波前相位调控的激光束聚焦特性研究

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摘要

波前相位调节技术在理论上和实际应用中都引起了极大的关注。波前相位调

节技术为光束优化和超越经典的衍射极限提供了一种方法，在激光测量分析、光存

储、显微光学、光学微操纵等领域中有着广泛的应用。例如，在激光测量分析系统和

显微系统中，利用相位调节可以调节焦深和焦斑大小，便于系统设计和实现；在光存储

系统中，大焦深可以降低伺服系统跟踪和探测器机械定位难度，小焦斑可提高光存

储密度；另外，自 Ashkin 开发光镊技术以来，光镊技术得到了迅速的发展，促进

了很多领域快速发展，特别是在生命科学领域，吸引了大量的研究人员，如何增

加光镊装置的有效性、灵活性和可控性一直是研究热点，波前相位调节技术由于

其低成本、高灵活性和可控性而倍受瞩目。

本文主要研究了几种相位板的参数变化引起激光束聚焦特性的变化，讨论焦

点区域的光强分布、焦移、焦深及光梯度力分布等聚焦光学性质随相位板各参数

的变化规律。在以下几个方面取得了有价值的研究成果：

首先采用标量衍射理论，系统研究了同轴分区相位板各参数变化对双曲余弦

高斯光束焦点区域光强分布的影响。相位板由三个同心圆域组成：中心圆区，内

圆环，外圆环。其相位变化分别是 0，



，0，即内圆环的相位变化是可调的。模

拟结果表明焦点区域聚焦特性的变化由各区域的半径和相位变化量的改变而引

起。研究了此种相位板引起的焦深随参数的变化规律和焦深变化过程中焦裂发生

及焦点合并的规律：增大内圆环的外半径，焦深沿轴向变大，相位板可以调节焦

深，在适当选择参数下，可增大焦深 6 倍。当内圆环的外半径增大，焦点会变宽

再破裂成两个，这两个焦点间距离随内圆环的外半径的改变而变化。随着内圆环

的外半径的增大，焦深先增大再减小三次，因此有三个焦深峰值，三个焦深峰值

的位置随着偏心参数的减小而向小半径处移动，同时峰值的大小也减小，当内圆

环的外半径对应的汇聚角接近 arcsin(NA)时，两个强度峰值重叠合并为一个强度

峰值，此时出现最大焦深。内圆环的相位变化也影响焦深的大小，当相位变化



为



时，焦深的变化效果达到最大值。研究了此种相位板引起的焦移和焦点跳跃现象：

当相位板的几何参数选定后，调节环形区域相位可以产生有规律的焦移。强度峰

值往远离光阑的方向移动并随着内圆环相位变量的增大快速减小，同时在焦点附

近出现一个新的峰值，并在与原来峰值同一方向上移动，其强度迅速增大并成为

最大强度峰值，这表明发生了焦移。当相位变化量达到



时，相位的增加只是改变

了峰值移动的方向。可调控的焦移和焦开关可被应用于生成可控制光镊。研究了

此种相位板参数变化引起的焦点区域的梯度力变化：相位板可以调节焦点区域梯

度力，通过改变相位板各区域的半径的大小，可以改变光梯度力分布形式，同时

会出现多个光陷阱，光陷阱的形状也会发生非常明显的变化，改变相位板的相位

变换量，可以使光陷阱移动，这种相位板可用于构成可控光镊。

其次，在比较标量衍射理论和矢量衍射理论的适应范围的基础上，用基于德

拜近似的矢量衍射理论分析了带有相位拓朴数的圆形及环形相位板调控高斯光束

聚焦特性及形成环形焦斑和双环形焦斑的光强分布特征，分析了相位拓朴数对焦

点区域光场强度分布的影响。研究了带有相位拓朴数环形相位板的拓朴数及环形

区域相对半径的变化引起的焦点区域的梯度力变化形式，当圆环区域相位以一定

拓扑数呈现拓扑变化时，相位板可以调节光学系统焦点区域的光梯度力分布。在

改变相位板几何尺寸或相位变化的拓扑数时，一些奇特的光梯度力分布会出现，

形成有趣的光陷阱，例如，三角形、四边形、五边形和六边形光陷阱。因此，可

以通过调节相位板拓朴数及相对半径的变化来调节焦点区域的梯度力变化形式，

形成各种非常有规则的几何形状的光镊。

再次，采用基于德拜近似条件的矢量衍射理论，分别在不同数值孔径聚焦系

统下，研究了非螺旋型相位板将线性相位变化引入高斯光束时，相位变化引起的

焦点区域的光强变化，并且改变相位变化方向及速率可调节焦点区域光强分布形

状。且在低数值孔径下产生光旋涡。在高数值孔径下发生焦移，焦裂，焦点跳跃

等现象。

最后，分析了圆柱形矢量光束在高数值孔径系统中的聚焦特性。并比较了均

匀偏振光与圆柱形矢量光束的高数值孔径聚焦性质的异同。把偏振旋转和相位变

换结合设计成三区域偏振旋转相位板，通过模拟计算讨论其相位改变量和偏振旋

转角的改变对圆柱形矢量光束的聚焦特性调制效应及梯度力分布形式的影响。模

拟结果表明：同心分区相位板各部分的半径、相移和偏振旋转角的改变调制了圆

柱形矢量光束的波前相位和偏振分布，焦点区域的光强度分布也会发生改变，光

梯度力方向及大小也明显变化，会产生许多可控的梯度力分布模式。这些结果表

明偏振旋转相位板对圆柱形矢量光束的调制效应，可以用来构成可调控光镊，实

现对微粒的收集、分离和合并。

关键词：相位调制聚焦特性焦深焦移梯度力

III

ABSTRACT

Effect of the phase plate in focusing optical systems attracts much attention for

both theoretical and practical reasons. From a theoretical viewpoint, the fabrication

methods of the phase mask offers a strategy to optimize beams and overcome the limits

of diffraction. From a practical perspective, there are numerous applications that benefit

from it including photolithography, confocal scanning microscopy, optical storage,

Optical manipulation, etc.

We investigated the effect of phase plates in focusing optical system. Some results

are shown as follow:

Focusing properties of Hyperbolic-Cosine-Gaussian beam induced by a phase plate

were investigated. The pure phase apodizer consists of three concentric zones: center

circle zone, inner annular zone and outer annular zone, and the phase variance of inner

annular zone is adjustable. Results show that for certain radii of zones, increase the

phase variance of the inner zone, intensity peak moves far from optical aperture and

