CN102147539B

CN102147539B - Method for generating one-dimensional periodic structure light field based on pure-phase type liquid crystal spatial light modulator

Info

Publication number: CN102147539B
Application number: CN2011100806669A
Authority: CN
Inventors: 赖天树; 陈科; 李佳明
Original assignee: Sun Yat Sen University
Current assignee: Sun Yat Sen University
Priority date: 2011-03-30
Filing date: 2011-03-30
Publication date: 2012-06-27
Anticipated expiration: 2031-03-30
Also published as: CN102147539A

Abstract

The invention discloses a method for generating a one-dimensional periodic structure light field based on polarization modulation of a single light beam. An experimental device is shown in a figure of an abstract. A pure-phase type liquid crystal spatial light modulator 3 adjusts an incident ray polarized light, so that a one-dimensional circular polarization sinusoidal periodically-distributed light field can be generated. The light field passes through a polarizing film 4, so that a one-dimensional strength sinusoidal periodically-distributed light field can be generated. Compared with the conventional method for generating the one-dimensional strength sinusoidal periodically-distributed light fields by coherent superposition of two light beams, the method provided by the invention has the advantages that: the experimental device is easy; the generated periodic structure light fields are stable; and a computer is easy to control, and parameters are easy to adjust.

Description

A method for generating a one-dimensional periodic structured light field based on a phase-only liquid crystal spatial light modulator

技术领域 technical field

本发明涉及一种一维周期结构的光场产生方法。其特点是利用纯相位型空间光调制器直接调制光束的偏振态分布，产生强度和圆偏振度一维周期变化的光场。在半导体输运动力学测量和微结构光刻制做领域具有重要应用价值。The invention relates to a method for generating a light field of a one-dimensional periodic structure. It is characterized in that the polarization state distribution of the light beam is directly modulated by a pure phase-type spatial light modulator, and a light field with one-dimensional periodic changes in intensity and degree of circular polarization is generated. It has important application value in the fields of semiconductor transport dynamics measurement and microstructure lithography.

背景技术 Background technique

一维周期结构光场在现代科学技术领域具有广泛的应用价值。传统的产生方法是使用两束非平行传播的线偏振光束的相干迭加，在交迭区域产生一维周期结构的光场，而周期由两束光的夹角决定。两束偏振平行的光迭加能够产生光强度一维周期变化的光场。这种周期光场在一维正弦型光栅的光刻制作、半导体中电子双极输运动力学测量方面得到应用。两束偏振正交或垂直的光迭加能够产生圆偏振度或偏振态一维周期变化的光场。这种周期光场在半导体中电子自旋输运动力学测量方面得到应用。然而，这种双光束相交迭加产生方法的缺点是明显的，需要两束光，增加了光路的复杂性。此外，产生的周期结构容易受到两束光之间的光程差波动而漂动。同时，对于飞秒脉冲激光束，还需要精确调节两束光的光程，使之几乎相等，因为容许的光程误差仅几十微米。这些缺点，限制了这种双光束相干迭加产生一维周期结构光场方法的广泛应用，增加了设备的复杂性和实验操作难度。因而，发明新的、简单的一维周期光场产生方法是非常必要的。One-dimensional periodic structured light field has wide application value in the field of modern science and technology. The traditional generation method is to use the coherent superposition of two non-parallel propagating linearly polarized beams to generate a one-dimensional periodic structure light field in the overlapping region, and the period is determined by the angle between the two beams. The superposition of two beams of parallel polarized light can generate a light field with one-dimensional periodic variation of light intensity. This periodic light field is applied in the lithographic fabrication of one-dimensional sinusoidal gratings and the measurement of electron bipolar transport dynamics in semiconductors. The superposition of two beams of orthogonally polarized or vertically polarized light can generate a light field with one-dimensional periodic changes in the degree of circular polarization or polarization state. This periodic light field has applications in the measurement of electron spin transport dynamics in semiconductors. However, the shortcoming of this double-beam intersection and superimposition method is obvious, requiring two beams, which increases the complexity of the optical path. Furthermore, the resulting periodic structure is susceptible to drift by fluctuations in the optical path difference between the two beams. At the same time, for the femtosecond pulsed laser beam, it is also necessary to precisely adjust the optical path of the two beams to make them almost equal, because the allowable optical path error is only tens of microns. These shortcomings limit the wide application of this method of coherently superimposing two beams to generate a one-dimensional periodic structured light field, and increase the complexity of the equipment and the difficulty of experimental operation. Therefore, it is very necessary to invent a new and simple one-dimensional periodic light field generation method.

