Spectral anomalies of diffracted pulsed Bessel beams in dispersive media

Starting from the Huygens–Fresnel diffraction integral, the analytical expression for the power spectrum of diffracted pulsed Bessel beams in a dispersive media is derived and used to study the spectral anomalies of pulsed Bessel beams in the far field. Numerical results are given to illustrate the dependence of the anomalous spectral behavior on the pulse parameters, aperture parameter and dispersive properties of the medium. It is shown that, near phase singularities, anomalous spectral behavior may take place. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.     

Spectral anomalies of diffracted pulsed Hermite-cosh-Gaussian beams in dispersive media

Starting from the Huygens–Fresnel diffraction integral, the analytical expressions for the power spectra of diffracted pulsed Hermite-cosh-Gaussian (HChG) in dispersive media are derived and used to study the spectral anomalies of pulsed HChG. Numerical results are given to illustrate the dependence of spectral anomalies behavior on the decentered parameter, truncation parameter and dispersive property of the medium. The potential applications of spectral anomalies of ultrashort pulsed beams in the information encoding and information transmission are considered.     

Spectral anomalies of diffracted pulsed Hermite--Gaussian beams in dispersive media

This paper derives and uses the recurrence expressions for the power spectra of diffracted pulsed Hermite-Gaussian （HG） beams in dispersive media to study the spectral anomalies of pulsed HG beams in the far field. Numerical results are given to illustrate the dependence of spectral switches on the pulse parameters, truncation parameter and dispersive property of the medium. The potential application of spectral anomalies of ultrashort pulsed beams in information encoding and transmission is discussed.     

Spectral behavior of pulsed Bessel beams focused by a dispersive lens

Starting from the Huygens–Fresnel diffraction integral, the analytical expression for the power spectrum of pulsed Bessel beams focused by a dispersive aperture lens is derived and used to study the spectral anomalies of pulsed Bessel beams in the focused field. Numerical calculation results are given to illustrate the dependence of spectral anomalous behavior on the pulse parameters, truncation parameter and material dispersion of the lens. It is shown that near the phase singularities the spectral anomalies may take place. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.     

Spectral anomalies of diffracted pulsed cosh-Gaussian beams in dispersive media

Starting from the Rayleigh–Sommerfeld diffraction integral, the closed-form expressions for the near- and far-field power spectra of diffracted pulsed cosh-Gaussian (ChG) beams propagating in dispersive media are derived, and the anomalous behavior of the far-field spectrum of diffracted pulsed ChG beams in dispersive media is studied. It is shown that near the phase singularities, the spectral switch may take place. The truncation parameter, decentered parameter and pulse duration of pulsed ChG beams and the dispersive property of the medium affect the behavior of the spectral switch of pulsed ChG beams.     

Spectral anomalies of pulsed Hermite-cosh-Gaussian beams focused by an aperture lens

The spectral behaviors of pulsed Hermite-cosh-Gaussian (HChG) beams focused by an aperture lens are studied. The propagation equation for the power spectra of pulsed HChG beams focused by an aperture lens is derived and used to study the spectral anomalies of pulsed HChG beams in the focused field. Numerical results are given to illustrate the dependence of spectral anomalies behavior on the pulse parameter and truncation parameter. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.     

Propagation of ultrashort pulsed beams in dispersive media

Starting from the Rayleigh diffraction integral, the propagation equation of ultrashort pulsed beams in dispersive media is derived without making the paraxial approximation and slowly varying envelope approximation (SVEA). The spatiotemporal properties of ultrashort pulsed beams in dispersive media, such as spectrum redshifting, narrowing and pulse distortion are illustrated with pulsed Gaussian beams. It is stressed that the “antibeam“ behaviour of ultrashort pulsed beams can be avoided, if a suitable truncation function is chosen.     

贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性

 对等衍射长度贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性作了研究,结果表明,通过选择适当的空间参数,贝塞尔-高斯脉冲光束沿轴上传输时,脉冲宽度不变。传输距离小于无衍射长度时,随衍射角增加,功率谱形状未变,脉冲波形保持不变;传输距离大于无衍射长度时,随衍射角增加,光谱由蓝移变为红移,脉冲展宽。     

部分空间相干部分光谱相干厄米-高斯脉冲电磁光束的偏振特性

基于非稳态场的相干理论,对部分空间相干部分光谱相干二维厄米-高斯脉冲电磁光束在自由空间传输时的偏振特性做了详细的数值研究.结果表明,脉冲电磁光束的偏振度分布由光束阶数、光束的空间相关长度、时间相干长度和场点位置等因素共同决定.研究表明,当空间相关长度趋于零或无穷大时,轴上点偏振度趋于一固定值,与光束阶数和场点位置无关....     

Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic Cosh-Gaussian pulsed beams

Based on the generalized Rayleigh–Sommerfeld diffraction integral, the analytical expression for 3×3 cross-spectral density matrix of nonparaxial spatially and spectrally partially coherent electromagnetic Cosh-Gaussian (ChG) pulsed beams propagating in free space is derived, and used to formulate the spectral density and spectral degree of polarization of electromagnetic pulsed beams at the z-plane. It is found that the parameters f and f_αα are the key parameters in determining the nonparaxiality of spatially and spectrally partially coherent electromagnetic ChG pulsed beams. And the decentered parameter, pulse duration and temporal coherence length can change the nonparaxial behavior of the electromagnetic ChG pulsed beams. The effect of decentered parameter, pulse duration and temporal coherence length on the spectral density and spectral degree of polarization of electromagnetic ChG pulsed beams is illustrated through numerical calculations. Propagation of nonparaxial spatially and spectrally partially coherent electromagnetic Gaussian Schell-model pulsed beams can be treated as a special case when the decentered parameter of electromagnetic ChG pulsed beams approaches to zero.     

超短脉冲复宗量厄米高斯光束

从超短高斯脉冲光束出发,根据复宗量厄米函数的性质,用理论解析推导的方法,给出了一组新的超短脉冲光束的解析解,称为超短复宗量厄米高斯脉冲光束。此脉冲光束解的每个频率分量都是复宗量厄米高斯光束,时间脉冲的形状是任意的,具有相同的衍射距离参量,并且可以描述短于一个光学周期的超短脉冲。对这种超短脉冲光束及其在自由空间中的传输过程进行了较为细致的研究,分析了超短复宗量厄米高斯脉冲光束的轴上光强、光强的横向分布、等衍射性质、脉冲极性反转、脉冲延迟等基本性质。讨论了引入缓变包络近似后出现的时空奇异性。     

Temporal and spectral properties of ultrashort pulsed Laguerre-Gaussian beams in dispersive media

The temporal and spectral properties of ultrashort pulsed Laguerre-Gaussian (LG) beams propagating in dispersive media are studied both theoretically and numerically. It is shown that the on-axis pulse broadens with increasing propagation distance and the on-axis spectrum is blueshifted. For the off-axis spectrum the blueshifts decrease and then the spectrum becomes redshifted as the radial distance increases. The propagation of ultrashort pulsed LG beams in free space and of ultrashort pulsed Gaussian beams can be regarded as special cases of our results, and some interesting properties are discussed.     

Propagation properties of ultrashort chirped pulsed Gaussian beams in the free space

Based on the Rayleigh diffraction integral and complex analytical signal representation, the free-space analytical propagation equation and its Fourier spectrum for ultrashort chirped pulsed Gaussian beams with constant diffraction length are derived. The effect of chirp parameter on the spatiotemporal and spectral properties is illustrated with analytical formulas and numerical calculation results. It is shown that the axial spectra of ultrashort chirped pulsed Gaussian beams become broadened with increasing chirp parameter. For single optical cycle, the transversal intensity distribution is affected by increasing chirp parameter, but almost not affected for several optical cycles. Moreover, the positive or negative sign of the chirp parameter has no effect on the spectral distribution and intensity distribution.     

