Focus depth characteristics of lenses with long focal depth designed by a focal depth function

The validity of a focal length function is investigated in designing optical element with long focal depth and high lateral resolution. The designed lenses with different starting focal length are studied. Two focusing performance measures, focal depth and lateral resolution, are presented. Comparing with the conventional lens and optical element designed by other focal length function, numerical results of the designed optics element indicate that the long focal depth and high lateral resolution are achieved. The validity of the focal length function is confirmed. Meanwhile, the designed optical element is similar with the lens with spherical aberration. It means that one can easily implement long focal depth by applying appropriate phase modulation to a lens with spherical aberration.     

Extending the depth of focus with high NA lens axicon

Based on vectorial Debye theory, tight focusing of x-polarized beam with high NA lens axicon is studied. The high NA lens axicon utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distribution in the focal region is illustrated by numerical calculations. We show that the high NA lens axicon system can generates a sub wavelength beam (0.826λ) with depth of focus around 10λ.     

High-resolution optical coherence tomography over a large depth range with an axicon lens

In optical coherence tomography, axial and lateral resolutions are determined by the source coherence length and the numerical aperture of the sampling lens, respectively. Whereas axial resolution can be improved by use of a broadband light source, there is a trade-off between lateral resolution and focusing depth when conventional optical elements are used. We report on the incorporation of an axicon lens into the sample arm of an interferometer to overcome this limitation. Using an axicon lens with a top angle of 160 degrees , we maintained 10-microm or better lateral resolution over a focusing depth of at least 6 mm. In addition to having high lateral resolution, the focusing spot has an intensity that is approximately constant over a greater depth range than when a conventional lens is used.     

采用非线性相位拟合法设计长焦深透镜

针对惯性约束聚变(ICF)激光等离子体诊断系统应用的需求,提出一种采用非线性相位拟合法设计单透镜代替理想对数轴锥镜的方法。对所要得到的球面透镜与理想对数轴锥镜的相位进行拟合,求解得出所需要的球面透镜参量。设计了用于激光等离子体诊断系统的长焦深透镜,并对透镜的焦深、轴向光场均匀性、横向均匀性、焦斑旁瓣等指标进行分析。数值分析结果表明,长焦深透镜具有与理想对数轴锥镜相同的相位分布,焦深、轴向光场均匀性、横向均匀性、焦斑旁瓣均符合设计要求,验证了非线性相位拟合法的正确性。     

Demonstration of image-zooming capability for diffractive axicons

Diffractive axicons are optical components producing achromatic nondiffracting beams. They thus produce a focal line rather than a focal point for classical lenses. This gives the interesting property of a long focal depth. We show that this property can be used to design a simple imaging system with a linear variable zoom by using and translating a diffractive axicon as the only optical component.     

Focus shaping of tightly focused TEM11 mode cylindrically polarized Laguerre Gaussian beam by diffractive optical element

We study the focus shaping of tightly focused TEM₁₁ mode cylindrically polarized Laguerre Gaussian beam with high numerical aperture lens axicon system is investigated theoretically by vector diffraction theory. The intensity pattern at the focus can be tailored by appropriately adjusting the rotation angle. We show that the high NA lens axicon system can generates a sub wavelength focal spot, focal hole, focal splitting and flat-topped focal shapes with extended depth of focus.     

应用于ICF等离子体诊断系统的长焦深光学元件设计

 针对惯性约束聚变激光等离子体诊断系统的特殊需求,提出采用对数型轴锥镜来实现长焦深功能,并采用超高斯边缘匀滑、中心切趾及选择合适的器件参数等方法优化了长焦深器件的性能。模拟实验证明,为了得到满足要求的长焦深、小焦斑、小旁瓣和均匀的轴上及横向光场分布的聚焦光束,对数型轴锥镜的焦深应为3~5 mm;元件中心须采用切趾,而且切趾半径应为15~60 mm;元件边缘宜采用5阶超高斯匀滑。设计出焦深长达3 mm、轴上光强均匀、旁瓣峰值小于中心强度的2%且横向光斑较均匀的长焦深器件,可以满足激光等离子体诊断的要求,并用菲涅耳衍射积分对该元件光场的模拟实验验证了该方法的可行性。     

