Solutions for the propagation of light in nonlinear optical media with spatially inhomogeneous nonlinearities

In this paper, we present solutions for the nonlinear Schrödinger (NLS) equation with spatially inhomogeneous nonlinearities describing propagation of light in nonlinear media, under two sets of transverse modulation forms of inhomogeneous nonlinearity. The bright soliton solution and Gaussian solution have been obtained for one set of inhomogeneous nonlinearity modulation. For the other, bright soliton solution, black soliton solution and the train solution have been presented. Stability of the solutions has been determined by exact soliton solutions under certain conditions.     

Asymptotic theory of plane soliton self-focusing in two-dimensional wave media

An asymptotic method is developed to describe a long-term evolution of unstable quasi-plane solitary waves in the Kadomtsev-Petviashvili model for two-dimensional wave media with positive dispersion. An approximate equation is derived for the parameters of soliton transversal modulation and a general solution of this equation is found in an explicit form. It is shown that the development of periodic soliton modulation, in an unstable region, leads to saturation and formation of a two-dimensional stationary wave. This process is accompanied by the radiation of a small-amplitude plane soliton. In a stable region, an amplitude of the modulation is permanently decreasing due to radiation of quasi-harmonic wave packets. The multiperiodic regime of plane soliton self-focusing is also investigated.     

A UNIVERSAL MODULATION FUNCTION AND A GENERALIZED ANALYTICAL SOLUTION FOR PHOTOREFRACTIVE TWO WAVE COUPLING

We proposed a universal form of the modulation function,and derived a generalized analytical solution of the two wave coupled equation in transmission geometry in photorefractive crystal corresponding to the universal modulation function. The generalized analytical solution can be transformed into different analytical solutions reported in previous works on different conditions.In addition, other new analytical solutions can be obtained from the generalized analytical so lution,and an example is given in the present paper.     

A UNIVERSAL MODULATION FUNCTION AND A GENERALIZED ANALYTICAL SOLUTION FOR PHOTOREFRACTIVE TWO-WAVE COUPLING

We proposed a universal form of the modulation function,and derived a generalized analytical solution of the two wave coupled equation in transmission geometry in photorefractive crystal corresponding to the universal modulation function. The generalized analytical solution can be transformed into different analytical solutions reported in previous works on different conditions.In addition, other new analytical solutions can be obtained from the generalized analytical so lution,and an example is given in the present paper.     

Exact spatial soliton solution for nonlinear Schrödinger equation with a type of transverse nonperiodic modulation

In this paper, we analyze (2 + 1)D nonlinear Schrödinger (NLS) equation based on a type of nonperiodic modulation of linear refractive index in the transverse direction. We obtain an exact solution in explicit form for the (2 + 1)D nonlinear Schrödinger (NLS) equation with the nonperiodic modulation. Finally, the stability of the solution is discussed numerically, and the results reveal that the solution is stable to the finite initial perturbations.     

Three-to-one internal resonances in a general cubic non-linear continuous system

A general continuous system with an arbitrary cubic non-linearity is considered. The non-linearity is expressed in terms of an arbitrary cubic operator. Three-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a beam resting on a non-linear elastic foundation.     

Photon statistics for single-molecule nonlinear spectroscopy

We develop the theory of nonlinear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. We find general expressions for the photon counting statistics and the exact solution to the problem for the Kubo-Anderson process. In the limit of impulsive pulses the information on the photon statistics is contained in the molecule's dipole correlation function. The selective limit, the semiclassical approximation, and the fast modulation limit exhibit rich general behaviors of this new type of spectroscopy. We show how the design of external fields leads to insights on ultrafast dynamics of individual molecules that are different from those found for an ensemble.     

Frequency-dependent steady-state distribution of optical power in multimode fibres

A new approach to the steady-state solution of the optical power flow equation in multimode fibres is presented. It takes into account the dependence on the modulation frequency of the optical guided power, starting from a very general trial solution. The steady-state attenuation coefficient and optical power distribution (in amplitude and delay) can be numerically evaluated for any kind of index profile and fibre perturbation.     

