WO2024016450A1 - Method for calculating tight focusing three-dimensional spin density by using mode decomposition of optical system - Google Patents
Method for calculating tight focusing three-dimensional spin density by using mode decomposition of optical system Download PDFInfo
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- the invention relates to the field of optical technology, and in particular to a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system.
- angular momentum is also an important property of light.
- Light has two different types of angular momentum, spin angular momentum and orbital angular momentum, which are respectively related to the circular polarization state and spiral phase of light.
- spin angular momentum causes the particle to spin
- orbital angular momentum causes the particle to rotate around the optical axis. Therefore, spin angular momentum and orbital angular momentum can also be distinguished based on the different mechanical effects they exhibit when interacting with particles.
- the spin angular momentum and orbital angular momentum of light are independent and conserved under free space propagation.
- optical spin-orbit interactions occur under various conditions, such as light-matter interactions in anisotropic media, evanescent waves, scattering, and tightly focused systems.
- the coupling between spin angular momentum and orbital angular momentum is called spin-to-orbit conversion.
- the coupling between the spin angular momentum and the external orbital angular momentum will cause a spin-related displacement, that is, the spin Hall effect.
- the technical problem to be solved by the present invention is to provide a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system that reduces calculation difficulty and shortens calculation time.
- the present invention provides a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, which includes the following steps:
- the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens is:
- C(r′1, r′2) is the 3 ⁇ 3 cross spectral density function on the focal plane of the tight focusing lens
- C′(r 1 , r 2 ) is the cross spectrum of the rear surface of the tight focusing lens.
- r′ 1 and r′ 2 respectively represent the compact
- i represents an imaginary number; f and ⁇ represent compact numbers respectively.
- q 2 (r′, k 1 , k 2 ) is the pulse function of the nonlinear optical system, and is the response of the output point r′ to the pulses of points k 1 and k 2 .
- step S3 includes:
- the cross-spectral density function at the light source is expressed in the form of mode decomposition, as follows:
- C(r′, r′) is the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens; Represents the response of output point r′ to a single pulse of input point k.
- the integral term in the absolute value in formula (12) is equivalent to the output signal of the linear system.
- the three-dimensional spin density is expressed by the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens as:
- the present invention also provides an electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor.
- the processor executes the program, the steps of any one of the above methods are implemented. .
- the present invention also provides a computer-readable storage medium on which a computer program is stored.
- a computer program is stored on which a computer program is stored.
- the invention also provides a system for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, which includes the following modules:
- the equivalent module is used to equate the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system;
- the output signal calculation module is used to calculate the output signal of the nonlinear optical system using the input signal and pulse function of the nonlinear optical system according to the nonlinear system theory and Richard Wolf diffraction theory.
- the output signal of the optical system is expressed as a 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens;
- a mode decomposition module for converting the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems using mode decomposition theory
- the three-dimensional spin density calculation module is used to calculate the three-dimensional spin density represented by the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens according to the definition of spin angular momentum.
- the present invention equates the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system, and calculates the output signal of the nonlinear optical system.
- the output signal is expressed as 3 on the focal plane of the tight focusing lens.
- ⁇ 3 cross spectral density function and then use the mode decomposition theory to convert the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems, and finally obtain a 3 ⁇ 3 cross spectral density function on the focal plane of the tight focusing lens
- Three-dimensional spin density represented by the spectral density function Three-dimensional spin density represented by the spectral density function.
- the invention reduces the calculation difficulty and calculation time of tightly focused spin density and promotes research on optical spin-orbit interaction.
- Figure 1 is a flow chart of a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in a preferred embodiment of the present invention.
- the present invention utilizes the mode decomposition theory of optical systems.
- an optical system illuminated by completely coherent light is called a linear optical system
- an optical system illuminated by partially coherent light is called a nonlinear optical system.
- the relationship between its input signal and output signal can be obtained through simple linear transformation.
- the calculation of its output signal will involve complex integrals and require a lot of calculation time.
- the output signal of the linear optical system is first obtained, and then these output signals are superimposed to obtain the output of the nonlinear optical system. signal, thus reducing the computational difficulty and calculation time of nonlinear optical systems.
- the partially coherent light tight focusing process is a nonlinear optical system.
- the output signal of the tight focusing system is expressed as the superposition of a series of linear signals, and the spin density can be calculated using the output signal. This method reduces the computational difficulty and time of tightly focused spin density and will promote the study of optical spin-orbit interactions.
- the input signal of the nonlinear optical system is the transmittance function determined by the tight focusing lens and polarization state
- the pulse function is determined by the cross-spectral density function C(r 1 , r 2 ) of the light source and the coordinates of the light source surface (x, y) and the wave number space (k x , k y )
- the output signal represents the cross-spectral density function C (r′ 1 , r′ 2 ) at the focal plane.