发明内容 Contents of the invention

本发明发展了一种简单的、基于纯相位型液晶空间光调制器调制单光束产生一维周期结构光场的方法。产生方法的原理如图1所示。与目前报道的双光束相干迭加产生一维周期结构光场方法对比，本发明的新方法具有如下四个优点。第一，实验装置结构简单；因为只需要一束光。第二，产生的一维周期结构光场稳定；因为不存在双光束相干迭加中两束光的光程抖动引起的一维周期结构漂动。第三，不需要光程匹配调节。即使对飞秒激光脉冲，也不涉及光程匹配调节问题，因为使用单光束。第四，计算机控制，容易改变周期光场的参数。The invention develops a simple method for generating a one-dimensional periodic structured light field by modulating a single light beam based on a pure phase liquid crystal spatial light modulator. The principle of the generation method is shown in Figure 1. Compared with the currently reported method of coherently superimposing two beams to generate a one-dimensional periodic structured light field, the new method of the present invention has the following four advantages. First, the experimental setup is simple in structure; because only one beam of light is needed. Second, the generated one-dimensional periodic structure light field is stable; because there is no one-dimensional periodic structure drift caused by the optical path jitter of the two beams in the coherent superposition of the two beams. Third, no optical path matching adjustment is required. Even for femtosecond laser pulses, there is no optical path matching adjustment problem involved, because a single beam is used. Fourth, computer control makes it easy to change the parameters of the periodic light field.

本发明的光学原理如图1所示。其关键特征在于引入纯相位型液晶体空间光调制器3。众所周知，纯相位型液晶空间光调制器(PPLCSLM)中液晶分子同向排列，并且液晶分子具有双折射效应。设正入射穿过PPLCSLM的光，其寻常和非寻常光分量的偏振方向分别沿X，Y方向。非寻常光的折射率n_e随施加电压而变化，而寻常光的折射率n₀不随施加电压而变化。所以，当在PPLCSLM的某一空间单元或象素上施加电压V时，通过该象素的光的非寻常和寻常光分量之间的相位差φ为：The optical principle of the present invention is shown in FIG. 1 . Its key feature is the introduction of a pure phase liquid crystal spatial light modulator 3 . It is well known that the liquid crystal molecules in the phase-pure liquid crystal spatial light modulator (PPLCSLM) are aligned in the same direction, and the liquid crystal molecules have a birefringence effect. Assuming that the light that is normally incident through the PPLCSLM, the polarization directions of its ordinary and extraordinary light components are along the X and Y directions, respectively. The refractive index _ne of extraordinary light changes with the applied voltage, while the refractive index _n0 of ordinary light does not change with the applied voltage. Therefore, when a voltage V is applied to a certain spatial unit or pixel of the PPLCSLM, the phase difference φ between the extraordinary and ordinary light components of the light passing through the pixel is:

$φ φ ((x x,, y the y,, V V)) = = \frac{22 π π}{λ λ} [[{n no}_{e e} ((x x,, y the y,, V V)) - - {n no}_{00}]] d d - - - - - - ((11))$

式中x，y为象素单元的位置坐标，V为该象素上的施加电压，也是坐标x，y的函数，必要时可以明确写为V(x，y)，λ为光波长，d为液晶层的厚度。In the formula, x, y are the position coordinates of the pixel unit, V is the applied voltage on the pixel, which is also a function of the coordinates x, y, and can be clearly written as V(x, y) if necessary, λ is the wavelength of light, d is the thickness of the liquid crystal layer.

