Spectrum apodization of a time-dependent Gaussian pulse incident on the apodized circular aperture in far-field

The diffraction spectral intensity characteristics of a time-dependent Gaussian pulse from an apodized circular aperture in the far field are studied both theoretically and numerically. It is shown that the apodization of the diffracted Gaussian pulse spectrum can be found. Also the red or blue shift of the spectral intensity maximum of the incident pulse is presented.     

Focal shift of apodized truncated hyperbolic-cosine-Gaussian beam

Focal shift of hyperbolic-cosine-Gaussian beams induced by pure phase apodizer was investigated theoretically. The pure phase apodizer consists of three concentric zones: center circle zone, inner annular zone and outer annular zone. And the phase variance of the inner annular zone is adjustable. Results show that intensity peak moves far from optical aperture and then shrinks sharply for certain radii of zones with increasing phase variance of the inner annular zone. Simultaneously, one new intensity peak occurs near optical aperture, moves far from the optical aperture, and then becomes intensity maximum peak, and repeats the evolution process of the former intensity peak. Tunable focal shift occurs with focal switch. Decreasing the phase variance can change the move direction of the intensity peaks. In addition, the maximum distance between the two intensity peaks can be altered by beam parameters of cosh parts, and the distance value increases and then decreases with increasing beam parameters of cosh parts for certain radii of zones. Tunable focal shift is also discussed to construct optical tweezers.     

Tukey窗函数用于数字全息图的切趾研究

提出采用Tukey窗函数对数字全息图进行切趾处理的方法,以削弱数字全息像再现过程中的孔径衍射效应,抑制再现波前的起伏.模拟实验结果表明,该方法显著改善了再现像中央区域的强度和相位分布,适用于微小物体的显微测量及微小形变测量等领域.     

Fresnel zone plate with apodized aperture for hard X‐ray Gaussian beam optics

Fresnel zone plates with apodized apertures [apodization FZPs (A‐FZPs)] have been developed to realise Gaussian beam optics in the hard X‐ray region. The designed zone depth of A‐FZPs gradually decreases from the center to peripheral regions. Such a zone structure forms a Gaussian‐like smooth‐shouldered aperture function which optically behaves as an apodization filter and produces a Gaussian‐like focusing spot profile. Optical properties of two types of A‐FZP, i.e. a circular type and a one‐dimensional type, have been evaluated by using a microbeam knife‐edge scan test, and have been carefully compared with those of normal FZP optics. Advantages of using A‐FZPs are introduced.     

厄米-高斯光束在内含硬边光阑光学系统中的传输

把硬边光阑从复杂光学系统中“移”出来,即把任意一个含有硬边光阑的复杂光学系统体现到含有入射光瞳和出射光瞳的光学系统中，使硬边光阑的作用转化为出射光瞳的作用，以便求出观察面上的解析解。对入射面上的二维厄米 高斯光束，利用柯林斯公式和入射光瞳与出射光瞳的物像关系，可得到所要求观察面的场分布和解析结果，通过数值模拟验证了其正确性。通过分析计算得到如下结论：对于任意一个含有硬边光阑的复杂光学系统，都可以把光阑的作用从系统中“移”出来，把其看作是出射光瞳的作用，从而可以较为简便地求出观察面上的场分布。     

Smallest focal hole

We study theoretically routes toward the most confined dark channel that can be obtained using high angular aperture focusing. One possible solution is to use a radially polarized beam combined with an optical singularity. Another possibility is to use an azimuthally polarized light beam combined with an annular aperture or a phase filter. Our results suggest that a focal hole of full-width at half maximum of approximately 0.3λ₀/NA is achievable, where λ₀ is the wavelength in vacuum and NA is the numerical aperture of the focusing system. Finally, we show that by letting a phase-shifted plane wave and a focused scalar wave interfere only one point in the focal plane will exhibit zero intensity. Advantages and disadvantages of the schemes are discussed.     

Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere

An analytical formula for the average intensity of cosh-Gaussian (ChG) beams diffracted by an aperture in turbulent atmosphere is derived and some limiting cases are discussed. By using the average intensity formula, some numerical simulation comparisons are made and some special cases are studied, especially the influences of the ChG beam parameter (Ω₀), the propagation distance, the aperture and its size on the average normalized intensity distribution. It is determined that the evolution properties of the average normalized intensity profile in turbulent atmosphere with aperture are different not only from those of free space with aperture but also from those in turbulent atmosphere without aperture. PACS 42.68.Bz; 42.79.Ag; 42.25.Fx     

The on-axis average intensity for Gaussian beam excitation limited by an annular aperture in turbulent atmosphere

Starting with a Gaussian beam excitation limited by an annular aperture, the on-axis average intensity is presented in turbulent atmosphere. The on-axis average intensity profile is evaluated by altering the outer and inner radius of an annular aperture, the propagation distance and wavelength. The results show that the outer radius of an annular aperture within a certain size impacts the on-axis intensity distributions. When the propagation distance or the outer radius of an annular aperture is large enough, the on-axis average intensity distributions is not affected by the size of the annular aperture. By calculation and analyses, the variation of the inner radius of the annular aperture and the wavelength of the Gaussian beam that impact on the axial average intensity distributions is also discussed.     

非均匀偏振光束通过环状光阑的传输

 使用光束相干偏振矩阵方法,推导出非均匀偏振光束通过环状光阑后偏振度和光强分布的表达式,研究了非均匀偏振光束通过环状光阑后偏振度和光强的变化。结果表明,在横平面上通常偏振度为非均匀分布,但在中心区域近似为均匀分布,均匀分布范围与非均匀偏振光束参数、光阑遮拦比和传输距离有关。初始为均匀分布的光强通过光阑后变为具有中心主极大和小衍射旁瓣的非均匀分布。     

Focal shift in focused truncated gaussian beams

It is known that under certain circumstances the point of maximum intensity in a focused aberration-free wave is not at the geometrical focus, but is closer to the focusing lens. In the present note such a focal shift is analyzed for the case of a gaussian beam, focused by a thin lens, which fills a circular aperture of any prescribed radius, the waist of the beam being assumed to be located in the aperture plane. Many previously known results follow as limiting cases of our analysis.     

Focusing in a largeF-number optical system

The true focal spot of a focusing system may be defined as either the location of the maximum on-axis intensity or the location of the minimum beam diameter that contains a certain fraction of the power. Diffraction causes this true focus to be shifted from the ideal geometrical optics prediction, the effect being greatest at largeF-numbers. Specifically, a theoretical and experimental study is made of the largeF-number focusing properties of a thin lens in contact with a uniformly illuminated aperture. The results are clarified by a comparison to the focal spot shift for a Gaussian beam.     

部分相干椭球光笼

 从理论上研究部分相干光束经透镜聚焦的三维光强分布。研究结果表明,在几何焦点附近的光强分布不仅依赖于入射部分相干光束的光强分布,而且还依赖于入射光束的空间相干度。基于这一点,提出了一种控制部分相干光束的空间相干度,在几何焦点附近获得了类似椭球光笼形状的光强分布的新方法。通过控制入射部分相干光的空间相干度,来改变聚焦在几何焦点附近的三维光强分布,从而获得希望得到的光强分布。     

Effect of deviation from plane wave conditions on the Doppler spectrum from an ultrasonic blood flow detector.

Deviation from plane wave conditions within the ultrasound beam of a Doppler blood flow detector leads to a non-linear relationship between the phase angle of the back-scattered signal and the scatterer position. This in turn leads to frequency modulation of the Doppler signal and an increase in the Doppler spectrum width. The relationship between the ultrasound beam and the observed signal spectrum has been investigated by employing a computer-based model of the ultrasound field which enabled the calculation of: 1, pressure (amplitude and phase angle) field distributions from plane disc and focused transducers with unapodized and apodized aperture field distributions; 2, the Doppler signal from a scatterer moving through the field; and 3, the spectrum of this signal. The increase in spectral width resulting from deviations from plane wave conditions was calculated by comparing this spectrum with that of the signal from which frequency modulation had been removed.     

