Probe beam amplification and phase conjugation self-oscillation ina Kerr medium

In a highly-nonlinear thin Ker medium, the intersection of a strong pump beam and a much weaker probe beam produces a sizeable diffracted beam whose presence changes both the transmitted probe beam gain and the phase conjugation self-oscillation thresholds. An analytical calculation of these effects involving degenerate multiwave mixing processes is presented     

Kerr效应对超高斯光束聚焦特性的影响

利用菲涅耳-基尔霍夫衍射积分公式,对一维超高斯光束通过克尔介质的聚焦特性进行了研究.在相位延迟为-2 rad~2 rad的范围内进行了计算.模拟结果表明,正Kerr效应将提高聚焦强度、增大相对焦移量和降低几何焦平面的峰值光强;而负Kerr效应,则会降低聚焦强度、增大相对焦移量和降低几何焦平面的峰值光强.可以将这两种的情况联合起来进行讨论,并可以通过增大光束的菲涅耳数来降低Kerr效应对其聚焦特性的影响.     

A simple analytic approach to degenerate four-wave mixing by comparison with real-time holography

A simple analytic theory for degenerate four-wave mixing (DFWM) is presented. From the fundamental relationship between real-time holography and DFWM simple expressions for the DFWM signal are developed. The basic assumption in our approach is that the four waves are coupled only by the grating created by the forward-probe interference and that the intensities of the forward beam and the probe beam are not affected by the four-wave interaction. In general, this is only true when the backward pump beam intensity is much smaller than both the forward beam intensity and the probe beam intensity. However, within this restricted parameter range we obtain simple analytic expressions for the DFWM signal including the effects of linear losses in the nonlinear medium. For thin nonlinear media the signal intensity is determined by a squared Bessel-function of first order, and for thick nonlinear media the signal intensity is determined by a squared sine-function. The theory is restricted to small values of the signal reflectivity. Finally, we have investigated the DFWM signal from a CdS-sample with aQ-switched frequency doubled Nd:YAG laser. At a sample temperature of 375 K we obtain a third-order susceptibility ofchi^{(3)} = 4.4 cdot 10^{-7}ESU. We apply the theory to these experiments.     

Mean field theory of optical bistability in a phase-conjugate resonator using nearly degenerate four-wave mixing

A mean field theory of nearly-degenerate four-wave mixing is developed for the optical bistability, which has recently been found in a phase-conjugate resonator consisting of a normal mirror and a phase-conjugate mirror under relatively strong pumping. The bistability in transmission of the probe beam occurs as the mirror separation or the probe offset frequency is changed, but for a limited range of probe beam intensity. This behavior is explained as occurring under injection-locked conditions because of combined effects of tilting and broadening, or narrowing of the resonance curves due to nonlinearities in the phase-conjugate reflectivity arising from pump depletion.     

Theory of amplitude and phase effects in 2-D-two-wave mixing

The two-wave mixing process in a photorefractive medium is investigated including nonuniform amplitude distributions of the pump and signal waves, plane-aberrated phase fronts, absorption, and arbitrary grating phase shift φ. The resulting system of two-dimensional coupled-wave equations is solved numerically with the aid of a two-dimensional Runge-Kutta method. Numerical data are shown to explain the gain distributions and image distortion properties in photorefractive amplifiers of the crossed beam, transmission and reflection grating type. A simple relation is presented describing the amplitude-phase crosstalk in two-wave mixing. One example is illustrated showing the possibility for compensating for aberrations using special pump and/or signal beam profiles with a grating phase shift different from 90°     

Theory of photorefractive phase conjugators with mutuallyincoherent beams

Plane-wave analysis of the recently demonstrated photorefractive phase conjugators with mutually incoherent beams is presented. Based on four-wave mixing theory, two important configurations, the bird-wing phase conjugator and the mutually incoherent beam coupler are investigated by solving coupled nonlinear equations with beam depletion and absorption. Various intensity performances are theoretically analyzed. Different configurations of this kind of mutually incoherent phase conjugators are compared. Competition of different processes is discussed. Experimental data are well fitted by the theory     

