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.     

Spectral anomalies of pulsed Hermite-Gaussian beams in Young’s interference experiment in dispersive media

Starting from the Huygens-Fresnel diffraction integral, the recurrence expression for the power spectra of pulsed Hermite-Gaussian beams in Young’s interference experiment in dispersive media are derived and used to study the spectral anomalies of pulsed Hermite-Gaussian beams in the far field. The results of numerical calculation are given to illustrate the dependence of spectral anomalous behavior on the pulse parameter, slit parameter, diffraction angle and dispersive property of medium. The potential application of spectral anomalies of pulsed Hermite-Gaussian beams in information encoding and information transmission in dispersive media is 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 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 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.     

Propagation of the kurtosis parameter of Hermite-cosh-Gaussian beams

Starting from the propagation equation of Hermite-cosh-Gaussian (HChG) beams and the intensity moments definition, an analytical expression for the propagation of the kurtosis parameter of unapertured HChG beams passing through paraxial optical ABCD systems is derived and illustrated numerically. Special interesting cases are discussed, in particular, the kurtosis parameter of HChG beams at the waist plane is obtained readily from our general propagation expression.     

The propagation properties and kurtosis parametric characteristics of Hermite-cosh-Gaussian beams passing through fractional Fourier transformation systems

Based on the Collins diffraction integral formula and irradiance moments, the propagation properties and kurtosis parametric characteristics of Hermite-cosh-Gaussian (HChG) beams passing through fractional Fourier transformation systems with spherically aberrated lenses are analyzed in detail. The closed-form expressions for the propagation equation and kurtosis parameter of HChG beams passing ideal fractional Fourier transformation systems are also obtained. By using an efficient algorithm some numerical calculations are also performed in this paper. The results show that the spherically aberrated lenses greatly influence on the intensity distribution and kurtosis parameter of HChG beams passage through fractional Fourier transformation systems. The intensity distribution and kurtosis parameter of HChG beams passage through two types of Lohmann's systems with spherically aberrated lenses, respectively, are no longer equal even in the case of the same fractional order and the same spherical aberration coefficients. The fundamental periods of the two types of Lohmann's systems with spherically aberrated lenses are different, 4 for the type I and 2 for the type II. Therefore, the two optical setups for implementing the fractional Fourier transformation are no longer equivalent in the presence of spherically aberrated lenses.     

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.     

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.     

Propagation properties of partially coherent Hermite–cosh-Gaussian beams through atmospheric turbulence

The analytical expression of partially coherent Hermite–cosh-Gaussian (HChG) beams propagating through atmospheric turbulence is derived and used to study their propagation properties through atmospheric turbulence. It is shown that partially coherent HChG beams propagating through atmospheric turbulence undergo several stages of evolution and a decrease of the spatial correlation length speeds up the evolution process. The smaller the spatial correlation length and the larger the beam orders are, the less the beam-width spreading of partially coherent HChG beams is affected by turbulence. At a sufficiently long propagation distance the beam-width spreading of partially coherent HChG beams with smaller Ch-part parameter and smaller waist width is less affected by turbulence. The results are illustrated by numerical examples, and the validity of the results is interpreted physically.     

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。     

Intensity Moments of Hermite-Cosh-Gaussian Laser Beams

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｉｎｒｅｃｅｎｔｙｅａｒｓ ,ａｎｉｎｔｅｒｅｓｔｉｎｇｓｏｌｕｔｉｏｎｏｆｔｈｅ ｐａｒａｘｉａｌｗａｖｅｅｑｕａｔｉｏｎ ,ｋｎｏｗｎａｓｔｈｅＨｅｒｍｉｔｅ ｓｉｎｕｓｏｉｄａｌ Ｇａｕｓｓｉａｎ (ＨＳＧ )ｂｅａｍｓ,ｈａｓｂｅｅｎｉｎｔｒｏｄｕｃｅｄｂｙＣａｓｐｅｒｓｏｎａｎｄＴｏｖａｒ[1,2 ] .ＡｓｏｎｅｏｆｔｈｅｓｐｅｃｉａｌｅｘａｍｐｌｅｉｎＨＳＧｆａｍｉｌｙ ,ｔｈｅＨｅｒｍｉｔｅ ｃｏｓｈ Ｇａｕｓｓｉａｎ(ＨＣｈＧ)ｂｅａｍｓ′ｓｆｉｅｌｄｄｉｓｔｒｉｂｕｔｉ…     