Hamming切趾技术提高体光栅光谱合成功率的研究

体光栅光谱合成技术是获得高功率激光输出的一种有效途径,体光栅衍射旁瓣是影响合成光束数目的主要因素。采用了Hamming切趾技术对体光栅旁瓣进行抑制,建立了Hamming切趾体光栅的折射率分布模型,分析了Hamming切趾体光栅的衍射特性,给出了Hamming切趾体光栅光谱合成效率公式,分析了切趾光栅对光谱合成效率的影响。计算结果表明:体光栅切趾后有效减小了体光栅对相邻合成光束的衍射损耗,切趾后,在20 nm的带宽内,谱合成光束的数目由13束增加为20束,谱合成效率达75.3%,光谱合成功率提高为切趾前的1.5倍。     

Hermite hyperbolic/sinusoidal Gaussian beams in ABCD systems

For a Hermite hyperbolic/sinusoidal Gaussian beam with focusing properties, passing through an arbitrarily shaped rectangular aperture on the source plane and an on-axis x–y asymmetric ABCD system, the receiver plane expression is derived using the Collins integral. The specific example of a single thin lens placed on the propagation path is examined at selected source, propagation and optical element parameters. Viewing the progress of the beam in propagation, we find that subjecting the source beam to an aperture will give rise to excessive spreading during propagation. The lens setup will act to concentrate the energy of the beam around its focal point as expected, while in some circumstances it will also execute beam profile changes. By adjusting the aperture opening in the shape of a narrow slit, the beam will become aligned in the opposite direction after propagating after having traveled sufficiently. The results are presented as intensity graphs in the form of contour plots and 3D illustrations.     

Focal shifts in diffracted converging spherical waves

It is known from a number of publications that when a converging, monochromatic spherical wave is diffracted at a circular aperture, the point of maximum intensity of the diffracted wave may not be at the geometrical focus of the incident wave, but may be located closer to the aperture. In the present note we show that when the incident wave is uniform and the angular semi-aperture is small, the ratio of such a shift Δ? of the point of maximum intensity to the distance ? between the geometrical focus and the plane of the aperture depends only on the Fresnel number N of the aperture when viewed from the geometrical focus. The effect becomes significant when N ? 5. When N = 1, for example, |Δ?| ≈ 0.4 ? and the maximum intensity is approximately twice as large as the intensity at the geometrical focus.     

The relay propagation of partially coherent cosh–Gaussian–Schell beams in turbulent atmosphere

We have studied the relay propagation of a partially coherent cosh–Gaussian–Schell beam in turbulent atmosphere. Analytical expressions for both the cross-spectral density at the relay system and average intensity at the target are derived. By using the analytical expressions some special cases are studied and some numerical simulation comparisons are made, especially the effects of the coherence of the beam, turbulence strength, aperture and its size on the relay propagation. Our study shows that the effects of diffraction and coherence of initial beam on the intensity profiles at the relay system are so small that they can be neglected when the effects due to turbulence are large enough. Even though the correction to the receiving beam at relay system is important, it is not necessary to improve the receiving beam when the effect of turbulence over the travel path is strong. A high peak intensity at target can be obtained by optimizing these factors, such as propagation distance, aperture and spatial correlation length.     

Fraunhofer diffraction pattern of apodized semicircular apertures

The far-field diffraction pattern of apodized semicircular apertures is described. The exact amplitude is given using incomplete cylinder functions. The paper also presents a simple approximation for the intensity that is suitable for further computations when the aperture is part of an optical system.     

高功率无移相器自旋转波束扫描天线设计

设计了一种无移相器结构的平板高功率天线,通过辐射层自旋转方式改变口径场相位分布,从而实现空间波束扫描,满足轻质、低剖面集成要求,辐射增益36 dB,波束扫描范围-30°至+30°,GW级功率容量,满足Ku波段工作的系统指标与能力要求。对天线进行了实物加工与测试,测试结果说明该天线具有良好的波束扫描特性和较高的口径辐射效率。无需加载移相馈电网络便可改变波束指向,具有伺服简单,结构紧凑,平面化、低剖面、轻质等优点,可广泛应用于机载、车载、舰载等高功率微波系统的表面共形发射。     

Cylindrical vector axisymmetric Bessel-modulated Gaussian beam

Focusing properties of the cylindrical vector axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) in high numerical aperture system is investigated theoretically by vector diffraction theory. Results show that intensity distribution in focal region can be altered considerably by beam parameter μ and polarization angle. Polarization angle may adjust transverse intensity distribution, for instance from one focal spot to one ring shape. While μ alters axial intensity distribution remarkably, focal splitting may occur with tunable focal shift, and real value μ also may induce local intensity minimum. For certain case, with increasing imaginary value μ, transverse focal spot shrinks accompanied with higher full width half maximum of axial intensity distribution.