如图1所示，当起偏器2的偏振方向与Y轴成45度角，而其透射的线偏振光的振幅为A时，此线偏振光透过PPLCSLM后，对应坐标为(x，y)的象素的透射光场E可表示为：As shown in Figure 1, when the polarization direction of the polarizer 2 forms an angle of 45 degrees with the Y axis, and the amplitude of the linearly polarized light transmitted by it is A, after the linearly polarized light passes through the PPLCSLM, the corresponding coordinates are (x, The transmitted light field E of the pixel in y) can be expressed as:

$E E. ((x x,, y the y,, V V)) = = (\begin{matrix} {E E.}_{x x} \\ {E E.}_{y the y} \end{matrix}) = = \frac{A A}{\sqrt{22}} (\begin{matrix} 11 \\ {e e}^{iφ iφ ((x x,, y the y,, V V))} \end{matrix}) - - - - - - ((22))$

式中E_x，E_y分别表示光场的X，Y分量。In the formula, E _x and E _y respectively represent the X and Y components of the light field.

上式描述一个任意的光偏振态。通过控制施加电压V(x，y)，使相位差φ(x，y，V)分别等于0，π/2，π和3π/2，则可以分别对应地获得线偏振，右旋圆偏振，旋转90度的线偏振和左旋圆偏振光。显然，相位φ(x，y，V)变化2π，这些偏振态重复出现。所以，控制不同象素的施加电压V(x，y)，使φ(x，y，V)随坐标x周期变化，则可以产生偏振态一维周期变化的光场。The above equation describes an arbitrary polarization state of light. By controlling the applied voltage V(x, y) so that the phase difference φ(x, y, V) is equal to 0, π/2, π and 3π/2 respectively, linear polarization and right-handed circular polarization can be obtained correspondingly, Linearly polarized and left-handed circularly polarized light rotated 90 degrees. Clearly, the phase φ(x, y, V) varies by 2π and these polarization states repeat. Therefore, by controlling the applied voltage V(x, y) of different pixels so that φ(x, y, V) changes periodically with the coordinate x, a light field with one-dimensional periodic change of the polarization state can be generated.

附图说明 Description of drawings

图1一维周期结构光场产生装置原理图Figure 1 Schematic diagram of one-dimensional periodic structured light field generating device

图1中，1为入射光束；2为偏振片，用于将入射光束1转换为线偏振光；如1已是线偏振光，则应将其偏振方向调节到与2的偏振方向一致，以便光能量损失最小；2中斜线表示容许通过的线偏振方向，与Y轴成45度角；3为纯相位型液晶空间光调制器，由计算机控制；4为偏振片，其中斜线表示偏振方向，与Y轴成45度角；虚线框表示4是可以依据产生不同性质的一维周期结构光场需要而增减的。In Figure 1, 1 is the incident light beam; 2 is a polarizer, which is used to convert the incident light beam 1 into linearly polarized light; if 1 is already linearly polarized light, its polarization direction should be adjusted to be consistent with that of 2, so that The light energy loss is the smallest; the oblique line in 2 indicates the linear polarization direction that is allowed to pass through, and is at an angle of 45 degrees to the Y axis; 3 is a pure phase liquid crystal spatial light modulator, controlled by a computer; 4 is a polarizer, and the oblique line indicates polarization The direction is at an angle of 45 degrees to the Y-axis; the dotted line box indicates that 4 can be increased or decreased according to the needs of generating a one-dimensional periodic structured light field with different properties.

具体实施方式 Detailed ways

依据上述原理，本发明已具体实施了两个实例，分别产生一维强度正弦周期分布和一维圆偏振度正弦周期分布光场。According to the above principles, the present invention has concretely implemented two examples, respectively generating a one-dimensional intensity sinusoidal periodic distribution light field and a one-dimensional circular polarization degree sinusoidal periodic distribution light field.

