On-axis spectral shifts and spectral switches of Gaussian Schell-model beams focused by an astigmatic aperture lens

Starting from the propagation law of partially coherent light, the on-axis spectral shifts and spectral switches of Gaussian Schell-model (GSM) beams focused by an astigmatic aperture lens are studied. It is shown that, as compared with an aberration-free case whose spectral shifts and spectral switches are induced by spatial correlation and aperture diffraction, the spectral shifts and spectral switches of GSM beams also depend upon the astigmatism of the lens for an astigmatism case. Detailed numerical calculations are made to illustrate the behavior of spectral shifts and spectral switches of GSM beams focused by an astigmatic aperture lens.     

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 properties of spatially and spectrally partially coherent cosh-Gaussian pulsed beams focused by an aperture lens

The analytical expression for the spectrum of spatially and spectrally partially coherent cosh-Gaussian pulsed (ChGP) beams focused by an aperture lens is derived and used to study their spectral properties at the focal plane and on the axis. The effect of the truncation parameter, spatial correlation parameter, decentered parameter and temporal coherence length on the spectral shifts and spectral switches of spatially and spectrally partially coherent ChGP beams is stressed. The results are illustrated numerically and interpreted physically.     

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.     

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.     

超短脉冲经线性小孔阵列衍射时的光谱开关特性

研究了超短高斯脉冲光束经线性排列的矩形光阑阵列衍射后的远场光谱奇变现象。基于菲涅耳积分公式,通过将光阑函数展开为有限项复高斯函数的叠加,得到了超短脉冲光束经线性排列的小孔光阑阵列衍射后的谱强度解析表达式,并对衍射场的光谱红移和蓝移现象进行了数值计算和分析,分析了小孔间距和光阑半径对光谱强度的影响。研究表明:在衍射场的某些观测点,即在调制函数为零的位置附近,存在光谱开关现象。     

Propagation properties of Gaussian beams through the anamorphic fractional Fourier transform system with an eccentric circular aperture

As known, it is important for the propagation of Gaussian beams in optics. In this paper, based on the expanding a hard-edge circular aperture function as a finite sum of complex Gaussian functions and the scalar Rayleigh-Sommerfeld diffraction formula, an approximation analytical solution for Gaussian beams propagating through the anamorphic fractional Fourier transform system with an eccentric circular aperture is performed. Then, the detailed numerical calculation for the two-dimensional Gaussian beams in the above-mentioned optical system is presented. The simulation also shows that different location and size of aperture result in the change of diffracted field, including location, intensity and width. All these characteristics help us understand Gaussian beams propagation better.     

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 focused hollow Gaussian beams at the geometrical focal plane

On the basis of diffraction integral and the expansion of the hard-aperture function into a finite series of complex Gaussian functions, an approximate expression for spatially fully coherent polychromatic hollow Gaussian beams passing through aperture lens is obtained. Detailed numerical results indicate that remarkable spectral changes always occurs near the points where the field amplitude has zero value. The effects of truncation parameter, Fresnel number and the beam order on spectral shifts and spectral switches are investigated numerically.     

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.     

Spectral anomalies and spectral switches of partially coherent and polychromatic light diffracted at an aperture

Inrecentyearsanewbranchofmodernphysicalopticscalledsingularoptics[1]hasbeendeveloped.In2002theworkinsingularopticswasextendedfrommonochromaticlighttospatiallyfullycoherentandpolychromaticlightbyGburetal.[2—4].Itwasfoundthat,whenaconverging,spatiallyfullycoherentandpolychromaticsphericalwaveisdiffractedatanaperture,anomalousspectralchangestakeplaceclosetozerosoftheintensityinthefarfield;i.e.thespectrumisredshiftedatsomepoints,blueshiftedatothers,andsplitintotwolineselsewhere.Thepredictionsofsp…     

Effect of vectorial nature on spectral anomalies of ultrashort pulsed beams from a hard-edged aperture

Based on the vectorial Rayleigh–Sommerfeld diffraction integrals, the analytical expression for the spectral intensity of a vectorial nonparaxial ultrashort pulsed Gaussian beam diffracted at a rectangular hard-aperture is derived. The results of the far-field and paraxial cases can be regarded as special cases of the general expression. Effect of vectorial nature on spectral anomalies of ultrashort pulsed beams passing through a hard-edged aperture is analyzed in detail. It is shown that the spectral switch near the phase singularity, which is predicated under the condition of the scalar paraxial theory, disappears with the increasing effect of the vectorial and nonparaxial nature.     