- the linear optical system only needs to calculate a simple linear transformation, as follows:
- C * (x') represents the output signal of the linear system
- t * (x) represents the input signal
- q (x', x) is the pulse signal of the output point x' at the input point x.
- C(x′) and t(x) represent the output signal and input signal of the nonlinear optical system respectively
- q 2 (x′, x 1 , x 2 ) is the kernel function of the second-order Volterra series ( Volterra kernel), which represents the double-pulse signal of the output point x′ at the input point x 1 and x 2 , that is, the pulse function.
- q 2 (x′, x 1 , x 2 ) is a 6D complex function, which makes the calculation of nonlinear optical systems difficult.
- the nonlinear optical system can be expressed as a series of incoherent superpositions of linear systems through mode decomposition theory, thereby simplifying the above calculations.
- the present invention applies this theory to the calculation of spin density under tight focusing systems.
- the partially coherent light emitted by the light source is a transverse electric field propagating along the z-axis.
- the ensemble average of the cross-spectral density function of this partially coherent light is expressed as:
- U(r 1 ) and U(r 2 ) represent the optical signals (amplitudes) of the two points r 1 and r 2 at the light source respectively, the angle brackets represent the ensemble average, * represents the complex conjugate, and T represents the transformation of the matrix.
- the relationship between the optical signals on the front and rear surfaces of the tight focusing lens is:
- t 0 (r) represents the transmittance function
- U′(r) represents the optical signal on the rear surface of the tightly focused lens
- U(r) represents the optical signal on the front surface of the tightly focused lens
- the first and second matrices on the right side of formula (5) respectively represent the x, y, and z directions of the partially coherent light of radial polarization (RP) and angular polarization (AP) in the space after passing through the tightly focusing lens. Portion size. Therefore, the cross-spectral density function of the back surface of a tight focusing lens is expressed as:
- C (r 1 ′, r 2 ′) is the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens;
- C′ (r 1 , r 2 ) is the cross spectrum of the rear surface of the tight focusing lens Density function;
- r′ 1 and r′ 2 respectively represent the compact
- i an imaginary number;
- f and ⁇ represent respectively The focal length of the tight focusing lens and the wavelength of the partially coherent light emitted by the light source;
- k 1 and k 2 respectively represent the corresponding coordinates of points r 1 and r
- this nonlinear optical system can also be called a bilinear system.
- formula (11) is substituted into the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens to obtain:
- C(r′, r′) is the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens; Represents the response of output point r′ to a single pulse of input point k.
- formula (12) can be considered as a series of impulse responses as The superposition of modular squares of a system of modes.
- ⁇ 0 represents the dielectric constant in vacuum
- ⁇ is the angular frequency of the light source.
- ⁇ n (r′) represents the expansion mode of the cross-spectral density function at the focal plane.
- the components of the spin density in the three directions of space x, y, and z are expressed as:
- the three-dimensional spin density is expressed by the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens as:
- S x (r′), S y (r′), and S z (r′) respectively represent the components of the spin density in the three directions of space x, y, and z; double quotes indicate taking the imaginary part; C yz (r′, r′), C zy (r′, r′), C zx (r′, r′), C xz (r′, r′), C xy (r′, r′) and C yx (r′, r′) is the element in the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens.
- the method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in the present invention is used to calculate the three-dimensional spin density of a radially polarized Gaussian Scher mode beam after being tightly focused.
- the specific calculation process is as follows:
- t 0 (r 1 ) and t 0 (r 2 ) respectively represent the transmittance function of the tight focusing lens to the light source at two points r 1 and r 2 . It is known that the polarization state of the incident light is radially polarized, t 0 (r 1 ) and t 0 (r 2 ) can be expressed as:
- C xx (r′, r′) is the output signal after the nonlinear optical system, that is, the first item in the 3 ⁇ 3 cross-spectral density function matrix of the field.
- the cross-spectral density function at the light source is expressed in the form of mode decomposition as:
- C nxx (r′, r′) is the n-th completely coherent mode decomposed by C xx (r′, r′), F is the Fourier transform symbol, and C nxx (r′, r′) can be Fast calculation of Lieye transform.
- the integral term in the absolute value of formula (29) is the output signal of the linear system with completely coherent light incident, that is, the mode system.
- Formula (29) can be considered as a series of impulse responses as Coherent superposition of modular squares of a system of modes.
- the other eight items of the cross-spectral density function matrix are C xy (r 1 ′, r 1 ′), C xz (r 1 ′, r 1 ′), C yx (r 1 ′, r 1 ′), C yy (r 1 ′, r 1 ′), C yz (r 1 ′, r 1 ′), C zx (r 1 ′, r 1 ′), C zy (r 1 ′, r 1 ′), C zz (r 1 ′, r 1 ′) can be obtained in the same way.