then shrinks sharply. Simultaneously, one new intensity peak occurs near focal spot and

then becomes intensity maximum peak, tunable focal shift companied with focal switch.

Decrease the phase variance may change the move direction of the focal shift. In

addition, the distance between the two intensity peaks can be altered by decentered

parameter of the beam, increase and then decreases with increasing decentered

parameter. The tunable focal shift is also discussed to construct controllable optical

tweezers.When the geometric parameters are chosen, many interesting phenomena

occur by altering the phase shift of inner annular portion. The focal shift changes

regularly and the focal switch may accompany. Focal shift can be used to construct

controllable optical tweezers. And focal shift and focal switch can construct

transportation band for micro particles and realize transportation and manipulation.

Focal splitting and focal depth of hyperbolic-cosine-Gaussian beams induced by

the phase apodizer is also investigated. Numerical simulations show that the evolution

of the focal shape is altered considerably by changing the radii of zones and the

decentered parameters in cosh parts of the beam. Increase inner radius of the outer

annular zone, focal spot broadens along optical axis, splits into two peaks, then the two

peaks combine back into one peak. In this process, the focal depth increases and then

decreases three times, so three focal depth peaks occur. And the distance of the two

peaks for bigger radius is very small. With decreasing decentered parameters in cosh

part of the beam, position of the three focal depth peaks shift toward to small radius,

and the peak values also fall simultaneously. With high numerical aperture, the vector

diffraction theory is used to study the effect of phase plate on intensity distribution in

axial direction. In high numerical aperture system, the focal depth increases three times

by adjusting geometric parameters. Under certain geometric parameters, the focal depth

can also increases 6 times. However, when phase plate is used to alter focal depth, the

care must be put on focal split.

The evolution of the gradient force pattern of hyperbolic-cosine-Gaussian beams

induced by the phase plate is numerically investigated. The results show that the

proposed plate may induce tunable gradient force on the particles in focal region. The

optical trap shape is tunable obviously and multiple traps may occur with changing

geometrical parameters of the phase plate. Optical trap shift may be induced by

changing the phase variance of the inner annular zone portion. The phase plate may be a

very promising method of transporting trapped particles and can be used to construct

controllable optical tweezers.

Vector diffraction theory is employed to investigate the focusing properties of the

Gaussian beam induced by phase plate with topological charge.The phase plate may

alter the wavefront phase of an incoming beam by topological charge. Both the circular

phase distribution and the annular phase distribution plates are investigated. Numerical

simulations show that the focal intensity distribution depends on topological charge.

