有球差多色高斯光束衍射引起的光谱开关

从空间频率域交叉谱密度函数的传输公式出发，推导出有球差多色高斯光束被硬边光阑衍射 后轴上光谱的解析公式，无像差的结果作为本公式的特例.对所得公式作了详细的数值计算 和物理分析.结果表明，球差高斯光束被硬边光阑衍射后近场的光谱与无像差时比较 有蓝移、红移，也会出现光谱开关.着重分析了球差对光谱开关的影响. 关键词： 现代光学 光阑衍射 光谱开关 球差 多色高斯光束     

等束宽超短脉冲光束的远场特性

利用角谱法和复解析信号法推导出了等束宽超短高斯脉冲光束在远场的解析传输公式及其傅里叶谱.研究了若干个甚至一个光周期数的等束宽超短高斯脉冲光束的远场特性，并与等衍射长度超短高斯脉冲光束作了比较.研究表明，等束宽超短高斯脉冲光束在远场存在脉冲展宽、光谱变窄、离轴光谱红移、轴上光谱蓝移等特性. 关键词： 角谱法 复解析信号法 等束宽超短高斯脉冲光束     

超短辛格高斯脉冲光束的频谱性质

给出了自由空间中超短辛格高斯脉冲光束在频率域传输的方程．对超短辛格高斯脉冲光束的功率谱进行了研究．结果表明：超短辛格高斯脉冲光束的轴外频谱具有红移、频谱变窄等性质．超短辛格高斯脉冲光束的光谱在衍射角不为零时有红移现象，并且随着衍射角的增加光谱红移也逐渐增大，频谱宽度逐渐变窄．在十倍瑞利距离处的数值模拟结果表明，衍射角等于3°时的频谱宽度仅为衍射角为0°时频谱宽度的四分之一．     

衍射扭曲高斯-谢尔模型光束在远场的光谱移动和光谱开关

从部分相干光的传输理论出发,研究了被光阑衍射扭曲高斯-谢尔模型光束远场的光谱变化规律。结果表明,扭曲高斯-谢尔模型光束在远场也会出现光谱移动和光谱开关效应。与衍射高斯-谢尔模型光束情况相比,光谱移动和光谱开关效应不仅与光束空间相关性、截断参量和源光谱谱宽有关,光束的扭曲因子也会对衍射扭曲高斯-谢尔模型光束远场的光谱移动和光谱开关效应产生影响。通过数值计算结果详细讨论了光束扭曲因子影响衍射扭曲高斯-谢尔模型远场光谱的规律。     

超短脉冲贝塞尔-高斯光束在自由空间的传输特性

 使用复解析信号法研究了束宽与频率无关的超短脉冲贝塞尔-高斯光束在自由空间的传输特性。研究表明：在无衍射长度内，超短脉冲贝塞尔-高斯光束的横向光强分布几乎不变并集中在传输轴附近，轴上脉冲随传输距离增加而展宽。在无衍射长度外，横向光强分布显著扩展。随传输距离增加，轴上光谱蓝移先增加，达到极大值后逐渐减小，最后在远场趋于一渐近值。对单周期的超短脉冲贝塞尔-高斯光束的轴上光谱蓝移先增加，达到极大值0.50 fs^-1。然后逐渐减小，在远场蓝移趋于渐近值0.16 fs^-1。     

有振幅调制和相位畸变光束的远场光谱移动与光谱开关

基于瑞利衍射公式,研究了被光阑衍射的具有振幅调制和相位畸变光束的远场光谱变化规律。结果表明,有振幅调制和相位畸变光束在远场也会出现光谱异变现象和光谱开关效应,光阑截断参数、光束的相位畸变参数、振幅调制参数、光强调制参数对远场光谱的跃迁量和光谱开关产生影响。通过数值计算结果分析讨论了光阑截断参数及光束各参数影响远场光谱的规律。     

平顶高斯光束经含失调圆孔光阑的失调光学系统的传输特性

为分析平顶高斯光束通过光学系统传输时圆孔光阑失调和光学元件失调对平顶高斯光束传输特性的影响,利用失调圆孔光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了平顶高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,给出了输出光束场分布与光束参量、光阑孔径尺寸、光阑和光学元件失调量等的定量关系.针对特定光学系统定量分析了各失调量对输出光束场分布的影响,结果表明各元件失调都对输出光束强度分布产生较大影响.但在各失调量较小的情况下,透镜失调对输出光束传输特性的影响比光阑失调对输出光束传输特性的影响更明显.     

超短脉冲复宗量拉盖尔-高斯光束

从超短高斯脉冲光束出发。根据拉盖尔多项式的性质,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,称为超短复宗量拉盖尔-高斯脉冲光束。此脉冲光束解的每个频率分量都是复宗量拉盖尔-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,分析了超短复宗量拉盖尔一高斯脉冲光束的轴上光强、光强的横向分布、衍射性质、脉冲极性反转、脉冲延迟等。讨论了引入缓变包络近似后出现的时空奇异性。     

洛伦兹光束经光阑失调傍轴光学系统的传输

基于广义衍射积分公式和光阑函数的复高斯展开,导出了一洛伦兹光束经一个带圆形光阑失调傍轴光学系统的近似解析传输公式.作为一般公式的特例,还给出了洛伦兹光束经一无光阑失调傍轴光学系统的解析传输式.作为数值计算的例子,运用所得到的公式分析了洛伦兹光束经带光阑失调薄透镜的传输特性.结果表明：不同强度的衍射即圆形光阑半径的大小明显影响衍射光束的归一化强度分布及其传输变化规律. 关键词： 洛伦兹光束 失调傍轴光学系统 光束传输     