- the spin density component can be obtained:
- the present invention equates the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system, and calculates the output signal of the nonlinear optical system, which is expressed as a 3 ⁇ 3 signal on the focal plane of the tight focusing lens.
- Cross spectral density function, and then use mode decomposition theory to convert the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems, and finally obtain a 3 ⁇ 3 cross spectral density function on the focal plane of the tight focusing lens represents the three-dimensional spin density.
- the invention reduces the calculation difficulty and calculation time of tightly focused spin density and promotes research on optical spin-orbit interaction.
- a preferred embodiment of the present invention also discloses an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor.
- the processor executes the program, it implements what is described in the above embodiment. Method steps.
- a preferred embodiment of the present invention also discloses a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the method described in the above embodiment are implemented.
- the preferred embodiment of the present invention also discloses a system for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, which includes the following modules:
- the equivalent module is used to equate the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system;
- the output signal calculation module is used to calculate the output signal of the nonlinear optical system using the input signal and pulse function of the nonlinear optical system according to the nonlinear system theory and Richard Wolf diffraction theory.
- the output signal of the optical system is expressed as a 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens;
- a mode decomposition module for converting the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems using mode decomposition theory
- the three-dimensional spin density calculation module is used to calculate the three-dimensional spin density represented by the 3 ⁇ 3 cross-spectral density function on the focal plane of the tight focusing lens according to the definition of spin angular momentum.
- the system for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in the embodiment of the present invention is used to implement the aforementioned method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system. Therefore, the specific implementation of the system can be seen
- the foregoing embodiments of a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system therefore, for its specific implementation, refer to the corresponding description of the above method embodiments and will not be introduced here.
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Abstract
A method for calculating tight focusing three-dimensional spin density by using mode decomposition of an optical system. The method comprises: enabling partially coherent light emitted by a light source, a tight focusing lens, and a space behind the tight focusing lens to be equivalent to a nonlinear optical system (S1); calculating an output signal of the nonlinear optical system, the output signal being expressed as a 3×3 cross-spectral density function on a focal plane of the tight focusing lens (S2); by using a mode decomposition theory, converting the output signal of the nonlinear optical system into incoherent superposition of output signals of a series of linear optical systems (S3); and finally obtaining three-dimensional spin density represented by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens (S4). The calculation difficulty and the calculation time for tight focusing spin density are reduced, and the research on the interaction of optical spin orbits is promoted.
Description
本发明涉及光学技术领域,特别涉及一种利用光学***的模式分解计算紧聚焦三维自旋密度的方法。The invention relates to the field of optical technology, and in particular to a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system.
光除了具有线性动量外,角动量也是光的一个重要的性质。光有两种不同类型的角动量,自旋角动量,轨道角动量,它们分别与光的圆偏振态,螺旋相位有关。在过去的几十年的研究中,人们发现光与物质的相互作用时,可以导致线性动量从光转移到物质之间,从而对物质施加力,并使光镊等技术成为可能。当光的角动量与粒子相互作用时,自旋角动量使粒子自转,轨道角动量可以使粒子绕着光轴旋转。因此自旋角动量和轨道角动量也可以依据它们在与粒子相互作用时所展现出的不同的力学效应来区分。光的自旋角动量和轨道角动量作为两个不同的自由度,在自由空间传播下是相互独立和守恒的。事实上,光学自旋轨道相互作用在各种条件下发生,如各向异性介质中的光-物质相互作用、倏逝波、散射和紧聚焦***。自旋角动量与轨道角动量之间得耦合称为自旋到轨道得转换。自旋角动量与外部的轨道角动量之间耦合会出现与自旋相关的位移,即自旋霍尔效应。In addition to linear momentum, angular momentum is also an important property of light. Light has two different types of angular momentum, spin angular momentum and orbital angular momentum, which are respectively related to the circular polarization state and spiral phase of light. In the past few decades of research, it has been discovered that when light interacts with matter, it can cause linear momentum to be transferred from light to matter, thereby exerting a force on matter and making technologies such as optical tweezers possible. When the angular momentum of light interacts with a particle, spin angular momentum causes the particle to spin, and orbital angular momentum causes the particle to rotate around the optical axis. Therefore, spin angular momentum and orbital angular momentum can also be distinguished based on the different mechanical effects they exhibit when interacting with particles. The spin angular momentum and orbital angular momentum of light, as two different degrees of freedom, are independent and conserved under free space propagation. In fact, optical spin-orbit interactions occur under various conditions, such as light-matter interactions in anisotropic media, evanescent waves, scattering, and tightly focused systems. The coupling between spin angular momentum and orbital angular momentum is called spin-to-orbit conversion. The coupling between the spin angular momentum and the external orbital angular momentum will cause a spin-related displacement, that is, the spin Hall effect.