Solid immersion axicon: maximizing nondiffracting or Bessel beam resolution

A new type of optical configuration--a solid immersion axicon (SIAX)--is proposed. Similar to a solid immersion lens for Gaussian beams, a SIAX increases the diffraction-limited resolution for propagating Bessel beams by a factor of the refractive index of the media. For incident radial polarization, the scheme generates the smallest focal spot available for nondiffracting beams. The configuration can be implemented with either refractive or diffractive axicons. The scheme may find use in microscopy, imaging, lithography and data storage, and other applications requiring nondiffracting beam characteristic features such as very large focal depth.     

Intensity distribution and focal depth of axicon illuminated by Gaussian Schell-model beam

In view of second-order coherence theory, the generalized diffractive axicon illuminated by partially coherent Gaussian Schell-model (GSM) beams is analyzed. An analytical equation for focal depth of axicon without aperture illuminated by spatial partially coherent GSM beam is derived. We showed that the off-axis images can be evaluated by using the method of stationary phase at any correlation state, hence we demonstrated that the intensity distribution of diffracted beam is a superposition of Bessel Beams of various orders. We also showed that the diffracted beam is nondiffractive only on the boundaries of the focal depth.     

平顶飞秒激光经圆锥透镜在熔融石英中成丝及超连续辐射

实验研究了平顶飞秒激光经圆锥透镜后在熔融石英中的成丝及超连续辐射.与高斯飞秒激光的成丝对比发现,平顶飞秒激光可以获得在圆锥透镜焦深区域内强度分布更为均匀的等离子体细丝,这一特征更有利于飞秒激光在固体介质中进行微纳加工等领域的应用.并且,在不损伤熔融石英的条件下,平顶飞秒激光成丝可以获得更高能量、更高转换效率的超连续辐射,这是因为若产生光强相近的细丝,平顶飞秒激光所需的初始激光能量更高,此激光能量下产生的细丝长度更长、均匀性更好.     

Design and properties of binary axilens

A novel optical element, axilens, proposed by Davidson et al., for achieving extended focal length is introduced. We propose a method to design the binary axilens which has high diffraction efficiency. Using computer numerical simulation, we designed 4 axilenses each has different parameters. In this paper we present our results and make comparison with that in ref. [1]. The properties of binary axilens such as the focal depth, the lateral resolution and the intensity distribution along axis is discussed.     

Design and properties of binary axilens

A novel optical element, axilens, proposed by Davidson et al., for achieving extended focal length is introduced. We propose a method to design the binary axilens which has high diffraction efficiency. Using computer numerical simulation, we designed 4 axilenses each has different parameters. In this paper we present our results and make comparison with that in ref. [1]. The properties of binary axilens such as the focal depth, the lateral resolution and the intensity distribution along axis is discussed.     

圆锥透镜对倾斜球面波光束的衍射模式

由于球面波入射圆锥透镜所产生的出射光束具有焦深长和中心光斑直径较小的特点,适合激光通信以及长距离测量.在实际使用中,入射球面波很可能与圆锥透镜的光轴发生倾斜.研究了圆锥透镜对倾斜球面波光束的衍射特性,通过基尔霍夫衍射理论以及稳相法分析,分析了其径向衍射光场分布形式,并用计算机进行了仿真.使用了半径为15 mm、底角为1°的圆锥透镜进行实验,并对仿真结果进行了验证.仿真和实验证明,减小入射球面波曲率半径、出射光束传输距离和入射光束倾斜角都可以减弱入射光束倾斜对衍射图的影响.     

