Misinterpretation yields supervelocities during transmission of wave packets through a barrier

This paper is concerned with the transmission time of an incident Gaussian wave packet through a symmetric rectangular barrier. Following Hartman (J. Appl. Phys. 33, 3427 (1962)), the transmission time is usually taken as the difference between the time at which the peak of the transmitted packet leaves the barrier of thickness and the time at which the peak of the incident Gaussian wave packet arrives at the barrier. This yields a corresponding transmission velocity which appears under certain conditions as a supervelocity, i.e. becomes larger than the corresponding propagation velocity in free space which is the group velocity for electrons or the velocity of light for photons, respectively. By analysing the propagation of a broadband wave packet (which leads in free space to an extremely concentrated wave packet at a certain time) we obtain the pulse response function of the barrier and show that the insertion of the barrier is physically unable to produce a supervelocity. Therefore, the peak of an incident Gaussian wave packet and the peak of the transmitted wave packet are in no causal relationship. The shape of the transmitted wave packet is produced from the incident wave by convolution with the pulse response of the barrier. This yields a distortion of the shape of the wave packet which includes also the observed negative time shift of the peak. We demonstrate further that the phenomenon of Hartman's supervelocities is not restricted to barriers with their exponentially decaying fields but occurs for instance also in transmission lines with an inserted LCR circuit. Received 7 January 1999 and Received in final form 22 April 1999     

The Sommerfeld precursor in photonic crystals

We calculate the Sommerfeld precursor that results after transmission of a generic electromagnetic plane wave pulse with transverse electric polarization, through a one-dimensional rectangular N-layer photonic crystal with two slabs per layer. The shape of this precursor equals the shape of the precursor that would result from transmission through a homogeneous medium. However, amplitude and period of the precursor are now influenced by the spatial average of the plasma frequency squared instead of the plasma frequency squared for the homogeneous case.     

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases.     

飞秒啁啾Gauss型脉冲在稠密Λ型三能级原子介质中的传播

利用由预估校正(PC)- 时域有限差分(FDTD)法求得的不含慢变包络近似(SVEA)和旋转波近似(RWA)的全波Maxwell-Bloch方程的数值解, 研究了飞秒啁啾Gauss型激光脉冲(以下简称啁啾脉冲)在稠密Λ型三能级原子介质中的传播.研究表明,啁啾系数(C)的正负及大小的变化对脉冲传播特性有显著的影响,而且这个影响与脉冲面积的大小密切相关.面积小于4π的啁啾脉冲,在介质中传播时不发生分裂,且啁啾脉冲逐渐演化为一个近似的无啁啾(C=0)脉冲,这一特点不随啁啾系数的改变而     

Retrieving the Amplitude and Phase Parameters of an Ultrashort Wave Packet by Autocorrelation Methods

Based on an analysis of the signal of an interferometric intensity autocorrelator, we demonstrate theoretically and experimentally a simple technique for retrieving the temporal distributions of the amplitude and phase of an ultrashort light pulse. Assuming that a phase-modulated wave packet has a Gaussian envelope, we derive an analytical expression for the autocorrelator signal in the cases of linear- and quadratic-chirp optical pulses. The experimental and theoretical results are in excellent agreement. In particular, we show that a linear chirp (quadratic phase modulation) can be measured with a good experimental accuracy of no worse than 10%. This yields the possibility of measuring the parameter k₂, which describes the dispersion characteristics of a medium in the second order of the dispersion theory, with the same accuracy. Measuring a quadratic chirp by the proposed method is possible only if such a chirp is sufficiently large.     