一束光被大数值孔径的透镜聚焦的过程我们称为紧聚焦,在过去的几十年中,紧聚焦光场的特性得到了广泛的研究,并被应用于光学显微镜、捕获和材料加工,因此紧聚焦***下的自旋轨道相互作用得到了人们广泛的关注。2007年,赵等人发现了发现圆偏振光经过紧聚焦后,自旋角动量可以转化为轨道角动量,称为自旋到轨道转换。最近,姚等人发现不携带自旋的涡旋光束经过紧聚焦后,轨道角动量可以转换为纵向的自旋角动量,称为轨道到自旋转换。入射光拓扑、束腰宽度、瞳孔半径与束腰半径的比值等参数对这种轨道到自旋转换的影响已经被大量研究。对紧聚焦自旋密度的计算是这些研究工作的基础,完全相干光紧聚焦后的焦面处的自旋密度分布,只需要计算一个二重积分便可以得到,但是对于部分相干光聚焦后的焦面处的自旋密度分布会涉及一个四重积分增大了计算难度和计算时间,阻碍了对紧聚焦自旋轨道相互作用的研究。The process of focusing a beam of light by a lens with a large numerical aperture is called tight focusing. In the past few decades, the characteristics of a tightly focused light field have been extensively studied and applied to optical microscopy, capture and material processing. Therefore, the spin-orbit interaction in tightly focused systems has received widespread attention. In 2007, Zhao et al. discovered that after tightly focusing circularly polarized light, spin angular momentum can be converted into orbital angular momentum, which is called spin-to-orbit conversion. Recently, Yao et al. discovered that after a vortex beam carrying no spin is tightly focused, the orbital angular momentum can be converted into longitudinal spin angular momentum, which is called orbit-to-spin conversion. The influence of parameters such as incident light topology, beam waist width, and the ratio of pupil radius to beam waist radius on this orbit-to-spin conversion has been extensively studied. The calculation of tightly focused spin density is the basis of these research works. The spin density distribution at the focal plane after tightly focusing completely coherent light can be obtained by calculating only a double integral. However, for partially coherent light after focusing The spin density distribution at the focal plane will involve a quadruple integral, which increases the computational difficulty and time, hindering the study of tightly focused spin-orbit interactions.
发明内容Contents of the invention
本发明要解决的技术问题是提供一种降低计算难度、缩短计算时间的利用光学***的模式分解计算紧聚焦三维自旋密度的方法。The technical problem to be solved by the present invention is to provide a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system that reduces calculation difficulty and shortens calculation time.
为了解决上述问题,本发明提供了一种利用光学***的模式分解计算紧聚 焦三维自旋密度的方法,其包括以下步骤:In order to solve the above problems, the present invention provides a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, which includes the following steps:
S1、将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***;S1. Equivalent the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens to a nonlinear optical system;
S2、根据非线性***理论和理查德沃夫衍射理论,利用所述非线性光学***的输入信号和脉冲函数计算出所述非线性光学***的输出信号,所述非线性光学***的输出信号表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数;S2. According to the nonlinear system theory and Richard Wolf diffraction theory, use the input signal and pulse function of the nonlinear optical system to calculate the output signal of the nonlinear optical system. The output signal of the nonlinear optical system Expressed as a 3×3 cross-spectral density function on the focal plane of a tightly focused lens;
S3、利用模式分解理论将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加;S3. Use mode decomposition theory to convert the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems;
S4、根据自旋角动量的定义,计算得到由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。S4. According to the definition of spin angular momentum, calculate the three-dimensional spin density represented by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens.