Kerr效应对依赖强度耦合J-C模型中纠缠交换的影响

在多个原子分别与多个腔场发生依赖强度耦合的相互作用系统中,运用全量子理论,研究了Kerr介质对纠缠信息在原子与腔场之间周期性可逆交换传递过程的影响.结果表明: Kerr介质对初始腔场为真空态或最低Fock态组成的纠缠态等一些特殊情形不产生任何影响.而对一般Fock态|nk>(nk≠0)都会改变其纠缠信息转换的相位和周期. Kerr效应越强烈转换周期就越短,相反,可以利用选取不同Kerr介质来控制纠缠信息交换传递的快慢.另外,相位的改变也与腔场中光子数nk(k=1,2,3,…,M)有关.     

Nonlinear response of the photorefractive phase conjugator: aperturbation analysis

Using perturbation theory, an examination is made of the fidelity of the photorefractive degenerate four-wave mixing phase conjugator. The general case is considered in which the probe is spatially varying (a beam) and temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane-wave components. Carrying out the perturbation procedure up to the third order, the authors found that the components of the probe interact in pairs, so that the reflectance of each component of the conjugate wave is a combination of a linear term, a self-nonlinear term, and a term representing crosstalk with all other components of the probe. The crosstalk effect as a function of the frequency difference exhibits resonance behavior     

Polarization properties of two-wave mixing under an alternatingelectric field in BSO crystals

The coupled-wave theory is extended to analyze the two-wave mixing interaction under an alternating electric field in a sillenite crystal. Within the undepleted pump beam approximation, an analytical expression which allows prediction of the phase, the polarization state, and the amplitude of the amplified beam is derived. It is shown that all these features usually oscillate. These predictions are confirmed by experiments     

被Kerr介质包围的J—C模型中光场位相特性

本文应用Pegg-Barnett位相理论讨论了被Kerr介质包围的J-C模型中光场的位相性质。     

Effects of side diffractions and phase modulations on phaseconjugation in a Kerr medium

The effects of side diffractions, generated from the interaction of a weak probe beam and its phase conjugate with two strong counterpropagating pump waves, and the effect of various intensity-dependent self- and mutual-phase modulations on the intensities of the probe beam and its phase conjugate are analytically studied in the nonpump-depletion limit. The results show that the conditions for the existence of, and threshold pump intensity parameters for, the divergence in the intensities of the probe and other generated beams are highly dependent on the wave-mixing angles and are different from the usual four-wave mixing phase conjugation process where the diffractions are not taken into account     

Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser

We demonstrate intracavity degenerate four-wave mixing in the saturable gain medium of a dye laser. The dye laser is a synchronously pumped bidirectional ring laser that produces pulses of 4 ps duration. The dynamics of the interaction provides information on the phase coherence of the pulses. A simple theory of transient degenerate four-wave mixing is presented that accurately describes the measurements.     

Propagation of TM modes in a circular dielectric waveguide filled with a medium with Kerr nonlinearity

Eigenmodes propagating in a cylindrical dielectric waveguide of circular cross section filled with a nonlinear medium whose nonlinearity is described by the Kerr law are analyzed. The nonlinear eigenvalue boundary problem for the nonlinear Helmholtz equation is considered. An iterative numerical method for obtaining the approximate solutions is developed. Numerical results are presented.     

高速调幅光束的光折变四波混频的理论研究

对高速调幅光束的光折变四波混频进行了理论研究。在无泵浦非耗竭近似下，给出了复耦合系数为任意值时稳态四波混频耦合波方程组的解析解。对方波调制光束情况进行了模拟计算。     

Propagation analysis of forward degenerate four-wave mixing

We discuss the propagation problem associated with the forward four-wave degenerate mixing induced by the third-order non-linear susceptibilitychi_{(-omega; omega, omega, -omega)}^{(3)} = chi_{1}^{(3)} + ichi_{2}^{(3)}. Exact analytical solutions are presented of two-photon resonances, evidencing the influence of the Kerr effect on the efficiency of the process. Around a two-photon resonance, we solve the problem of the nearly parallel propagation of two beams undergoing auto and induced two-photon absorption (TPA). The resonant interaction is studied in detail and analytical solutions are provided with operational accuracy for current experimental conditions. We show by the way that in the two-beam two-photon experiments, when the phase matching condition is fulfilled, although TPA is governed bychi_{2}^{(3)}, the real part ofchi^{(3)}must be considered in a substantial way. All the above solutions are put in a form simple enough that the numerical computations can be performed on a programmable calculator.     

