Influence of the chirp on the intensity distributions of an apertured pulse

Starting from the Huygens–Fresnel diffraction integral and the Fourier transform, the propagation expression of a chirped pulse passing through a hard-edged aperture is derived. Using the obtained expression, the intensity distributions of the pulse with different chirp in the near and far fields are analyzed in detail. Due to the modulation of the aperture, many intensity peaks emerge in the intensity distributions of the chirped pulse in the near field. However, the amplitudes of the intensity peaks decrease on increasing the chirp, which results in the smoothing effect in the intensity distributions. The beam smoothing brought by increasing the chirp is explained physically. Also, it is found that the radius of the intensity distribution of the chirped pulse decreases when the chirp increases in the far field.     

Smoothing effect in the broadband laser through a dispersive wedge

The propagation expression of a broadband laser passing through a dispersive wedge is derived on the basis of the Huygens-Fresnel diffraction integral. Smoothing effects caused by the phase perturbation of the dispersive wedge on the intensity profiles are investigated in detail. The phase perturbation of the dispersive wedge induces a relative transverse position shift between the diffraction patterns of different frequency components. The relative transverse position shift is of great benefit to the fill of the intensity peaks of some patterns in the valleys of others when these patterns are overlapped and thus the smoothing effect is achieved.     

无外加氟施主产生KrF准分子发射谱实验研究

We report a new technique to suppress the low-spatial-frequency rings and ripples (LSFRs) of laser near-field intensity distribution in the spatial filter (SF) used in ICF laser drivers. This technique employs a spatial filter with Gaussian transmission, instead of the hard-edged pinhole, at the confocal plane of a Newtonian telescope. The resulting beam has a super-Gaussian transverse intensity profile without the LSFRs that certainly appear when a hard-pinhole was used as a filter in the conventional technique.     

Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

Transformation of a hollow Gaussian beam into a ring-shaped beam using a phase aperture

Propagation of a hollow Gaussian beam diffracted by a circular phase aperture is studied without making the paraxial approximation. The analytical expression of the intensity of the apertured hollow Gaussian beam is presented in the far field. The influences of the truncation parameter and the order of hollow Gaussian beam on the intensity distributions are discussed. It is shown that a circular ?-phase aperture can be used to transform a hollow Gaussian beam into a ring-shaped beam in the far field with the appropriate parameters.     

Approximate analytical representation of Wigner distribution function for Gaussian beams passing through ABCD optical systems with hard aperture

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.     

Measuring temporal fluctuation on femtosecond scale in a random medium

We report an observation of femtosecond optical fluctuations of transmitted light when a coherent femtosecond pulse propagates through a random medium. They are a result of random interference among scattered waves coming from different trajectories in the time domain. Temporal fluctuations are measured by using cross-correlated frequency optical gating. It is shown that a femtosecond pulse will be broadened and distorted in pulse shape while it is propagating in random medium. The real and imaginary components of transmitted electric field are also distorted severely. The average of the fluctuated transmission pulses yields a smooth profile, probability functions show good agreement with Gaussian distribution.     

Axial distribution of Gaussian beam limited by a hard-edged aperture

In this letter, the axial distribution of Gaussian beam limited by a hard-edged aperture is studied. We theoretically analyze the axial diffraction of Gaussian beam limited by a hard-edged aperture, and give the simpler formulas of the axial diffraction intensities of Gaussian beam in Fresnel diffraction field and Fraunhofer diffraction field. The corresponding numerical calculation of axial diffraction intensity distribution of Gaussian beam with different wave waist is provided and the evolution of the diffraction distribution with the wave waist of Gaussian beam is explained. As the especial cases of the truncated Gaussian beam,the Gaussian beam in free space and the parallel light limited by the aperture are discussed too, and the system parameters of the truncated Gaussian beam which can cause it to equal to these cases are given.The theoretical results conform to the numerical analysis.     

Spectral anomalies of diffracted chirped Gaussian pulses and their potential applications

Starting from the Rayleigh-Sommerfeld diffraction integral and without invoking the paraxial approximation, analytical expressions for the field distribution, far-field power spectrum and temporal far-field distribution of chirped Gaussian pulses diffracted at a circular aperture are derived, which enables us to study the spectral anomalous behavior of diffracted chirped Gaussian pulses in the far field. The potential applications of spectral anomalies of ultrashort pulses are discussed. It is found that at the critical angle the spectral switch appears. The frequency difference between the two equal heights of spectral switches increases and the corresponding critical diffraction angle slightly increases as the chirp parameter increases and pulse duration decreases. In a certain region of the truncation parameter, the critical angle decreases with increasing truncation parameter. By suitably varying the pulse duration, chirp parameter and truncation parameter, information encoding and transmission are achievable in the use of chirped Gaussian pulses.     

Propagation analysis of flattened circular Gaussian beams with a circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with aperture in turbulent atmosphere have been studied by using the extended Huygens-Fresnel principle. From the study and numerical calculation, the effects of aperture on the propagation of flattened Gaussian beams in turbulent atmosphere have been illuminated. It shows that when the value of the truncation parameter δ is bigger, for example δ?2, the effects of aperture on the propagation properties are too small to be neglected. But when the truncation parameter δ is smaller, for example δ<2, the effects of aperture are complex. The peak value of the average intensity descends more rapidly and the beam spot spreads quicker with aperture than that without aperture when the propagation distance increases. Meanwhile, with the propagation distance increasing, the average intensity profiles of flattened Gaussian beams gradually convert into Gaussian average intensity profiles. In addition, some limiting cases are also discussed. It agrees with the existing results.     