作为本发明的进一步改进,所述紧聚焦透镜焦平面上3×3的交叉谱密度函数为:As a further improvement of the present invention, the 3×3 cross-spectral density function on the focal plane of the tight focusing lens is:
其中,C(r′1,r′2)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数;C′(r
1,r
2)为所述紧聚焦透镜后表面的交叉谱密度函数;r
1和r
2分别表示光源处两点的空间坐标,r
1=(x
1,y
1),r
1=(x
2,y
2);r′
1和r′
2分别表示紧聚焦后r
1和r
2两点的空间坐标,r′
1=(x
1,y′
1),r′
2=(x′
2,y′
2);i表示虚数;f和λ分别表示紧聚焦透镜的焦距和光源发出的部分相干光的波长;k
1和k
2分别表示点r
1和r
2在波数空间中对应的坐标,k
1=(k
1x,k
1y,k
1z),k
2=(k
2x,k
2y,k
2z);dS
1=sinθ
1dθ
1dφ
1和dS
2=sinθ
2dθ
2dφ
2分别表示点r
1和r
2处的积分微元,φ
1和φ
2分别是点r
1和r
2的方位角,且φ
1=arctan(y
1/x
1),φ
2=arctan(y
2/x
2);θ
1是点r
1和紧聚焦透镜焦点的连线与光轴之间的夹角,θ
2是点r
2和紧聚焦透镜焦点的连线与光轴之间的夹角,且满足0≤θ
1≤arcsin(NA/n
t),0≤θ
2≤arcsin(NA/n
t);NA和n
t分别表示紧聚焦透镜的数值孔径和和成像空间的折射率。
Among them, C(r′1, r′2) is the 3×3 cross spectral density function on the focal plane of the tight focusing lens; C′(r 1 , r 2 ) is the cross spectrum of the rear surface of the tight focusing lens. Density function; r 1 and r 2 respectively represent the spatial coordinates of two points at the light source, r 1 = (x 1 , y 1 ), r 1 = (x 2 , y 2 ); r′ 1 and r′ 2 respectively represent the compact The spatial coordinates of the two points r 1 and r 2 after focusing, r′ 1 = (x 1 , y′ 1 ), r′ 2 = (x′ 2 , y′ 2 ); i represents an imaginary number; f and λ represent compact numbers respectively. The focal length of the focusing lens and the wavelength of the partially coherent light emitted by the light source; k 1 and k 2 respectively represent the corresponding coordinates of points r 1 and r 2 in the wave number space, k 1 = (k 1x ,k 1y ,k 1z ), k 2 = (k 2x ,k 2y ,k 2z ); dS 1 = sinθ 1 dθ 1 dφ 1 and dS 2 = sinθ 2 dθ 2 dφ 2 represent the integral differential elements at points r 1 and r 2 respectively, φ 1 and φ 2 are the azimuth angles of points r 1 and r 2 respectively, and φ 1 = arctan (y 1 /x 1 ), φ 2 = arctan (y 2 /x 2 ); θ 1 is the angle between point r 1 and the focus of the tight focusing lens The angle between the line and the optical axis, θ 2 is the angle between the line connecting point r 2 and the focus of the tight focusing lens and the optical axis, and satisfies 0 ≤ θ 1 ≤ arcsin (NA/n t ), 0 ≤θ 2 ≤arcsin(NA/n t ); NA and n t respectively represent the numerical aperture of the tight focusing lens and the refractive index of the imaging space.
作为本发明的进一步改进,As a further improvement of the present invention,
sinθ
1=k
1z/k
0,x
1=-f k
1x/k
0,y
1=-f k
1y/k
0
sinθ 1 =k 1z /k 0 , x 1 =-f k 1x /k 0 , y 1 =-f k 1y /k 0
sinθ
2=k
2z/k
0,x
2=-f k
1z/k
0,y
1=-f k
1y/k
0
sinθ 2 =k 2z /k 0 , x 2 =-f k 1z /k 0 , y 1 =-f k 1y /k 0
其中,
表示光源发出的部分相干光的波数;代入公式(7),得到:
in, Represents the wave number of partially coherent light emitted by the light source; substituted into formula (7), we get:
令r′
1=r′
2=r′,此时,C(r′
1,r′
2)表示为:
Let r′ 1 =r′ 2 =r′. At this time, C(r′ 1 , r′ 2 ) is expressed as:
令:make:
q
2(r′,k
1,k
2)=C(k
1,k
2)h
*(r′,k
1)h(r′,k
2)
q 2 (r′, k 1 , k 2 )=C (k 1 , k 2 )h * (r′, k 1 )h (r′, k 2 )
此时,公式(9)表示为:At this time, formula (9) is expressed as:
其中,q
2(r′,k
1,k
2)是非线性光学***的脉冲函数,是输出点r′对点k
1和k
2两点脉冲的响应。
Among them, q 2 (r′, k 1 , k 2 ) is the pulse function of the nonlinear optical system, and is the response of the output point r′ to the pulses of points k 1 and k 2 .
作为本发明的进一步改进,步骤S3包括:As a further improvement of the present invention, step S3 includes:
S31、将光源处的交叉谱密度函数表示为模式分解的形式;S31. Express the cross-spectral density function at the light source in the form of mode decomposition;
S32、将光源处的交叉谱密度函数的模式分解形式代入所述紧聚焦透镜焦平 面上3×3的交叉谱密度函数,以将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加。S32. Substitute the mode decomposition form of the cross-spectral density function at the light source into the 3×3 cross-spectral density function on the focal plane of the tight focusing lens to convert the output signal of the nonlinear optical system into a series of linear optical systems incoherent superposition of the output signals.