Modulation bandwidth of planar waveguide laser with 1D photonic crystal mirrors

An analysis of the 3-dB modulation bandwidth in planar waveguide laser based on 1D photonic crystal structures is presented. The theoretical model takes into account the gain saturation effect, transverse and longitudinal field distribution. A small-signal perturbation solution of the coupled laser rate equation is used to obtain relations describing the dynamic operation. In paper, the distributed Bragg resonator DBR created as 1D photonic crystal is considered. The active waveguide is surrounded by 1D photonic crystal mirrors consisting of alternately placed stripes with different refractive indices. In particular, the influence of the photonic crystal parameters on the 3-dB modulation bandwidth is investigated.     

Exact spatial soliton solution for nonlinear Schrödinger equation with nonperiodic modulation of nonlinearity and linear refractive index

In this paper, we analyze (2 + 1)-dimensional nonlinear Schrödinger equation with nonperiodic modulation of nonlinearity and linear refractive index in the transverse direction, and obtain an exact solution in explicit form using an ansatz method. Finally, the stability of the solution is discussed numerically, and the result reveals that the solution is stable to the finite initial perturbations.     

基于注入半导体激光器的微波副载波相位调制信号产生

光载无线技术是解决终端超宽带无线通信的重要方法,光信号与微波/毫米波信号的融合处理技术在光-无线的数据格式转换中至关重要.提出了一种基于相位调制信号光注入Fabry-Perot型半导体激光器实现微波副载波相位调制信号产生的方法.光学注入半导体激光器的输出光场会产生一周期(P1)振荡效应, P1振荡产生的边带实现了相位调制信号光的调制分量的放大,被放大的调制分量与注入光载波在激光器腔内拍频形成微波副载波.注入光相位的变化导致新产生的微波副载波相位变化, 实现了注入信号光相位信息转化为微波副载波相位信息.本系统完成1.3 Gb/s, 2.7 Gb/s, 2 Gb/s光相位调制信号到微波副载波相位调制信号的转换,并测量了微波的单边带相位噪声. 通过光电转换和电域混频将还原出的光基带信号与原信号进行逻辑对比,证明了数据信息转换的正确性.     

Model of electron beam transformation in a narrow tube

The problem of transformation of an electron beam in a long narrow conducting tube is considered. General wave solutions for the propagation of an arbitrary (including aperiodic) modulation of a homogeneous beam are obtained in the case of weak modulation. The solution corresponding to harmonic modulation is compared to the solutions obtained earlier and described in the literature. The problem of beam transformation corresponding to the bunching regime in high-power klystrons is also considered (including overtaking). A discrete analytic solution to the problem is obtained in the ??frozen beam approximation.?? This solution is tested for the problem of spilling of a monovelocity bunch and for the problem of the efficiency of a two-cavity klystron with infinitely narrow gaps. In both cases, physically correct results are obtained.     

The Improvement of Performance for Continuous-Variable Quantum Key Distribution with Imperfect Gaussian Modulation

Gaussian modulation is one of the key steps for the implementation of continuous-variable quantum key distribution (CVQKD) schemes. However, imperfection in the Gaussian modulation may introduce modulation noise that can deteriorate the performance of CVQKD systems. In this paper, we mainly investigate how to improve the performance of a CVQKD system from different aspects. First, we explore the several different origins, impacts and monitoring schemes for the modulation noise in detail. Then, we discuss the practical performance of a CVQKD system with an untrusted noise model and neutral party model, respectively. These analyses indicate that the neutral party model should be reasonably regarded as a general noise model, which will passively and greatly raise the performance of the system. Further, we propose a dynamic auto-bias control scheme to actively resist the modulation noise which comes from the drift of bias point of the amplitude modulator. Together these methods contribute to the improvement of the practical performance of CVQKD systems with imperfect Gaussian modulation.