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.     

Spectral shifts and spectral switches of spatially and spectrally partially coherent pulsed beams in Young’s interference experiment

Taking the Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the far-field spectrum of diffracted GSMP beams in Young’s interference experiment is derived, and used to study the spectral shifts and spectral switches of GSMP beams in the far field. Numerical calculation results are given to illustrate the dependence of spectral shifts and spectral switches on the obscuration ratio ε, temporal coherent length T_c, spatial correlation parameter β and diffraction angle α. It is shown that the critical angle α_c of the first- and second-order spectral switches moves away from the z axis with increasing T_c, but α_c of the third-order spectral switch moves towards the z axis with increasing T_c. The spectral transition height Δ decreases and spectral minimum S_min increases as T_c increases. α_c decreases, Δ increases and S_min decreases as β increases. The potential application of spectral switches of spatially and spectrally partially coherent pulsed beams in information encoding and transmission is proposed.     

Effect of astigmatism on spectral switches of partially coherent beams

A detailed study of the spectrum of partially coherent beams diffracted at an astigmatic aperture lens is performed. Considerable attention is paid to the effect of astigmatism on spectral switches of polychromatic Gaussian Schell-model beams. It is shown that the spectral switch can also take place in the vicinity of intensity minimum in a geometrical focal plane for the astigmatic case, but the astigmatism of the lens and the spatial correlation of the beam affect the critical position u_c, spectral minimum S_{min}, and transition height Δ of spectral switches.     

Spectral characteristic of a pulsed hollow Gaussian beam passing through a circular aperture

The spectral characteristics of a pulsed hollow Gaussian beam passing through a circular aperture are studied. Based on the vectorial Rayleigh diffraction integrals, the analytical expressions of the spectra for the complex analytic signal representation and for the complex amplitude envelope representation are derived, respectively, and the comparison between them is made. The influences of the truncation parameter and the beam order on the spectral shifts and on the spectral switches are illustrated. It is shown that the spectrum for the complex analytic signal representation and that for the complex amplitude envelope representation are obvious different as the pulse shorter than an optical period.     

Spectral switches of partially coherent nonparaxial beams diffracted at an aperture

Based on the generalized Rayleigh diffraction integral, the spectral shifts and spectral switches of nonparaxial partially coherent beams diffracted at an aperture are studied. Our main attention is paid to the effect of beam nonparaxiality on the spectral switches of partially coherent beams. It is shown that the spatial coherent parameter β, trunction parameter δ and waist width-to-central wavelength ratio w₀/λ₀ affect the behavior of spectral switches. Only when β, δ and w₀/λ₀ satisfy certain conditions, can the difference between the nonparaxial and paraxial results be negligible. The discrepancy arises physically from the change of the spectral modifier by using the paraxial approximation.     

Spectral shifts and spectral switches of partially coherent vector beams propagating through an astigmatic aperture lens

By using the polarization matrix and propagation equation of the cross-spectral density function matrix, the spectral shifts and spectral switches of partially coherent vector beams propagating through an astigmatic aperture lens are studied, where the effect of lens astigmatism and beam cross-correlation on the spectral switches is stressed. It is shown that the critical position, spectral transition height and spectral minimum at spectral switches depend on the astigmatism. The beam cross-correlation plays a role in spectral switches under the condition that a polarizer is inserted. The spectral switch vanishes when the astigmatic coefficient is larger than a certain value, or the cross-correlation length is less than a certain value.