作为本发明的进一步改进,光源处的交叉谱密度函数表示为模式分解的形式,如下:As a further improvement of the present invention, the cross-spectral density function at the light source is expressed in the form of mode decomposition, as follows:
其中,C(k
1,k
2)表示光源处的交叉谱密度函数;k
1和k
2分别表示光源处两点在波数空间中对应的坐标;
和
分别表示点k
1和k
2的交叉谱密度函数分解的第n个完全相干模式,n=1,2,……,N,N为完全相干模式总数;β
n表示第n个完全相干模式的权重,T表示转置;
Among them, C (k 1 , k 2 ) represents the cross-spectral density function at the light source; k 1 and k 2 respectively represent the corresponding coordinates of the two points at the light source in the wave number space; and Represents the n-th completely coherent mode decomposed by the cross-spectral density function of points k 1 and k 2 respectively, n=1, 2,...,N, N is the total number of completely coherent modes; β n represents the n-th completely coherent mode Weight, T represents transpose;
S32、将公式(11)代入所述紧聚焦透镜焦平面上3×3的交叉谱密度函数,得到:S32. Substitute formula (11) into the 3×3 cross-spectral density function on the focal plane of the tight focusing lens to obtain:
其中,C(r′,r′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数;
表示输出点r′对输入点k的单脉冲的响应,公式(12)中绝对值中的积分项等效于线性***的输出信号。
Among them, C(r′, r′) is the 3×3 cross-spectral density function on the focal plane of the tight focusing lens; Represents the response of output point r′ to a single pulse of input point k. The integral term in the absolute value in formula (12) is equivalent to the output signal of the linear system.
作为本发明的进一步改进,三维自旋密度由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示为:As a further improvement of the present invention, the three-dimensional spin density is expressed by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens as:
其中,S
x(r′),S
y(r′),S
z(r′)分别表示自旋密度的在空间x,y,z三个 方向上的分量;双引号表示取虚部;ε
0表示真空中的介电常数;ω是光源的角频率;C
yz(r′,r′),C
zy(r′,r′),C
zx(r′,r′),C
xz(r′,r′),C
xy(r′,r′)和C
yx(r′,r′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数中的元素。
Among them, S x (r′), S y (r′), and S z (r′) respectively represent the components of the spin density in the three directions of space x, y, and z; double quotes indicate taking the imaginary part; ε 0 represents the dielectric constant in vacuum; ω is the angular frequency of the light source; C yz (r′, r′), C zy (r′, r′), C zx (r′, r′), C xz (r ′, r′), C xy (r′, r′) and C yx (r′, r′) are elements in the 3×3 cross-spectral density function on the focal plane of the tight focusing lens.
本发明还提供了一种电子设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,所述处理器执行所述程序时实现上述任意一项所述方法的步骤。The present invention also provides an electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of any one of the above methods are implemented. .
本发明还提供了一种计算机可读存储介质,其上存储有计算机程序,该程序被处理器执行时实现上述任意一项所述方法的步骤。The present invention also provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of any one of the above methods are implemented.
本发明还提供了一种利用光学***的模式分解计算紧聚焦三维自旋密度的***,其包括以下模块:The invention also provides a system for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, which includes the following modules:
等效模块,用于将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***;The equivalent module is used to equate the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system;
输出信号计算模块,用于根据非线性***理论和理查德沃夫衍射理论,利用所述非线性光学***的输入信号和脉冲函数计算出所述非线性光学***的输出信号,所述非线性光学***的输出信号表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数;The output signal calculation module is used to calculate the output signal of the nonlinear optical system using the input signal and pulse function of the nonlinear optical system according to the nonlinear system theory and Richard Wolf diffraction theory. The output signal of the optical system is expressed as a 3×3 cross-spectral density function on the focal plane of the tight focusing lens;
模式分解模块,用于利用模式分解理论将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加;A mode decomposition module for converting the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems using mode decomposition theory;
三维自旋密度计算模块,用于根据自旋角动量的定义,计算得到由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。The three-dimensional spin density calculation module is used to calculate the three-dimensional spin density represented by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens according to the definition of spin angular momentum.
本发明的有益效果:Beneficial effects of the present invention:
本发明通过将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***,计算非线性光学***的输出信号,该输出信号表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数,再利用模式分解理论将非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加,最终得到由紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。本发明降低了紧聚焦自旋密度的计算难度和计算时间,促进了对光学自旋轨道相互作用的研究。The present invention equates the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system, and calculates the output signal of the nonlinear optical system. The output signal is expressed as 3 on the focal plane of the tight focusing lens. ×3 cross spectral density function, and then use the mode decomposition theory to convert the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems, and finally obtain a 3 × 3 cross spectral density function on the focal plane of the tight focusing lens Three-dimensional spin density represented by the spectral density function. The invention reduces the calculation difficulty and calculation time of tightly focused spin density and promotes research on optical spin-orbit interaction.