Superluminality and parelectricity: The ammonia maser revisited

It is well known that the inversion of populations in the ammonia maser leads to stimulated emission, and hence amplification, of microwaves. However, it is not well known that an inverted medium also leads to the superluminal propagation of off-resonance, finite-band-width wave packets, whose phase, group, energy, and signal velocities, as defined by Sommerfeld and Brillouin, all exceed the vacuum speed of lightc. Einstein causality is not violated, since the front velocity isc. The inversion of populations also implies a parelectric medium with negative electric susceptibility. (Parelectric media should not be confused withparaelectric media, which are ferroelectrics just above their Curie points.) The existence of a parelectric medium implies the possibility of the levitation of an electrical charge in the vacuum above this medium, as well as stable electrostatic configurations of charges placed inside an evacuated cavity surrounded by this medium. The apparent violation of Earn-shaw's theorem will be discussed. Numerical estimates for a proposed experiment to observe parelectricity will be given.Dedicated to Walther on the ocassion of his 60 birthday     

宽带啁啾脉冲激光非线性传输过程中的时空微扰研究

基于非线性薛定谔方程推导出大啁啾脉冲的传输方程,利用微扰理论,分析了啁啾脉冲激光的时空不稳定性. 理论上比较清楚的阐述了宽带脉冲激光在大啁啾情况下,其时空噪声的相互影响与相互作用情况及脉冲啁啾对噪声微扰调制的影响,发现在相同γI₀(非线性系数与峰值强度乘积)的情况下脉冲啁啾对噪声调制的增长没有直接影响. 最后我们在实验上利用非线性介质对啁啾脉冲的空间小尺度自聚焦过程进行了部分验证,同时也在数值上对宽带啁啾脉冲的时间噪声调制的增长进行了模拟分析,发现实验结果和模拟分析结论 关键词： 时空不稳定性 宽带脉冲激光 啁啾     

初始啁啾对双曲正割光脉冲线性传输特性的影响

采用分步傅里叶方法数值研究了初始线性啁啾和非线性啁啾双曲正割光脉冲在单模光纤反常色散区的线性传输特性，并与啁啾高斯脉冲的线性传输特性作了比较.给出了双曲正割光脉冲频谱宽度和时间带宽积随初始线性啁啾变化的表达式.结果表明，双曲正割脉冲在线性啁啾|C|>0.1时随传输距离的增加逐渐演化成近高斯型，在0≤|C|≤0.1时最后将演化为近双曲正割脉冲.|C|越小，脉冲时域波形越趋近双曲正割曲线.负啁啾对脉冲时域展宽的影响比正啁啾要大得多.当|C|≥0.5时，初始啁啾对双曲正割光脉冲展宽的影响比对高斯脉冲的影响更大.非线性啁啾双曲正割光脉冲在线性传输过程中会出现时域波形分裂现象，比具有相同啁啾的高斯脉冲时域波形分裂严重. 关键词： 频率啁啾 双曲正割光脉冲 线性传输 时域波形分裂     

Surface Emitting THz Wave Parametrical Oscillator Using MgO：LiNbO3

Room-temperature operation terahertz （THz） wave source is demonstrated using three MgO：LiNbO3 crystals which have a noncollinear arrangement. The experimental results show that the THz wave can be tunable from 0.8 THz to 3.0 THz, and the peak energy output is 103 pJ/pulse at 1.5 THz. The noncoilinear cavity configuration makes the THz beam have Gaussian-like spatial distribution, small divergence angle, perpendicularly eradiated from the crystal surface. The beam quality factor M2 is measured to be Mx^2 = 1.15, Mx^2 = 1.25 for characterizing the THz wave beam. Experiments also show that the THz beam can be focused by using a polyethylene lens, and the focal spot size is close to the diffraction limit.     

Pulse compression of a high-order harmonic

The fifth harmonic pulses of an intense femtosecond Ti:sapphire laser were experimentally shown to be negatively chirped by using an LiF plate as a positive dispersive medium. The chirp of the harmonic pulse originates from the intensity-dependent atomic dipole phase, which is estimated to be proportional to 25 U_p, where U_p is the ponderomotive energy. Consequently, we have succeeded in compressing the chirped pulses to 13 fs by compensating the intrinsic negative chirp. Chirp effects of the fundamental laser on the pulse width of the fifth harmonic were consistent with the negative chirp of the fifth harmonic.     