纠缠原子与光场作用体系的压缩特性

研究了Kerr介质中初始处于纠缠态的两二能级原子与相干光场相互作用体系的压缩特性.通过数值计算,讨论了原子偶极间相互作用耦合常数和Kerr介质与单模腔场相互作用的耦合强度对体系中的双原子偶极压缩和光场压缩的影响.结果发现在弱光场情况下,纠缠态原子偶极间相互作用和Kerr介质与光场作用越强,都使原子偶极振幅压缩现象从压缩状态退缩到无压缩状态;在强光场情况下,纠缠态原子偶极间相互作用越强,光场振幅压缩次数增多、振荡频率变慢;Kerr介质与光场作用越强,光场振幅压缩次数减少、振荡频率变快.     

Spatial soliton-induced guiding by cross-phase modulation

The authors show that spatial solitons are able to induce the stable guiding of a weak probe beam in a homogeneous Kerr-type nonlinear media through cross-phase modulation (XPM). The modes of the induced waveguide are derived from the propagation equation of the probe. Experiments have been performed in Kerr liquid CS₂, with beams of picosecond duration at infrared and visible wavelengths. Stable guiding of a green probe induced by an IR soliton beam has been demonstrated in several different experimental situations. Induced antiguiding and beam splitting are also reported for pump and probe of perpendicular polarizations. All results are in excellent agreement with numerical simulations of the propagation     

Phase focusing in linear-beam devices

The phenomenon of phase focusing in linear-beam devices is investigated theoretically by modifying the nonlinear interaction equations for devices such as the traveling-wave amplifier (TWA) to accommodate spatially-varying parameters and then investigating their use under a variety of operating conditions. Phase focusing can be accomplished either by tapering the RF circuit phase velocity or by applying a dc voltage gradient along the beam or structure. Both approximate analytical solutions and general computer solutions are presented for each of the phase-focusing techniques. The analytic solutions yield profiles which are explicit functions of tube length and these are compared with more general computer solutions where space-charge effects are included. An experimental S-band high-power TWA was constructed with a variable-pitch helix designed on the basis of the hard-kernel-bunch theory. Experimental data indicate an efficiency improvement from 18 per cent to 35 per cent and an improvement in the gain-frequency characteristics.     

Nonlinear space charge wave theory of distortion in a Klystron

We present a new view of nonlinear distortion in a klystron based on an analytically solvable nonlinear Eulerian model. The nonlinear contributions to the analytic solutions for the beam modulations are "nonlinear space charge waves" in the sense that they are produced by the nonlinear mixing of the linear space charge waves. For a single-frequency input, amplitude and phase distortion are shown to be results of "self-intermodulation" at the drive frequency, or mixing of harmonic distortions with the fundamental. The self-intermodulation contributions add out of phase with the linear space charge waves to produce gain compression and phase distortion. By comparing the results to a conventional large-signal Lagrangian model we find this physical picture is accurate for drive levels up to 1.2 dB of gain compression. For a two-frequency input we predict the third-order intermodulation distortion generation and suppression with the nonlinear space charge wave theory.     

Kerr介质中失谐量对级联三能级原子纠缠演化的影响

利用量子理论,采用数值计算的方法对体系纠缠熵进行分析,得出光场相干参量、模间光子数、Kerr介质系数以及失谐量对级联三能级原子纠缠演化的影响。结果显示：纠缠强度随光场强度的增强而逐渐增强,模间光子数的增加可以使纠缠变得稳定。Kerr效应在光子数较多时影响显著。Kerr系数不变时,失谐量的增加会使纠缠强度增强,但这种影响主要体现在相互作用初期。