上述说明仅是本发明技术方案的概述,为了能够更清楚了解本发明的技术手段,而可依照说明书的内容予以实施,并且为了让本发明的上述和其他目的、特征和优点能够更明显易懂,以下特举较佳实施例,并配合附图,详细说明如下。The above description is only an overview of the technical solution of the present invention. In order to have a clearer understanding of the technical means of the present invention, it can be implemented according to the content of the description, and in order to make the above and other objects, features and advantages of the present invention more obvious and understandable. , the following is a detailed description of the preferred embodiments, together with the accompanying drawings.
图1是本发明优选实施例中利用光学***的模式分解计算紧聚焦三维自旋 密度的方法的流程图。Figure 1 is a flow chart of a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in a preferred embodiment of the present invention.
下面结合附图和具体实施例对本发明作进一步说明,以使本领域的技术人员可以更好地理解本发明并能予以实施,但所举实施例不作为对本发明的限定。The present invention will be further described below in conjunction with the accompanying drawings and specific examples, so that those skilled in the art can better understand and implement the present invention, but the examples are not intended to limit the present invention.
为了解决紧聚焦自旋密度计算时间长和难度大的问题,本发明利用了光学***的模式分解理论。通常完全相干光照明的光学***称为线性光学***,部分相干光照明的光学***称为非线性光学***。对于线性光学***,它的输入信号和输出信号的关系通过简单的线性变换就可以得到。对于非线性光学***,它的输出信号的计算会涉及复杂积分,需要花费大量的计算时间。通过利用非线性光学***的模式分解理论,将非线性光学***分解成一系列的线性光学***的叠加,先得到线性光学***的输出信号,再将这些输出信号进行叠加从而得到非线性光学***的输出信号,从而降低了非线性光学***的计算难度和计算时间。部分相干光紧聚焦过程是一个非线性光学***,通过利用非线性光学***的模式分解理论,将紧聚焦***的输出信号表示成一系列线性信号的叠加,自旋密度就可以用输出信号计算得到。这种方法降低了紧聚焦自旋密度的计算难度和计算时间,会促进对光学自旋轨道相互作用的研究。下面进行详细介绍:In order to solve the problem of long time and difficulty in calculating tightly focused spin density, the present invention utilizes the mode decomposition theory of optical systems. Generally, an optical system illuminated by completely coherent light is called a linear optical system, and an optical system illuminated by partially coherent light is called a nonlinear optical system. For a linear optical system, the relationship between its input signal and output signal can be obtained through simple linear transformation. For nonlinear optical systems, the calculation of its output signal will involve complex integrals and require a lot of calculation time. By using the mode decomposition theory of nonlinear optical systems, the nonlinear optical system is decomposed into a series of superpositions of linear optical systems. The output signal of the linear optical system is first obtained, and then these output signals are superimposed to obtain the output of the nonlinear optical system. signal, thus reducing the computational difficulty and calculation time of nonlinear optical systems. The partially coherent light tight focusing process is a nonlinear optical system. By using the mode decomposition theory of nonlinear optical systems, the output signal of the tight focusing system is expressed as the superposition of a series of linear signals, and the spin density can be calculated using the output signal. This method reduces the computational difficulty and time of tightly focused spin density and will promote the study of optical spin-orbit interactions. Detailed introduction below:
如图1所示,为本发明优选实施例中利用光学***的模式分解计算紧聚焦三维自旋密度的方法,其包括以下步骤:As shown in Figure 1, it is a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in a preferred embodiment of the present invention, which includes the following steps:
S1、将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***;S1. Equivalent the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens to a nonlinear optical system;
S2、根据非线性***理论和理查德沃夫衍射理论,利用所述非线性光学***的输入信号和脉冲函数计算出所述非线性光学***的输出信号,所述非线性光学***的输出信号表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数;S2. According to the nonlinear system theory and Richard Wolf diffraction theory, use the input signal and pulse function of the nonlinear optical system to calculate the output signal of the nonlinear optical system. The output signal of the nonlinear optical system Expressed as a 3×3 cross-spectral density function on the focal plane of a tightly focused lens;
其中,非线性光学***的输入信号是由紧聚焦透镜和偏振态决定的透过率函数,脉冲函数是由光源的交叉谱密度函数C(r
1,r
2)、光源面的坐标(x,y)以及波数空间(k
x,k
y)决定的,输出信号表示的是焦面处的交叉谱密度函数C(r′
1,r′
2)。
Among them, the input signal of the nonlinear optical system is the transmittance function determined by the tight focusing lens and polarization state, and the pulse function is determined by the cross-spectral density function C(r 1 , r 2 ) of the light source and the coordinates of the light source surface (x, y) and the wave number space (k x , k y ), the output signal represents the cross-spectral density function C (r′ 1 , r′ 2 ) at the focal plane.