实例一一维圆偏振度正弦周期分布光场产生Example 1 One-dimensional circular polarization sinusoidal periodic distribution light field generation

实验装置原理图如图1所示，但偏振片4需拆除。通过控制PPLCSLM上各列象素上的电压随x周期变化，就能产生沿X轴圆偏振度正弦周期分布的光场。The schematic diagram of the experimental device is shown in Figure 1, but the polarizer 4 needs to be removed. By controlling the voltage on each row of pixels on the PPLCSLM to vary with the x period, a light field with a sinusoidal periodic distribution of the degree of circular polarization along the X axis can be generated.

假设要产生周期为Λ个象素宽度的一维圆偏振度正弦周期分布的光场，而对应方程(1)的相位差为0和2π的施加电压分别为V₀和V_2π，则当通过计算机，向PPLCSLM中各象素列上施加如下电压Assuming that a light field with a one-dimensional circular polarization degree of sinusoidal periodic distribution with a period of Λ pixel width is to be generated, and the applied voltages corresponding to equation (1) with a phase difference of 0 and 2π are V ₀ and V _2π respectively, then when passed Computer, apply the following voltage to each pixel column in PPLCSLM

$V V ((x x,, y the y)) = = {V V}_{00} + + \frac{{V V}_{00} - - {V V}_{22 π π}}{Λ Λ} RMod RMod ((\frac{x x}{Λ Λ})) - - - - - - ((33))$

时，各象素列产生的相位差为：When , the phase difference generated by each pixel column is:

$φ φ ((x x,, y the y,, V V)) = = \frac{22 π π}{Λ Λ} RMod RMod ((\frac{x x}{Λ Λ})) - - - - - - ((44))$

式中函数RMod()表示两整数相除，取余数。引入此函数是考虑到液晶的双折射相位差的电压可调范围有限，所以，本实例中只使用0-2π范围的相位差；x＝0，1，…，M-1，为PPLCSLM阵列的列指标；M为PPLCSLM中象素阵列的列数。The function RMod() in the formula means that two integers are divided and the remainder is taken. This function is introduced in consideration of the limited voltage adjustable range of the birefringent phase difference of the liquid crystal, so only the phase difference in the range of 0-2π is used in this example; x=0,1,...,M-1, is the PPLCSLM array Column index; M is the column number of the pixel array in PPLCSLM.

此时透过PPLCSLM的光场由方程(2)描述。此偏振态的圆偏振度P为：At this time, the light field passing through the PPLCSLM is described by equation (2). The degree of circular polarization P of this polarization state is:

P(x，y)＝sin(φ(x，y，V)) (5)P(x,y)=sin(φ(x,y,V))

因为相位差φ由方程(4)给出，是x坐标的线性函数；所以，方程(5)表明光场的圆偏振度随x正弦周期变化，即产生了一维圆偏振度正弦周期分布的光场。这样的光场在半导体中电子自旋输运动力学测试中具有重要应用价值。它激发半导体，能够产生瞬态自旋光栅。而目前的实验中，是使用两束偏振正交的线偏振光迭加产生这样的光场，导致实验装置复杂。Because the phase difference φ is given by Equation (4), which is a linear function of the x coordinate; therefore, Equation (5) shows that the degree of circular polarization of the light field changes with the sinusoidal period of x, that is, a one-dimensional distribution of the degree of circular polarization sinusoidal period is produced. light field. Such an optical field has important application value in testing the dynamics of electron spin transport in semiconductors. It excites semiconductors, capable of producing transient spin gratings. However, in the current experiment, two beams of orthogonally polarized linearly polarized light are superimposed to generate such a light field, which makes the experimental device complicated.

实例二一维强度正弦周期分布光场产生Example 2 One-dimensional intensity sinusoidal periodic distribution light field generation

实验装置原理图如图1所示。现在需要保留偏振片4，并且它的偏振方向与Y轴成45度角。透过空间光调制器3的光场由方程(2)描述。此光场透过4后，可表示为：The schematic diagram of the experimental device is shown in Figure 1. Now the polarizer 4 needs to be kept, and its polarization direction is at an angle of 45 degrees to the Y axis. The light field transmitted through the spatial light modulator 3 is described by equation (2). After this light field passes through 4, it can be expressed as:

E_P(x，y)＝E_x(x，y)sin45+E_y(x，y)cos45 (6)E _P (x, y) = E _x (x, y) sin45 + E _y (x, y) cos45 (6)

式中EP为透过偏振片4的光场；Ex，Ey分别表示入射光场的x，y分量，它们由方程(2)给出。Where EP is the light field passing through the polarizer 4; Ex and Ey respectively represent the x and y components of the incident light field, which are given by equation (2).

