a large increase in the reverberation time.      

Degenerate and two‐color resonant four‐wave mixing of C2− in a molecular beam environment

In this paper, we demonstrate that degenerate and two‐color resonant four‐wave mixing spectroscopy is applicable for the sensitive and selective characterization of negative ions in a molecular beam environment. Results are shown for C , which is produced by discharging a mixture of acetylene and argon prior to supersonic expansion. Substantial signal‐to‐noise ratios of ≈ 150 show that the method is generally applicable for high‐resolution optical double‐resonance spectroscopy of negative ions. A detection sensitivity for C of ≈ 10⁷ ions/cm³ is estimated. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of four-wave mixing on electromagnetically induced transparency in Λ-type system with a two-photon probe field

Using density matrix equation, we calculate analytically as well as numerically the effect of the four-wave mixing (FWM) field on electromagnetically induced transparency (EIT) in the rubidium 5S_{1/2}-5P_{3/2}-5D_{5/2} Λ-type system with a two-photon probe field. The calculated results are in good agreement with Fulton's experimental results in 1995 Phys. Rev. A 52 2302.