超短脉冲激光光束在一维反射型体全息光栅中的衍射

基于Kogelnik的耦合波理论,研究了在色散效应的影响下,超短脉冲激光光束在反射型体全息光栅中衍射的性质.研究给出了衍射光及透射光在频谱域及时间域的振幅及强度分布、光栅的光谱宽度及衍射效率随光栅参量及入射条件的变化.数值研究的结果表明,在光栅记录介质色散效应的影响下,衍射光束的光谱宽度减小,脉冲展宽,衍射效率降低.通过适当的选取光栅参量及入射条件,可以控制衍射和透射光束的频谱和时间强度分布,得到满意的衍射和透射光束的带宽和波形,从而可以将其应用于脉冲整形等技术中.     

Elimination of the spatial singularity of ultrashort pulsed beams in dispersive media

Under the condition that the propagation constant k in dispersive media should be larger than zero, a simple method is proposed to eliminate the spatial singularity of ultrashort pulsed beams propagating in dispersive media. Taking the pulsed Gaussian beam (PGB) as a typical example, the analytical propagation equation in the space–time domain is derived and the spatiotemporal propagation properties of PGBs in normal and anomalous dispersive media are discussed both analytically and numerically. The physical explanation of the results is presented.     

啁啾脉冲参数对合成光束的远场光强的影响

光束合成是提高激光功率及光束质量的一种有效方法,啁啾脉冲高斯光束的各参数都会影响合成的效果。利用夫琅禾费衍射积分公式导出了两束啁啾脉冲高斯光束合成的远场光强的解析式,得知远场光强与啁啾参数、脉宽及谱宽等参数有关。对远场光强进行了数值模拟,结果表明:对甚多束光束合成而言,单元激光间的啁啾参数增大、脉宽差值减小或者谱宽差值增大,均有利于轴上光强的增大及远场光强分布集中于传输轴附近。     

高阶贝塞尔脉冲光束通过色散光阑透镜的传输特性*

研究了高阶贝塞尔脉冲光束通过色散光阑透镜的光谱和时间空间特性.结果表明:脉冲光束在几何焦面上会出现光谱开关,透镜色散使产生光谱开关的临界位置向z轴移动|透镜一阶色散使几何焦面上峰值光强减小,并使脉冲波形产生显著时间移动和展宽,而二阶和高阶色散的影响较小.此外,光束阶数n和空间参量α也会影响横向光强分布.     

Diffraction-free and dispersion-free pulsed beam propagation in dispersive media

The diffraction of pulsed beams of light is formulated as an anomalously dispersive phenomenon. In a dispersive material, the effects of material group-velocity dispersion and diffraction on pulsed beam propagation can mutually cancel if the transverse profile of the pulse is suitably chosen.     

Changes in the spectral degree of polarization of nonparaxial stochastic electromagnetic pulsed beams

By using the generalized vectorial Rayleigh-Sommerfeld diffraction integral, the analytical expression for the spectral degree of polarization (SDP) of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams (SSSPCEPB) is derived, and used to study the changes in the SDP of SSSPCEPB in the nonparaxial regime. Similar to that of continuous beams, the f parameter and f_αα parameter of pulsed beams also play an important role in determining the nonparaxiality of SSSPCEPB. However, the pulse duration and temporal coherence length of the pulse can change the nonparaxiality of SSSPCEPB. The dependence of SDP on the f parameter, pulse duration and temporal coherence length is emphasized and illustrated numerically.     

非傍轴双曲余弦-高斯脉冲电磁光束远场特性

利用矢量瑞利-索末菲衍射积分公式,推导出了非傍轴部分空间相干部分光谱相干双曲余弦-高斯(ChG)脉冲电磁光束在自由空间传输时交叉谱密度矩阵的远场解析公式,并用来表示脉冲电磁光束的光谱密度(光强)和偏振度。结果表明,对非傍轴远场部分空间相干部分光谱相干ChG脉冲电磁光束,其非傍轴性主要由参数f, f决定,而离心参数、脉冲宽度和时间相干长度影响其非傍轴行为。非傍轴部分空间相干部分光谱相干高斯-谢尔模型脉冲电磁光束的远场传输可作为特例处理。