将方程(2)中各分量代入(6)式得：Substitute the components in equation (2) into equation (6) to get:

${E E.}_{P P} ((x x,, y the y)) = = \frac{A A}{\sqrt{22}} [[sin sin 4545 + + {e e}^{iφ iφ ((x x,, y the y,, V V))} cos cos 4545]] = = \frac{A A}{22} [[11 + + {e e}^{iφ iφ ((x x,, y the y,, V V))}]] - - - - - - ((77))$

光强度为：The light intensity is:

${I I}_{P P} ((x x,, y the y)) = = {| | {E E.}_{P P} ((x x,, y the y)) | |}^{22} = = \frac{{I I}_{00}}{22} [[11 + + cos cos ((φ φ ((x x,, y the y,, V V))]] - - - - - - ((88))$

式中I₀＝A²。In the formula, I ₀ =A ² .

当PPLCSLM上各象素列施加电压由方程(3)决定时，各象素的相位差如方程(4)所示。这时，相位差φ(x，y，V)是x坐标的线性函数；所以，方程(8)表明光场的强度随x正弦周期变化，即产生了一维强度正弦周期分布的光场。这样的光场在正弦周期光栅的光刻制作和半导体中电子双极输运动力学测量中都具有重要应用价值。而目前的实验测试中，是使用两束偏振平行的线偏振光相交迭加产生这样的光场，导致实验装置复杂。When the voltage applied to each pixel row on the PPLCSLM is determined by equation (3), the phase difference of each pixel is shown in equation (4). At this time, the phase difference φ(x, y, V) is a linear function of the x coordinate; therefore, Equation (8) shows that the intensity of the light field varies with the sinusoidal period of x, that is, a one-dimensional light field with a sinusoidal periodic distribution of intensity is produced. Such an optical field has important application value in the photolithographic fabrication of sinusoidal periodic gratings and in the measurement of electron bipolar transport dynamics in semiconductors. In the current experimental test, such a light field is generated by overlapping and superimposing two beams of parallel polarized linearly polarized light, which makes the experimental device complicated.

Claims

1. A method for generating a one-dimensional periodic structured light field, characterized by using a phase-only liquid crystal spatial light modulator to modulate a single beam instead of the traditional coherent superposition of two beams to generate a stable and easy-to-control one-dimensional periodic structured light field The linearly polarized light beam passes through the phase-only liquid crystal spatial light modulator, and when its plane of polarization forms an angle of 45 degrees with the ordinary polarization direction of the birefringence of the liquid crystal, and applies the voltage described in formula (1) to the pixel column of the liquid crystal spatial light modulator , it can produce a light field with a one-dimensional circular polarization sinusoidal periodic change;

V V ((x x,, y the y)) = = {V V}_{00} + + \frac{{V V}_{00} - - {V V}_{22 π π}}{Λ Λ} RMod RMod ((\frac{x x}{Λ Λ})) - - - - - - ((11))

In the formula, V ₀ and V _2π correspond to the voltages applied when the pixels of the liquid crystal spatial light modulator generate a phase difference of 0 and 2π, respectively; Λ is the number of pixels in the period of the one-dimensional periodic light field; x, y are the pixel units The position coordinates; the function RMod () means that two integers are divided and the remainder is taken.

2. The one-dimensional periodic structure light field generation method described in claim 1 is characterized in that the output light field can produce one-dimensional light intensity after a polarization direction and the liquid crystal ordinary light polarization direction become 45 degree angle polarizers again A light field that varies sinusoidally.