Intensity Moments of Hermite-Cosh-Gaussian Laser Beams

In this paper,attention is focused on the intensity moments of the Hermite-Cosh-Gaussian (HChG) laser beams from the zero-order to the fourth-order.The frequently used parameters such as the power in bucket (PIB),the beam width,the curvature radius,the far field divergence,the M2-factor,the Rayleigh length and the kurtosis are calculated in terms of the intensity moments.Figures show the influence of the mode index and the decentered parameter,which are the critical parameters of the HChG beams.Moreover,the center of the gravity of the radiation field and the symmetry are discussed along with the propagation axis.Finally,the power fraction within the beam width defined by the second moments is illustrated with numerical method.     

Regularities of radio-pulse propagation in transparent dispersive media

The distortions of pulsed radio signals in passage through a dispersive medium with a quadratic phase function are examined. These distortions are determined quantitatively by the relative pulse broadening. Analysis shows that the degree of envelope distortion is determined by a single dimensionless parameter and is practically independent of the signal spectrum. This parameter, which is called dispersion disphasing over the spectral interval, is easily calculated and is very useful for estimation of the degree of radio-pulse broadening. An example of its use for the simple case of pulse propagation through a parabolic ionospheric layer is provided.Moscow Physicotechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 9, pp. 943–951, September, 1993.     

被光阑像散透镜聚焦高斯-谢尔模型光束轴上的光谱开关

从部分相干光的传输理论出发,研究了高斯-谢尔模型光束通过光阑像散透镜聚焦的光谱异变和光谱开关。研究表明,在考虑像散的情况下,聚焦场轴上也会出现光谱异变和光谱开关。光谱异变和光谱开关不仅与空间相关性、截断参量、菲涅耳数和源光谱谱宽有关,透镜像散对光谱异变和光谱开关也会产生影响。通过数值计算结果,重点对透镜像散对光谱移动和光谱开关的影响进行了分析。与无像散情况相比,像散会使出现光谱开关的临界位置发生变化,当像散较大时出现光谱开关的临界位置明显向几何焦面移动,特别是当像散增加到一定数值时,光谱开关会消失。     

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.     

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.     

Changes in the spectral degree of coherence and spectral intensity of spatially and spectrally partially coherent cosh-Gaussian pulsed beams in free space

The analytical expressions for the spectral degree of coherence and spectral intensity of spatially and spectrally partially coherent cosh-Gaussian pulsed (ChGP) beams propagating in free space are derived. It is shown that the spectral degree of coherence and spectral intensity of spatially and spectrally partially coherent ChGP beams depend on the spatial correlation parameter, decentered parameter and temporal coherence length. Depending on the decentered parameter, the effective width of the spectral degree of coherence can be larger than, smaller than or equal to that of the spectral intensity. The results are illustrated by numerical examples.     

Changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic J0-correlated Schell-model pulsed beams propagating in free space

Taking the stochastic electromagnetic J ₀-correlated Schell-model pulsed (JSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the analytical expressions for the cross-spectral density matrix, spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic JSMP beams propagating in free space are derived, and used to study the changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic JSMP beams. It is shown that the on-axis spectrum is blue-shifted in free-space propagation and is dependent on the pulse temporal coherence length and spatial correlation parameter. The distribution of the on-axis spectral degree of polarization depends on the frequency and spatial correlation parameter. The spectral degree of coherence increases with increasing pulse temporal coherence length. The results derived are interpreted physically.