Theory of mode hopping and phase conjugation characteristics indegenerate four-wave mixing

A large-signal theory of noncollinear degenerate four-wave mixing (DFWM) is presented, taking into account the pump depletion and the full nonlinear polarization density appropriate for the noncollinear geometry. Phases of all of the interacting fields, as well as the amplitudes, are obtained as functions of the spatial coordinate. Owing to the completeness of the set of analytic solutions, considerable physical insights into the physics of DFWM are obtained. The DFWM exhibits a variety of rich behaviors, including hysteresis and bistability, multistability, and multiple isolated branches. The authors show that all of these behaviors can be explained in a unified way, that is, in terms of mode hopping characteristics     

Transient coherent degenerate four-wave mixing

A set of coupled equations is derived and used to analyze transient coherent degenerate four-wave mixing (DFWM) in a two-level system. The numerical results show that in the case of near-resonance, intense pumping, and short pulses, the properties of degenerate four-wave mixing have interesting coherent interaction characteristics, such as quasi-periodicity in the pump pulse area, probe pulse areas, and energy reflectivity, oscillatory behavior of the DFWM pulse, and generation of a DFWM signal in the case of delayed incidence, where the three incident pulses do not overlap in the medium     

Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects

The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.     

Thermally induced degenerate four-wave mixing

Time-dependent aspects of thermally stimulated degenerate four-wave mixing (DFWM) in absorbing liquid solutions have been theoretically investigated through a coupled electromagnetic-hydrodynamic theory originally formulated to study stimulated scattering processes. The various time scales involved in the interaction (including those characteristic of acoustic modes and thermalization effects) are identified and relevant laser and media parametrical relations are sorted out. Suitable approximation regimes are then outlined, corresponding to specific experimental situations of interest and allowing for relatively simple and tractable analytic relations to be derived. In particular, the effects of finite rise time of thermalization were studied and found to lead to a possibly strong angular dependence in the conjugate reflectivity. Acoustic modes and their influence on the process efficiency were also investigated. The calculations culminate in a set of guidelines for optimizing conjugation efficiencies, through judicious choice of dye-solvent combinations, "read" pump time delays, experimental arrangements, and laser pulse parameters.     

Time-delay characteristics of four-wave mixing among subpicosecondoptical pulses in a semiconductor optical amplifier

We have studied four-wave mixing (FWM) characteristics among subpicosecond optical pulses in a semiconductor optical amplifier for different time-delays between pump and probe beams, for the first time. Our experimental results have shown that an optimum time-delay shifted from the perfect pump-probe overlap condition with an increase in input probe beam energy. An optimum intensity of the pump beam has also been obtained to generate the maximum FWM signal     

亚甲基蓝掺杂聚乙烯醇四波混频的实验研究

为了研究在低功率连续He-Ne激光条件下亚甲基蓝掺杂聚乙烯醇薄膜简并四波混频的基本特性,采用简并四波混频技术研究了亚甲基蓝掺杂聚乙烯醇的相位共轭光与入射角度、前抽运光和后抽运光的变化关系,以及透射光栅和反射光栅对相位共轭光的影响.在实验中得到了最大的相位共轭反射率为0.27%.所得的结果对研究染料固化在固体基质中的非线性研究是有帮助的.     

Effects of unequal pump intensity in resonantly enhanced degenerate four-wave mixing

Experiments performed in SF6using a CO2laser show the effect of unequal pump intensity in resonantly enhanced degenerate four-wave mixing (DFWM). A two-level saturable absorber model was extended to include the effects of unequal pump intensity and the results show significant departure from typical nonsaturating behavior. The experimental results and theory show qualitative agreement.     

基于相敏放大的MPSK信号再生性能研究

详细描述了泵浦消耗情形下高非线性光纤中(HNLF) 简并四波混频(DFWM)的解析求解过程,结合第1类、 第3类椭圆积分和雅阁比椭圆函数给出了个导波光的输出功率和相位的表达式。为了方便计 算和分析,给出了特殊函数在Matlab中的计算命令。利用解析式分析了基于DFWM实现多电平 再生的必要条件, 研究了相敏放大过程中泵浦光初始相位和初始功率对MPSK 信号相位转移曲线的影响。研究 表明,调节泵 浦光初始相位可使相敏放大器(PSA)的相位转移曲线与输入信号的多电平相位匹配,优化光 纤长度或泵浦光初始功率可 获得最大的多电平相位再生抖动抑制性能,且优化的初始泵浦光功率与光纤长度近似呈反比 。采用 OptiSystem软件仿真了基于PSA的8PSK信号再生器的性能,仿真结果与理论 分析一致;当归 一化输入相位抖动为0.1时,该相位再生器的抖动抑制比为4.62,能够使系统的符号错误率降低2个数量级。     

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.     

Transient effects in degenerate four-wave mixing in saturable absorbers

The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.     