     

Optimal downlink power allocation in cellular networks

In this paper, we introduce a novel approach for power allocation in cellular networks. In our model, we use sigmoidal-like utility functions to represent different users’ modulation schemes. Each utility function is a representation of the probability of successfully transmitted packets per unit of power consumed by a user, when using a certain modulation scheme. We consider power allocation with utility proportional fairness policy, where the fairness among users is in utility percentage i.e. percentage of successfully transmitted packets of the corresponding modulation scheme. We formulate our power allocation optimization problem as a product of utilities of all users and prove that it is convex and therefore the optimal solution is tractable. We present a distributed algorithm to allocate base station powers optimally with priority given to users running lower modulation schemes while ensuring non-zero power allocation to users running higher modulation schemes. Our algorithm prevents fluctuation in the power allocation process and is capable of traffic and modulation dependent pricing policy. This can be used to flatten traffic and decrease the service price for users. We also compare our results with a benchmark algorithm and show that our algorithm performs better in allocating powers fairly to all users without dropping any user in order to maximize performance.     

Crossover from adiabatic to antiadiabatic quantum pumping with dissipation

Quantum pumping, in its different forms, is attracting attention from different fields, from fundamental quantum mechanics, to nanotechnology, to superconductivity. We investigate the crossover of quantum pumping from the adiabatic to the antiadiabatic regime in the presence of dissipation, and find general and explicit analytical expressions for the pumped current in a minimal model describing a system with the topology of a ring forced by a periodic modulation of frequency ω. The solution allows following in a transparent way the evolution of pumped dc current from much smaller to much larger ω values than the other relevant energy scale, the energy splitting introduced by the modulation. We find and characterize a temperature-dependent optimal value of the frequency for which the pumped current is maximal.     

Multi-layer structures described with the help of the superposition of two-layer solutions

For multi-layer systems consisting of e.g. three different layers, a solution method is proposed which relies on the superposition of two-layer solutions, determined separately from the two relative extrema of the inverse calibrated modulated IR phases. Starting from the two-layer solutions, the inverse calibrated IR phases are iteratively approximated using a three-layer model, whereby first the approximation for the relative extremum at low modulation frequencies is improved, while the solution for the extremum at high modulation frequencies is maintained constant. In the next step, the solution for the extremum at high modulation frequencies is improved, while the solution at low modulation frequencies remains constant. If the two relative extrema are measured at rather different modulation frequencies, this alternate iteration procedure rapidly converges, e.g. after six iterations, and the final solutions are found in the neighborhood of the initial two-layer solutions.     

Steady dark solitary waves emerging from wave-generated meanflow: the role of modulation equations

Various classes of steady and unsteady dark solitary waves (DSWs) are known to exist in modulation equations for water waves in finite depth. However, there is a class of steady DSWS of the full water-wave problem which are missed by the classical modulation equations such as the Hasimoto-Ono, Benney-Roskes, and Davey-Stewartson. These steady DSWs, recently discovered by Bridges and Donaldson, are pervasive in finite depth, arise through secondary criticality of Stokes gravity waves, and are synchronized with the Stokes wave. In this paper, the role of DSWs in modulation equations for water waves is reappraised. The intrinsic unsteady nature of existing modulation equations filters out some interesting solutions. On the other hand, the geometry of DSWs in modulation equations is very similar to the full water wave problem and these geometrical properties are developed. A model equation is proposed which illustrates the general nature of the emergence of steady DSWs due to wave-generated mean flow coupled to a periodic wave. Although the existing modulation equations are intrinsically unsteady, it is shown that there are also important shortcomings when one wants to use them for stability analysis of DSWs.     

折射率调制型光纤传感器在溶液浓度测量中的应用

本文详细报道了用折射率调制型光纤传感器测量溶液浓度的原理及实验装置。为了消除光源光强的不稳定性对测量精度提高的影响,我们提出用光学双稳态装置稳定光源的输出功率并将它用于实际测量中,实验结果表明:本方法用于测量溶液的浓度在灵敏度、精度和稳定度方面都有较大的提高,并且可用于在线监测。     

A general solution procedure for the forced vibrations of a system with cubic nonlinearities: Three-to-one internal resonances with external excitation

A general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam.     

群速弥散补偿的飞秒激光器的动态性能研究

本文研究了普通的CPM环型染料激光器和棱镜补偿光脉冲的群速度弥散及自相位调制的CPM环型染料激光器的动态性能;实验测量了锁模激光脉冲的光谱随可饱和吸收体DODCI的浓度变化,在腔内正群速度弥散过量时,光脉冲频率发生正啁啾,光谱分布发生反转。