Analysis of an optical logic gate using a symmetric coupler operating with pulse position modulation (PPM)

In this paper we propose the operation of an all-optical logical gate based in a symmetric nonlinear directional coupler (NLDC) operating with a pulse position modulation (PPM). The performance of a symmetric NLDC realizing two-input AND/OR logical functions, which can be applied in transmission and processing of signals in all-optical form in TDM systems, is examined. This integrated symmetric NLDC logical gate operates with two ultrashort soliton light pulses (2 ps), which are modulated in agreement with the technique of pulse position modulation (PPM). Initially, we evaluate the effect resulting of an increment in the PPM coding parameter offset (ε), for the temporal position of the output pulse, considering the anomalous group-velocity dispersion (GVD), nonlinear self phase modulation (SPM) and without loss propagation regime of input pulses, in the cores 1 and 2 of the NLDC. In this situation, we analyze the four possible situations for the two-input logical gate, modulating the 1 and 2 input pulses through temporal displacement and allowing a variation in the coding parameter offset. We can conclude that is possible to get AND/OR logical operations for the cores 1 or 2, without to insert PPM error, since a phase control (Δ?) exists applied in agreement with the logical level of the input pulse in the core 1. Finally we define the truth table, considering the adequate phase difference and coding parameter offset for the stable operation of the AND/OR logical gate based in the symmetric NLDC.     

Study of ultra-fast optical pulse propagation in a nonlinear directional coupler

We showed that the application of a soliton in a nonlinear coupler does not show a better switching performance than a Gaussian pulse, unlike what the existing theory expected. Like the Gaussian pulse, a soliton could also suffer distortion, broadening, or narrowing in a nonlinear directional coupler. In addition, by using a new normalized format the linearly coupled nonlinear Schrödinger equations were investigated. For the first time, we found that both the coupling behavior and the switching performance of pulses in a nonlinear coupler depend on the product of the coupling coefficient and the dispersion length. We also showed that for a given nonlinear coupler with a Gaussian-like or soliton-like pulse input, switching performance and whether a pulse breaks up or not mainly depend on the input pulse width, not the pulse shape. PACS 42.65.Tg; 42.65.Wi; 42.81.Qb     

Gain-induced soliton switching in fiber nonlinear directional coupler

With study for switching characteristics and output coupling ratio of fiber nonlinear directional couplers (NLDC), we found that the influence elements on the switching characteristics and output coupling ratio had gain of core 1 and 2, nonlinear coefficient of those, the input power and width of input soliton. We also found numerically that switching efficiencies were improved by controlling gain of core 1, different output coupling ratio would be obtained by controlling gain of core 1 or 2. And we can change the gain by changing pump power of the optical fiber amplifiers. From this, we also made fiber coupler which output coupling ratio was changeable.     

Switching Dynamic Analysis for Twin-Core Fibre Coupler Using Supermode Theory

Characteristics of optical switching in a twin-core fibre coupler are numerically analysed under short pulse input by using supermode theory. The dynamic nonlinear coupled superlnode equations are derived, The numerical results show that the input pulse width determines the power transfer and the pulse temporal profile in the output ports. The optimal switching characteristics can be obtained by selecting an appropriate initial pulse width. In addition, the switching characteristic curves are insensitive to the input pulse shape for either fundamental soliton pulse or Gaussian pulse input, but sensitive to pulse sharpness. A reduced switching power and a sharper switching transition can be obtained by using the sharp super-Gaussian pulse.     

Analysis of a gained nonlinear directional coupler pulse switch

We have investigated the switching performance of a gained (nonlinear directional coupler) NLDC switch in the presence of both 2nd and 4th order gain nonlinearities. In this system, we have achieved a nearly complete pulse switching at half beat length of the coupler which implies about 40% reduction in the switching length as compared to the switching length reported in Trillo et al. (1988). We have shown that at the half beat length the output energy of each branch is equal to that of the input energy and hence the gained NLDC switches have ability to be cascaded. Our initial investigations reveal that this gained NLDC switch has remarkable performance and potential to be used in ultra-fast optical communication systems.     

非线性光定向耦合器解的简化表达式

本文将非线性定向耦合器在任意输入情况的解进行了简化.在本文解的基础上,非线性光定向耦合器的工作点,即其开关、调制和放大应用(几乎所有应用)的输入条件能很容易地由解析式确定,并在理论上提出了非线性光定向耦合器一个新的应用:一束强光的相位可以由一束弱光的功率加以控制.     