平顶高斯光束经含失调圆孔光阑的失调光学系统的传输特性

为分析平顶高斯光束通过光学系统传输时圆孔光阑失调和光学元件失调对平顶高斯光束传输特性的影响,利用失调圆孔光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了平顶高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,给出了输出光束场分布与光束参量、光阑孔径尺寸、光阑和光学元件失调量等的定量关系.针对特定光学系统定量分析了各失调量对输出光束场分布的影响,结果表明各元件失调都对输出光束强度分布产生较大影响.但在各失调量较小的情况下,透镜失调对输出光束传输特性的影响比光阑失调对输出光束传输特性的影响更明显.     

Far-field spectral intensity characteristics of a time-dependent gaussian pulse from a circular mask with a linear circular apertures array

The spectral characteristics of a time-dependent Gaussian pulse from a circular mask with a circular apertures array in the far field are theoretically investigated and presented with numerical results. A rigorous treatment, with the Fresnel diffraction integral, to the spectral changes of a time-dependent Gaussian-shaped pulse passing through a circular mask with a linear circular apertures array is given and some properties of the spectral intensity under different situations are provided. Also an accurate and concrete criteria judging the condition for the red shift, blue shift of spectral intensity distributions is obtained as well.     

Far-field diffraction characteristics of a time dependent Gaussian-shaped pulsed beam from a rectangular mask with a circular aperture array

The diffraction characteristics of a broad-band light source from a rectangular mask with a circular aperture array in the far field are theoretically investigated with a rapid and precise mathematical derivation. We provide a rigorous treatment of a time dependent Gaussian-shaped pulsed beam passing through a rectangular mask with a circular aperture array and give more accurate and concrete criteria judging the timing for the spectral red shift, blue shift, and splitting of light distributions as well. In addition, the distortion of the space-time diffraction intensity distribution is also presented in detail. This study shows the mathematically analytic form for a pulsed beam incident on an array of small apertures, when the usage of lenses is not practical. Also, the energy distribution of the pulse in the frequency domain is presented to benefit the understanding of its applications in optics information systems.     

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 Intensity Distribution of a Time Dependent Gaussian Pulsed Beam From a Circular Aperture in the Near-Field Diffraction

The diffraction characteristics of a broadband light source from a circular aperture in the near-field are clarified theoretically via prompt and precise mathematical derivation. This paper provides a explicit way of treating in the case of time dependent Gaussian-shaped pulsed beam passing through a circular aperture and gives more accurate and concrete criteria for judging the timing of the spectral red shift, blue shift and splitting of light distributions. Furthermore, the results offer an understanding of the Gaussian beam quality of the output of an optical resonator in the near-field.     

Spectral shifts and spectral switches of a pulsed Bessel–Gauss beam from a circular aperture in the far field

The far-field spectral characteristics of a broadband-pulsed Bessel–Gauss beam passing through a circular aperture are studied. Based on the expansion of a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, the approximate analytical expression for the spectral distribution of the diffraction field is derived. The “aperture dispersion”, that is, the red and blue shifts of the spectral intensity maximum and the spectral intensity shape distortion and distribution under different conditions are studied and illustrated with numerical calculations. It is shown that the far-field, on-axis maximum spectral intensity always shifts to the right (blue shift) and the amount of the spectral shift is dependent on the source bandwidth only. However, for the cases of off-axis, when the observation angle θ approaches a critical value, a rapid spectral switch occurs.     

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.     

Propagation of a phase-locked circular dark hollow beams array in a turbulent atmosphere

The propagation of phase-locked circular dark hollow beams array in a turbulent atmosphere is studied. An analytical expression for the average intensity distribution at the receiving plane is obtained based on the extended Huygens-Fresnel principle. The effects of turbulence, dark parameter and beam order of the beams array on the intensity pattern are studied and analyzed. It is found that the intensity pattern of the phase-locked circular dark hollow beams array will evolve from a multiple-spot-pattern into a Gaussian beam spot under the isotropic influence of the turbulence. The intensity pattern of beam array with a larger dark parameter and beam order evolves into the Gaussian-shape faster with increasing propagation distance.     

Slanted hole array beam profiler (SHArP)-a high-resolution portable beam profiler based on a linear aperture array

We demonstrate a novel high-resolution portable beam profiler based on a slanted linear array of small apertures, termed a slanted hole array beam profiler (SHArP). The apertures are directly fabricated on a metal-coated CMOS imaging sensor. With a single linear scan, the aperture array can establish a virtual grid of sampling points for beam profiling. With our prototype, we demonstrate beam profiling of Gaussian beams over an area of 66.5 microm x 66.5 microm with a resolution of 0.8 microm (compare with the CMOS pixel size of 10 microm). The resolution can be improved into the range of submicrometers by fabricating smaller apertures. The good correspondence between the measured and calculated beam profiles proves the fidelity of our new beam profiling scheme.     

部分相干光束通过硬边光阑的推广光束传输M2因子

给出部分相干光通过硬边光阑后的强度二阶矩的计算公式，由此可得到部分相干光通过硬边光阑后的推广光束传输M^2因子。以部分相干高斯－谢尔模型光束为例，推导出相应的M^2因子，并作了数值计算和分析讨论。