产生不同类型局域空心光束的可拆式组合轴棱锥

提出一种产生尺寸可调局域空心光束的新型光学元件——可拆式组合轴棱锥,这种新型光学元件是在传统轴棱锥的中部沿其轴线方向贯通开设一圆孔,在圆孔内嵌设一第二轴棱锥组成。通过更换不同底角的第二轴棱锥(或第一轴棱锥),可形成不同尺寸的单个局域空心光束或周期性局域空心光束。从几何光学出发分析了产生局域空心光束的原理,计算了局域空心光束的相关参量。由衍射积分理论分析和模拟了新型光学元件的光强分布特性。几何光学和衍射理论所得分析结果基本吻合。     

Fresnel biprism as a 1D refractive axicon

Fresnel biprism is a one dimensional refractive element that has a lateral linear phase. Having been considered this element as a refractive axicon, its focal depth was evaluated theoretically and experimentally by means of Fresnel–Kirchhoff integral. It is shown that its focal length is a function of its refractive index and its apex angle. Experimental results are in very good agreement with theoretical work.     

梯度轴棱锥产生单个Bottle beam

首次提出一种新的梯度轴棱锥模型,这种梯度轴棱锥在传统的轴棱锥基础上,将轴棱锥顶点的锥角设计成具有一定的梯度.平面波入射到这种梯度轴棱锥,其衍射场会形成两个区域的Bessel光,并且在这两个Bessel光之间形成一个Bottle beam（局域空心光束）.由于Bottle beam具有三维封闭的空心区域和极高的强度梯度,可用作激光导管、光镊和光学扳手等,在生命科学和纳米科技中有重要应用.从几何光学角度分析了梯度轴棱锥形成单个Bottle beam的原理,由衍射及相干理论,分析和模拟了纵向剖面光强分布和横截面光强分布.研究结果对梯度轴棱锥的设计和应用具有指导意义. 关键词： 梯度轴棱锥 Bottle beam 轴棱锥 Bessel光     

Generation of sub wavelength super-long dark channel using high NA lens axicon

We investigate the focusing properties of a double-ring-shaped azimuthally polarized beam by a high numerical aperture (NA) lens axicon based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal hole of 0.5λ having large uniform focal depth of 48λ without any annular aperture. We also observed that the distribution of the total intensity near the focus has little variation with the degree of truncation β of the incident beam by the pupil. The authors expect such a super-long dark channel may find applications in optical, biological, and atmospheric sciences.     

Focusing properties of hyperbolic-cosine-Gaussian beams combining a helical axicon

Focus shape plays an important role in many optical systems, and has attracted much attention. In this article, the focusing properties of hyperbolic-cosine-Gaussian (cosh-Gaussian) beams through a helical axicon were investigated theoretically. Results show that intensity distribution in focal region can be altered considerably by the decentered parameter of cosh-Gaussian beam, axicon parameter and topological charge of the helical axicon. Many novel focal pattern may occur, including annular focus, rectangular focal shape, multiple-peak focal pattern. And in order to show the possible applications of these alter focal pattern, some optical gradient force distributions were also calculated and illuminated.     

Tight focusing of circularly polarized beam over high NA lens axicon with a diffractive optical element

We propose to use diffractive optical element in combination with high NA lens axicon to achieve a high depth of focus when illuminated by a circularly polarized beam. With this kind of system, the focal depth is increased to 12.816λ and the magnetic spot size is reduced to 0.3764λ. However, in the conventional lens with same NA, the FWHM of the magnetic spot is found to be 0.4308λ and its corresponding magnetization depth is only 0.888λ. The author expects that such a high focal depth strong longitudinal magnetic field with large magnetization depth can be widely used in high density magneto optic recording, laser machining, laser cutting and the scanning near-field magnetic microscope.     

相位光阑对光学系统中焦深的影响

焦深在高密度光盘存储系统中具有十分重要的作用,大焦深可以使调焦伺服系统容易跟踪盘面。采用标量衍射理论和基于德拜近似条件的矢量衍射理论,分别在低数值孔径和高数值孔径两种情况下,系统研究相位光阑对聚焦光学系统的轴向光强分布和焦深的影响。研究结果表明：相位光阑对光学系统的焦深影响很大,高数值孔径系统中,选择适当的相位光阑几何尺寸可以使焦深提高约6倍。