复合型变耦合系数定向耦合器开关特性的研究

研究了高斯—常数—高斯平滑连接的复合型变耦合系数定向耦合器的开关特性曲线。研究了耦合器各分段长度对开关曲线的影响。数值模拟发现,耦合器各组成部分的参量对耦合器开关曲线尾部的振荡及开关功率的大小均有影响,且呈现出一定的规律性。高斯型波导部分的相对长度以及直波导部分所占份额共同决定了耦合器开关曲线尾部的振荡大小,且开关曲线的振荡与耦合函数的傅里叶变换的振荡密切相关。     

Chaotic soliton switching generation using a nonlinear micro ring resonator for secure packet switching use

We propose a new design of the secure packet switching device using the nonlinear behaviors of soliton in a micro ring resonator, where the nonlinear penalty of light traveling in the device becomes beneficial. The chaotic signals are generated by a Kerr effects nonlinear type of the input soliton pulse in a micro ring resonator, where the control input power can be used to specify the output filtering signals. Some device parameters are chosen and simulated using the proposed model. The potential of using such a device for communication security is performed and discussed. For instance, the packet switching of the chaotic encoding data increases from the chaotic signal encoding of 100 bits⁻¹. Results obtained have shown the potential of using such a proposed device for the tunable bandpass and band-stop filters, in which packet switching data can be performed and secured.     

Vector soliton switching in a fiber nonlinear directional coupler

This paper reports a detailed numerical study of soliton switching in a high as well as low birefringent nonlinear coupler. It is shown that by controlling the polarization angle one can have nearly 100% transmission with excellent switching characteristics. It is shown that soliton remains stable during its propagation inside the coupler. However it is observed that high birefringent coupler exhibits relatively better soliton stability. We show that the coupler could be used as a soliton switch even at an input peak power less than the critical power, the power at which 50-50 power sharing takes place between the two cores, just by a judicious choice of the polarization angle.     

The effect of relative phase on the stability of temporal dark soliton in $${{\mathcal {}}}$$-symmetric nonlinear directional fiber coupler

In this paper, we numerically investigate the effect of relative phase on the stability of dark solitons in \({\mathcal {PT}}\)-Symmetric nonlinear directional coupler (NLDC), by considering gain in the bar and loss in the cross in the range of \(\theta =0^\circ\) to \(180^\circ\). The \({\mathcal {PT}}\)-Symmetric perturbed eigenfunctions are used to study the soliton stability. The results of simulations are shown that in the first half region of the relative phase the soliton is unstable while in the second one, is stable. In the stable region gain and loss cancel each other and also the perturbed eigenfunctions have no effect on solitons while in the unstable region solitons are amplified in the bar and attenuated in the cross except for some small intervals which the roles are changed. The behavior of such perturbation can be interpreted as self all-optical phase soliton switching and optical logic gates.     

A novel temporal dark-bright solitons conversion system via an add/drop filter for signal security use

We propose a new design of a security scheme by using the nonlinear behaviors of temporal dark and bright solitons within a micro-ring resonator system for signal security application. When a dark soliton pulse is input into the proposed system, the chaotic signal is generated, where the required bright soliton pulse can be retrieved and detected by the add/drop filtering device. The chaotic wave form can be cancelled by using an add/drop device, which can be connected and used in the communication link. By using the appropriate ring parameters, simulation results obtained have shown that the soliton conversion can be performed. The ring radii used are within the ranges from 5 to 10 μms and A_eff=0.10-0.50 μm². In application, the chaotic signal is generated and formed by the dark soliton within a nonlinear micro-ring device. This can be seen by using the add/drop device, where the bright soliton is formed and detected, which is available to use in communication link. The different temporal soliton response time is seen, the response times of 169 and 84 ns are noted for temporal dark and bright solitons, respectively, which can also be used to form the security key.     

Simulative demonstration of soliton pulse stability over the nonlinear regime in a birefringent optical fiber

In this paper, the results of numerical analysis are demonstrated for sech pulse (soliton) propagation in a birefringent optical fiber using computer modeling and simulation. Here, the initial pulse is polarized linearly and guided into the fiber at an angle of 45° to its polarization axes. The birefringence-induced time delay of 200 and 440 ps between X and Y polarization components has been reported at a fiber length of 631.72 km (10 soliton periods) by considering linear and nonlinear regimes, respectively. The Kerr nonlinearity, which stabilizes solitons against spreading due to GVD, also stabilizes them against splitting due to birefringence. A similar fact is true for the birefringent walk-off. Above a certain soliton order (N_th), the evolution scenario is qualitatively different and two orthogonally polarized components of the soliton move with a common group velocity despite their different modal indices or polarization mode dispersion (PMD) at a fiber length of 631.72 km (10 soliton periods) and 1264.344 km (20 soliton periods) over a nonlinear regime at θ≠45°. The physical effect responsible for this type of behavior is the cross-phase modulation (XPM) between the two polarization components.     