Giant Birefringence of Lithium Niobate Crystals in the Terahertz Region

Terahertz time-domaln spectroscopy （THz-TDS） is used to study the spectral response of lithium niobate crystals （LiNbO3） in the far infrared region. The optical constants are derived from the measured complex refractive index. A giant birefringence is observed in this material, and the average refractive-index difference between the ordinary wave and the extraordinary wave, no - ne, can reach up to about 1.6. Such a large birefrlngence is attributed to the different p honon modes orAl（z） and E （ x , y ）. This unusual property makes LiNbO3 a promising material to be used as a functional material in the terahertz region, e.g. employed as wave-plates and polarization separators.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.     

Optical fibre-grating pulse compression

Numerical simulation is used to consider non-linear pulse propagation in fibres and subsequent pulse compression in a dispersive delay line. It is shown that for small initial pulse powers the conventional non-linear Schrödinger equation (NSE) is quite accurate to describe the process of pulse propagation in fibres. In this case initially symmetrical pulses undergo squaring and spectral broadening in fibres, and frequency chirp is linearized over most of the pulse, while shapes of the pulse, spectrum and frequency chirp remain symmetrical at the output of the fibre. There is a certain optimum fibre lengthZ _opt which is determined by the initial pulse parameters and fibre characteristics for pulse compression in the dispersive delay line. When the fibre lengthZ>Z _opt the optical wave breaking effect distorts the linearity of the frequency chirp and thus deteriorates the quality of the compressed pulse. The region of NSE approximation accuracy is determined. It is demonstrated that at increase of the initial pulse power (initial pulse width makes no difference) the NSE approximation becomes inaccurate. So the pulse dynamics in the fibre were described by the modified NSE derived in the higher-order approximation of the method of slowly varying amplitudes from Maxwell's equations. In this case the shock wave appears at the trailing edge of the pulse, which accelerates the wave breaking process. This results in a decrease of the optimum fibre length and deterioration of compressed pulse parameters, compared with the NSE case. Spectral windowing of the extreme Stokes components of the pulse spectrum permits significant improvement in the quality of the compressed pulse. The main features of the compression of pulses with asymmetrical initial shape are also considered.     

Simulation of a chirped femtosecond relativistic laser pulse interaction with underdense plasma by using a hydrodynamic approach

A chirped laser pulse indicates that the laser frequency changes over the duration of the pulse: a positively (negatively) chirped pulse implies that the laser frequency increases (decreases) with time. In this paper, we use a simplified, fully relativistic hydrodynamic approach to simulate the influence of chirp on the propagation of a femtosecond relativistic laser pulse in underdense plasma. Based on this simplified cold‐fluid model, the influence of chirp on the main dynamics of the laser pulse, such as self‐steepening, red‐shift in the leading edge, variation of the frequency chirp, and the generated wakefields can be studied self‐consistently. The simulation results show that a pulse with a positive chirp results in a larger increment in the intensity parameter a₀ when propagating a certain distance into an underdense plasma compared with an un‐chirped and a negatively chirped pulse, which is largely because of a much greater forward shift of the peak amplitude and more severe pulse self‐steepening effect due to the frequency red‐shift at the leading edge when exciting a plasma wave. The ponderomotive force, which relates to the first‐order differential of the laser pulse intensity envelope, is expected to be stronger for a positively chirped pulse because of its steeper leading edge and larger intensity parameter a₀. As a result, the wakefield driven by the positively chirped laser pulse is more intense than that driven by an un‐chirped and a negatively chirped laser pulse, which is confirmed by our self‐consistent hydrodynamic simulation.     