With changing topological charge, focal intensity distribution may evolve into ring

shape, and some novel focal spots may occur. Focal intensity distribution evolving

process with integer topological charge differs considerably from that with fraction

topological charge. When the concentric annular phase plate is put in laser path, the

focal intensity distribution depends on both the inner radius and topological charge. For

small inner radius of the phase plate, doughnut shape focal pattern occurs. With

increasing inner radius, the diameter of the doughnut focal pattern decreases, and

doughnut shape disappears slowly in some cases. The evolution of gradient force

pattern induced by an annular phase distribution plate is numerically investigated in this

paper. Numerical simulations show that the proposed plate may induce the tunable

gradient force on the particles in the focal region. By adjusting the geometrical

parameters or changing the topological charge of the phase-shifting plate, some novel

trap patterns may occur, such as triangle shape trap, quadrangle shape trap, pentagon

shape trap, hexagon shape trap, and the shape of optical trap changes very considerably.

Therefore, the phase plate may be very advantageous for constructing tunable optical

traps. The method is more versatile in that it allows precise control of the parameters

and the possibility of generating specific patterns of optical vortices. The gradient force

pattern focal intensity distribution depends on both the annular width and topological

charge.

Nonspiral plate is investigated numerically by vector diffraction theory to observe

focusing properties of Gaussian beams. Both the low and high numerical-aperture

optical systems are considered in the investigation. It is found that the parameter of

numerical-aperture and phase vary rate of the phase plate influence focal intensity

distribution considerably. When nonspiral plate is used to provide linear phase variation

on one half of Gaussian beam, it may adjust focal spot considerably and conveniently

and introduce phase singularity into Gaussian beam, Changing vary rate of phase plate

or the parameter of numerical-aperture can alter optical intensity distribution, some

novel focal spots and focal switch may occur. Varying direction of phase also affects

focus shape.

The focusing properties in focal region of cylindrical vector beams through a

concentric zones phase plate is investigated theoretically. Numerical simulations show

that the evolution of the focal shape is very considerable by changing the radius, phase

shift and polarization rotation angle of each section portion of the vector beam.

Consequently, the focus shape will change.Which shows that the cylindrical vector

beam can be used to construct controllable optical tweezers.

The optical gradient force patterns in focal region of polarized is also investigated.

Numerical simulations show that the evolution of the focal shape is very considerable

by changing the radius, phase shift and polarization rotation angle of each section

portion of the vector beam. Consequently, the optical gradient force patterns will change.

There by, some interesting optical trap patterns may occur, which shows that polarized

beams can be used construct controllable optical tweezers.

Keywords: Phase plate focusing properties focal shift focal depth

gradient force

中文摘要

ABSTRACT

第一章绪论 ....................................................... 1

§1.1 激光聚焦特性研究概述 ........................................1

§1.1.1 焦移的研究历史与现状 ....................................1

§1.1.2 焦深的研究概述 ..........................................3

§1.2 光镊技术 ....................................................4

§1.2.1 光镊技术的理论研究 ......................................5

§1.2.2 光镊技术的发展 ........................................ 11

§1.2.3 国内光镊技术概况 .......................................14

§1.3 波前相位调控的研究概况 .....................................14

§1.4 本文的研究工作 .............................................15

第二章相位调制双曲余弦高斯光束聚焦特性研究 ....................... 18

§2.1 标量衍射理论 ...............................................18

§2.2 光学系统及原理 .............................................19

§2.3 相位调制双曲余弦高斯光束的焦移 .............................21

§2.4 相位调制双曲余弦高斯光束的焦深的变化 ...................... 28

§2.5 相位调制双曲余弦高斯光束的梯度力的变化 .....................35

§2.5.1 光梯度力 ...............................................35

§2.5.2 模拟结果与分析 .........................................36

§2.6 本章小结 .....................................................42

第三章带有拓朴数的相位板调制高斯光束的聚焦特性 ................... 44

§3.1 矢量衍射理论与标量衍射理论的适用范围 .......................45

§3.2 基于德拜近似的矢量衍射理论 .................................45

§3.3 光学系统及原理 .............................................49

§3.4 结果与讨论 .................................................52

§3.4.1 带有相位拓朴数圆形相位板调控高斯光束聚焦特性 ...........52

§3.4.2 带有相位拓朴数环形相位板调控高斯光束聚焦特性 ...........56

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摘要：

I摘要波前相位调节技术在理论上和实际应用中都引起了极大的关注。波前相位调节技术为光束优化和超越经典的衍射极限提供了一种方法，在激光测量分析、光存储、显微光学、光学微操纵等领域中有着广泛的应用。例如，在激光测量分析系统和显微系统中，利用相位调节可以调节焦深和焦斑大小，便于系统设计和实现；在光存储系统中，大焦深可以降低伺服系统跟踪和探测器机械定位难度，小焦斑可提高光存储密度；另外，自Ashkin开发光镊技术以来，光镊技术得到了迅速的发展，促进了很多领域快速发展，特别是在生命科学领域，吸引了大量的研究人员，如何增加光镊装置的有效性、灵活性和可控性一直是研究热点，波前相位调节技术由于其低成本、高灵活性...

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