Drift ion acoustic solitons in an inhomogeneous 2-D quantum magnetoplasma

Linear and nonlinear propagation characteristics of quantum drift ion acoustic waves are investigated in an inhomogeneous two-dimensional plasma employing the quantum hydrodynamic (QHD) model. In this regard, the dispersion relation of the drift ion acoustic waves is derived and limiting cases are discussed. In order to study the drift ion acoustic solitons, nonlinear quantum Kadomstev-Petviashvilli (KP) equation in an inhomogeneous quantum plasma is derived using the drift approximation. The solution of quantum KP equation using the tangent hyperbolic (tanh) method is also presented. The variation of the soliton with the quantum Bohm potential, the ratio of drift to soliton velocity in the co-moving frame, , and the increasing magnetic field are also investigated. It is found that the increasing number density decreases the amplitude of the soliton. It is also shown that the fast drift soliton (i.e., v_*>u) decreases whereas the slow drift soliton (i.e., v_*<u) increases the amplitude of the soliton. Finally, it is shown that the increasing magnetic field increases the amplitude of the quantum drift ion acoustic soliton. The stability of the quantum KP equation is also investigated. The relevance of the present investigation in dense astrophysical environments is also pointed out.     

三芯非线性光纤耦合器中的短脉冲光开关

利用变分法研究三芯非线性光纤耦合器中的短脉冲光开关,解析分析线性三耦合非线性Schr?dinger方程的结果与数值模拟符合得很好.并且得到在非线性光纤耦合器中孤子的耦合长度和开关阈值,与连续波情况和两芯光纤耦合器的结果不同. 关键词： 光纤耦合器 光开关 耦合长度 开关阈值     

Incoherent interaction between bright–bright photovoltaic soliton in an unbiased series two-photon photorefractive crystal circuit

We have investigated incoherent interaction between photovoltaic bright–bright soliton pairs in photorefractive crystals under steady-state condition in an unbiased series two-photon photorefractive crystal circuit in one dimension. The numerical scheme according to the Crank-Nicholson and Runge-kutta methods are applied to simulate the propagation of incoherent interaction for different normalized separation distances and different E₀. Results show that in the case of one-dimensional interaction between these photovoltaic solitons, attraction occurs and width of beams decreases with increasing biased field E₀ and two soliton interact in longer distance for smaller E₀. The result can be used for design optical switches that controlled by biased field.     

(1+1)维非局域非线性介质的边界对表面孤子的影响

对非局域非线性介质中, (1+1)维表面亮孤子进行了研究, 主要考虑了边界对孤子的影响. 首先, 在归一化系统中, 对于给定的边界条件, 求出了表面孤子的解析解, 得到了表面孤子的临界功率和平衡位置. 其次, 在数值模拟中, 发现当样品宽度太小时, 受到边界影响而很难形成表面孤子, 只有当样品宽度足够大时, 边界对孤子的影响可以忽略, 从而形成稳定传输的孤子, 并与解析的结果相似. 此外, 还考虑了在光束偏离平衡位置入射的情况下, 边界对孤子的影响, 发现此时光束在边界附近做周期性震荡, 相当于体介质中双光束相互作用的结果, 两者运动轨迹与震荡周期完全符合. 关键词： 非局域非线性 边界 样品宽度 周期震荡     

Phase-induced switching in fiber nonlinear directional coupler

A numerical study of soliton switching characteristics and the maximum output coupling by the relative phase change of a control pulse is carried out for input powers, coupled coefficient and input soliton width. It is shown that input powers ratio, coupled coefficient and input soliton width play important roles in this mode of soliton switching and that these effects may lead to useful soliton switching if the relative phase of the control pulse is monitored judiciously.     

Dynamics of bound vector solitons induced by stochastic perturbations: Soliton breakup and soliton switching

We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.     

Taylor collocation method for the numerical solution of the nonlinear Schrödinger equation using quintic B-spline basis

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrödinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L ₂ and L _∞ error norms are calculated to improve the accuracy of the numerical results.