Anomalous spectral behaviour of diffracted chirped Gaussian pulses in the near field

By using the Fourier transform method, analytical expressions for the axial power spectrum and near-field intensity in the spacetime domain of chirped Gaussian pulses diffracted at an aperture are derived, which permit us to study changes in spectral and temporal profiles of the chirped Gaussian pulses both analytically and numerically. Detailed numerical results and physical analysis show that spectral anomalies take place in the neighbourhood of certain critical distances, and the shifting of maximum and splitting of temporal intensity profiles appear. In particular, for ultrashort chirped pulses, there exists also spectral switch. Besides the truncation parameter, the chirp parameter and pulse duration affect the behaviour of spectral switches.     

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     

Vectorial structural properties of truncated beam generated by Gaussian mirror resonator in the near field

Internal vectorial structure of the beam generated by the Gaussian mirror resonator (GMR) diffracted through a hard-edged aperture are evaluated in the near-field. Based on the vectorial angular spectrum representation of electromagnetic fields and the paraxial approximation, TE and TM terms of intensity distributions of the beam in the near field are derived in analytical forms, respectively. Numerical results reveal that the behaviors of TE and TM terms not only depend on the parameters of mirror resonators but also relate to the truncated parameter of the aperture. It is also shown that the distributions of TE and TM terms would not keep detached from each other because of the unorthogonality of their vectorial structures in the near field.     

Bessel光束经椭圆环形孔径后的衍射光场

基于菲涅耳衍射积分理论及硬边孔径的复高斯函数展开法导出了Bessel光束经椭圆环形孔径后的光场表达式, 数值模拟了其光场的强度分布. 研究了Bessel光束经椭圆环形孔径后的光场变化及其传播过程; 在实验上利用轴棱锥输出的近似无衍射Bessel光, 通过椭圆环形孔径, 使用电荷耦合器件拍摄得到不同传播距离处的光强分布. 理论结果和实验结果均表明无衍射光束经椭圆环形孔径后会产生空心光束.     

Generation of electromagnetic waves in the terahertz frequency range by optical rectification of a Gaussian laser pulse in a plasma in presence of an externally applied static electric field

We propose a theoretical model for the generation of electromagnetic waves in the terahertz (THz) frequency range by the optical rectification of a Gaussian laser pulse in a plasma with an applied static electric field transverse to the direction of propagation. A Gaussian laser pulse can exert a transverse component of the quasi‐static ponderomotive force on the electrons at a frequency in the THz range by a suitable choice of the laser pulse width. This nonlinear force is responsible for the density oscillation. The coupling of this oscillation with the drift velocity acquired by electrons due to the applied static electric field leads to the generation of a nonlinear current density. A spatial Gaussian intensity profile of the laser beam enhances the generated THz yield by many folds as compared to a uniform spatial intensity profile.     

高斯脉冲在半导体光放大器中传输的解析表征

采用解析方法,在考虑材料损耗和色散的情况下,详细研究了无啁啾高斯脉冲和啁啾高斯脉冲在半导体光放大器中传输的物理过程,分析了强度增益、脉冲宽度和频率啁啾与线宽增强因子、色散系数、小信号增益特征参数及初始啁啾之间的关系。结果表明:当输入变换极限的高斯脉冲时,色散会引起增益压缩,脉冲展宽和频率啁啾;同样情况下,线宽增强因子越大,脉宽加宽越明显,输出脉冲啁啾越大,且随着线宽增强因子的增大,输出脉冲啁啾极大值向特征参数值较小的一边移动。当输入啁啾高斯脉冲时,初始脉冲啁啾越大,增益压缩越明显,啁啾系数为正时,脉冲单纯展宽,输出啁啾随特征参数的增大而逐渐减小,啁啾系数为负时,初始啁啾与群速度色散导致的啁啾相互竞争,致使脉冲先被压缩后被展宽;脉冲最窄处对应的特征参数随线宽增强因子的增大而先增大后减小,输出啁啾随特征参数的增大而经历振荡后趋于平稳。     

Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media

We study, both experimentally and theoretically, the process of second-harmonic generation by two noncollinear beams in ferroelectric crystals with a disordered distribution of ferroelectric domains. We show that this parametric process results in generation of second-harmonic wave in the direction transverse to the propagation of the fundamental beam. We demonstrate how this effect can be used for the femtosecond pulse characterization enabling the estimation of both width and chirp of the pulse.     

Near-field properties of diffraction through a circular subwavelength-size aperture

Analytical nonparaxial vectorial electric field expressions for both Gaussian beams and plane waves diffracted through a circular aperture are derived by using the vector plane angular spectrum method for the first time,which is suitable for the subwavelength aperture and the near-field region.The transverse properties of intensity distributions and their evolutions with the propagating distance,and the power transmission functions for diffracted fields containing the whole field,the evanescent field and the propagating field are investigated in detail,which is helpful for understanding the relationship between evanescent and propagating components in the near-field region and can be applied to apertured near-field scanning optical microscopy.     

Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere

It is shown that a general shaped laser beam will eventually approach a Gaussian average intensity profile after propagation in turbulent atmosphere. In our formulation, source field at the exit plane of the laser is taken as the product of arbitrary functions of source transverse coordinates with Gaussian exponential modulations. Following the expansion of the arbitrary functions in terms of Hermite polynomials, the average receiver intensity expression is derived using the extended Huygens-Fresnel principle and the conditions for the intensity profile to assume a Gaussian shape are stated. The results are illustrated by simulating various source field distributions.     

Propagation of Airy beams through a hard-edged aperture

Based on the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, we obtain the analytical formula for the propagation of the Airy beams in free space and through the fractional Fourier transformation (FrFT) system. According to the derived formulas, the propagation properties of the Airy beams in free space and through the FrFT plane with a hard-edged aperture are illustrated numerically.