Determination of the threshold for instability in four-wave mixingmediated by Brillouin scattering

The threshold for instability in Brillouin-enhanced four-wave mixing has been experimentally determined as a function of both the phase mismatch and the ratio of the pump beam intensities and is shown to agree with theoretical modeling. The effective input noise intensity for four-wave mixing in the unstable regime is compared to the noise in a stimulated Brillouin scattering amplifier and is found to be higher by a factor of three in the forward direction. Competition between two input signals has been investigated, and it is shown that the signal which arrives first dominates the interaction in the unstable regime     

常温常压下碘蒸气的简并四波混频光谱技术

报道了以碘蒸气为介质进行的前向简并四波混频(DFWM)布局光谱技术的试验研究。在试验中采用了具有自稳分光系统的前向简并四波混频布局。试验发现在常温常压条件下,由于碰撞猝灭会大大降低激光诱导荧光(LIF)光谱的检测灵敏度,几乎观察不到碘蒸气荧光光谱,但却可获得较强的碘蒸气的简并四波混频信号。这是目前已知测定了常温常压下I2在554～556 nm中的前向简并四波混频光谱。常温常压下气相介质的简并四波混频光谱技术,对痕迹量原子、分子和自由基的探测以及对燃烧诊断等方面的研究与应用具有重要意义。     

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     

Analysis of optical DEMUX characteristics based on four-wave mixingin semiconductor optical amplifiers

We have analyzed the basic characteristics of all-optical demultiplexing (DEMUX) based on four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) by solving a modified nonlinear Schrodinger equation by the finite-difference beam propagation method. Amplified spontaneous emission noise was not included in our model. The optimum pump pulsewidth for obtaining the high ON-OFF ratio is 1~3 ps for 1 ps, 250 Gb/s probe pulses. The shorter limit of the pulsewidth is due to detuning between the pump and probe frequencies, which is determined by the gain bandwidth of the SOA. In order to achieve faster DEMUX operation, an SOA with broader gain bandwidth is required. We also simulated pattern effects in the FWM signal. Power fluctuation in the FWM signal can be reduced by using a strong energy pump pulse and/or weak energy probe pulse. The energy fluctuation of the FWM signal decreases to less than 1% for a 30-bit, 250-Gb/s input probe pulse train with a pulse energy of 0.01 pJ. This small fluctuation should not disturb DEMUX operation. We have also examined DEMUX from time multiplexed signals by repetitive pump pulses. Strong energy pump pulses decrease the FWM signal intensity. However, there is no pattern effect due to gain saturation because the pump pulses are injected continuously     

掺半导体玻璃的简并四波混频

用简并四波混频研究了CdS_xSe_(1-x)半导体玻璃的三阶非线性光学特性。实验结果表明这种材料具有大的三阶非线性系数(x~(3)～10~(-8)esu)和快速非线性响应时间(<1ns)。     

Theory of degenerate four-wave mixing an anisotropic, opticallyactive photorefractive crystals

A theory is presented of degenerate four-wave mixing (DFWM) of arbitrary polarized waves in an anisotropic optically active photorefractive crystal. Using the method of coupled waves, a system of differential equations is deduced describing the coupling process. This system is specified to DFWM in crystals of the Bi₁₂GeO₂₀ -type and numerically solved based on the shooting method. Some peculiarities of phase conjugation in these crystal are discussed     

Detuning characteristics and conversion efficiency of nearlydegenerate four-wave mixing in a 1.5-μm traveling-wave semiconductorlaser amplifier

The optical nonlinearity in a semiconductor laser gain medium is investigated through copropagating nearly degenerate four-wave mixing (NDFWM) in a 1.5-μm InGaAsP traveling-wave laser amplifier (TWA). The FWM signal output powers vary symmetrically with the sign of probe detuning with respect to the pump frequency, while the pump and probe output powers vary asymmetrically. The NDFWM conversion efficiency from the probe input to the FWM signal output is a maximum of 8.3 dB around zero detuning and has positive gain in the range of ±6 GHz. This demonstrates highly efficient nonlinear interaction due to both large optical gain and large third-order susceptibility. The NDFWM efficiency is also investigated in connection with the TWA gain saturation characteristics and is found to be a maximum for operation around the saturation intensity of the TWA     

Fifth-harmonic generation in isotropic media

This paper presents a theoretical study of fifth-harmonic generation (FHG) in an isotropic media. Two schemes are discussed-cascade generation in which the fifth harmonic results from successive nonlinear interactions in two separate elements, and direct generation where the fifth harmonic is produced in an isotropic media with third-and fifth-order nonlinear susceptibilities. In the plane-wave approximation almost full conversion of the pumping energy into the fifth harmonic is found to be possible. FHG with a focused Gaussian beam is also investigated. To determine the optimum conditions for FHG in the cascade scheme, the theory of four-wave mixing of light beams with arbitrary confocal parameters and waist locations is developed. In media with third- and fifth-order nonlinearity, the fifth harmonic results from step and direct processes. The interference between these two processes is discussed. Numerical calculations are presented for metal vapor-gas mixtures and Nd:glass laser pumping radiation.     

Small signal analysis of THz optical-frequency conversion in aninjection-locked semiconductor laser

A theory of terahertz optical-frequency conversion using highly nondegenerate four-wave mixing (FWM) in an injection-locked semiconductor laser is presented, using small-signal analysis. The optical frequency conversion can be realized through the use of cavity-enhanced highly nondegenerate FWM in an injection-locked semiconductor laser in a range of 1-THz detuning frequency between the pump and the probe waves, when the probe frequency is tuned close to one of the resonance modes. The frequency conversion is mainly attributed to the nonlinear gain effect. The maximum bandwidth of the converted signal is increased by shortening the laser cavity length. The frequency conversion efficiency is asymmetrical with respect to both the zero detuning frequency and the resonance mode where the converted signal appears. The theoretical results agree with experiments     

Optical spectral inversion without frequency shift by four-wavemixing using two pumps with orthogonal polarization

We propose a method to obtain spectral inversion of a signal without shifting its frequency. We use four-wave mixing (FWM) in a semiconductor optical amplifier (SOA) with two pumps of orthogonal polarization. A conjugate field is generated with a polarization orthogonal to that of the incoming signal and is selected at the amplifier output by a polarizer. Using a commercially available pig-tailed SOA of 1.5-mm length, we obtain after the polarizer 21.5 dB of intensity ratio between conjugate and amplified incoming signal