Unique properties of microwave in interlayer exchange-coupled trilayer ferromagnetic films associated with negative imaginary part of permeability

Based upon Landau-Lifshitz equation and Maxwell's equations, we theoretically investigated properties of normally incident microwave propagation in interlayer exchange-coupled trilayer ferromagnetic film. It is found that, near resonance frequency of optic mode, imaginary part of permeability of one ferromagnetic layer is smaller than zero unusually, i.e., the ferromagnetic layer may be taken as an active medium. Thus a number of unique electromagnetic properties are presented, such as, the ferromagnetic layer becomes a left-handed material near low side of the resonance frequency of optic mode, and both phase velocity and time-averaged Poynting flow of the usually defined forward wave are negative simultaneously near high side of the resonance frequency. This work provides a feasible active medium to demonstrate the unique microwave properties.     

On Quantum-Classical Transition of a Single Particle

We discuss the issue of quantum-classical transition in a system of a single particle with and without external potential. This is done by elaborating the notion of self-trapped wave function recently developed by the author. For a free particle, we show that there is a subset of self-trapped wave functions which is particle-like. Namely, the spatially localized wave packet is moving uniformly with undistorted shape as if the whole wave packet is indeed a classical free particle. The length of the spatial support of the wave packet is given by the Compton wavelength so that the wave packet is more localized for particle with larger mass. Whereas for a particle of mass m in a macroscopic external potential, we show that the time needed by the corresponding self-trapped wave function to depart from a classical trajectory is of the order ∼m ² c/ℏ. We argue that it is the Compton wavelength that matters and not the de Broglie wavelength as in conventional semiclassical approach.     

Interaction of atomic wave packets with four-wave mixing: detection of rubidium and potassium wave packets by coherent ultraviolet emission

The observation of an atomic wave packet by use of a coherent, nonlinear-optical process is reported. Wave packets formed in K or Rb vapor by two-photon excitation of ns and (n-2)dstates (n=8 for K; n=11 , 12 for Rb) with red (~620-nm) , 80-100-fs pulses were detected by four-wave mixing in pump-probe experiments. The temporal behavior of the wave packet is observed by monitoring the coherent UV radiation generated near the alkali mp(2)P? (2)S(1/2) (7相似文献   

Negative refractive behavior of a two-dimensional negative-index photonic crystals using a wave vector diagram method

We have theoretically studied the negative refractive behavior and the focusing effect in a two-dimensional square-lattice photonic crystal made of air rods in a dielectric background. Detailed explanations are given for the effect of the negative refraction, and the imaging of the plano-concave lens is shown by the use of a wave vector diagram formalism. The typical negative refractive behavior is demonstrated by considering the Bloch mode with the wave vector inside the first Brillouin zone, because only those wave vectors inside the first Brillouin zone of multiple Brillouin zones have a definite meaning. The single propagating beam is analyzed by the use of the wave vector diagram formalism following the folding of the wave vectors. Good-quality focusing of a plane wave can be realized by using a photonic crystal plano-concave lens, while a plane wave is formed by a point source placed at the focal point. Our results are in good agreement with the experimental ones shown for a negative-index plano-concave lens by Vodo et al. [Appl. Phys. Lett. 86 (2005) 201108]. Finally, we also have shown the focusing behavior of a plane wave and a Gaussian pulse by a plano-concave lens structure with high-index modulation instead of air in the concave region.     

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

We show that the two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values for both the electric permittivity ? and the magnetic permeability μ in some frequency range. This follows from a recently proven general theorem. The negative values of ? and μ are found by a numerical simulation. Using values |?| and |μ| for the medium surrounding the PC slab we simulate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of ? and μ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.     

Effect of phase modulation of a laser pulse on the generation of a coherent totally symmetric phonon in a tellurium single crystal

The effect of phase modulation (resulting in a chirp of an ultrashort laser pulse) on the generation of a coherent A ₁ phonon in Te was studied. The amplitude of coherent oscillations was found to depend on the sign and value of the pulse chirp: the oscillation amplitude decreases as the chirp increases. For a positive chirp, this effect is twofold stronger than for a negative one. The frequency-resolved response of a bandwidth-limited pulse was studied, which revealed the difference of oscillations and the relaxation response for the Stokes and anti-Stokes frequencies. The detected phenomena can be used for coherent control of lattice dynamics.