线性光学***只需要计算一个简单的线性变换就可以得到,如下:The linear optical system only needs to calculate a simple linear transformation, as follows:
其中,C
*(x′)表示该线性***的输出信号,t
*(x)表示输入信号,q(x′,x)是输出点x′在输入点x的脉冲信号。
Among them, C * (x') represents the output signal of the linear system, t * (x) represents the input signal, and q (x', x) is the pulse signal of the output point x' at the input point x.
计算非线性光学***的输出信号与输入信号的关系式为:The relationship between the output signal and the input signal of the nonlinear optical system is calculated as:
其中,C(x′)和t(x)分别表示非线性光学***的输出信号和输入信号,q
2(x′,x
1,x
2)是二阶沃尔泰拉级数的核函数(Volterra kernel),它表示是输出点x′在输入点x
1和x
2两点的双脉冲信号,即脉冲函数。q
2(x′,x
1,x
2)是一个6D复函数,使得非线性光学***的计算比较困难。通过模式分解理论可将非线性光学***表示成一系列的线性***的非相干叠加,从而使上述计算得到简化。本发明将这一理论应用到了紧聚焦***下的自旋密度的计算。
Among them, C(x′) and t(x) represent the output signal and input signal of the nonlinear optical system respectively, and q 2 (x′, x 1 , x 2 ) is the kernel function of the second-order Volterra series ( Volterra kernel), which represents the double-pulse signal of the output point x′ at the input point x 1 and x 2 , that is, the pulse function. q 2 (x′, x 1 , x 2 ) is a 6D complex function, which makes the calculation of nonlinear optical systems difficult. The nonlinear optical system can be expressed as a series of incoherent superpositions of linear systems through mode decomposition theory, thereby simplifying the above calculations. The present invention applies this theory to the calculation of spin density under tight focusing systems.
在非线性光学***中,已知光源发出的部分相干光是沿z轴传播的横向电场,该部分相干光的交叉谱密度函数的系综平均表示为:In the nonlinear optical system, it is known that the partially coherent light emitted by the light source is a transverse electric field propagating along the z-axis. The ensemble average of the cross-spectral density function of this partially coherent light is expressed as:
C(r
1,r
2)=<U
*(r
1)U
T(r
2)> (3)
C(r 1 , r 2 )=<U * (r 1 )U T (r 2 )> (3)
其中,U(r
1)和U(r
2)分别表示光源处两点r
1和r
2光学信号(振幅),角括号表示的是系综平均,*表示复共轭,T表示矩阵的转置。紧聚焦透镜前后表面的光学信号的关系为:
Among them, U(r 1 ) and U(r 2 ) represent the optical signals (amplitudes) of the two points r 1 and r 2 at the light source respectively, the angle brackets represent the ensemble average, * represents the complex conjugate, and T represents the transformation of the matrix. Set. The relationship between the optical signals on the front and rear surfaces of the tight focusing lens is:
U′(r)=t
0(r)U(r) (4)
U′(r)=t 0 (r)U(r) (4)
其中,t
0(r)表示透过率函数;U′(r)表示紧聚焦透镜后表面的光学信号,U(r)表示紧聚焦透镜前表面的光学信号。当入射光的偏振态是柱矢量偏振时,其透过率函数可表示为:
Among them, t 0 (r) represents the transmittance function; U′(r) represents the optical signal on the rear surface of the tightly focused lens, and U(r) represents the optical signal on the front surface of the tightly focused lens. When the polarization state of the incident light is cylindrical vector polarization, its transmittance function can be expressed as:
其中,
是紧聚焦透镜的透过率函数;φ
0表示柱矢量偏振的初始相位;当φ
0=0°和90°分别表示的是径向偏振和角向偏振。公式(5)右边的第一个和第二个矩阵分别表示径向偏振(RP)和角向偏振(AP)的部分相干光经过紧聚焦透镜后的空间中x,y,z三个方向的分量大小。因此,紧聚焦透镜后表面的交叉谱密度函数表示为:
in, is the transmittance function of a tightly focused lens; φ 0 represents the initial phase of cylindrical vector polarization; when φ 0 =0° and 90° represent radial polarization and angular polarization respectively. The first and second matrices on the right side of formula (5) respectively represent the x, y, and z directions of the partially coherent light of radial polarization (RP) and angular polarization (AP) in the space after passing through the tightly focusing lens. Portion size. Therefore, the cross-spectral density function of the back surface of a tight focusing lens is expressed as:
它是一个3×3的矩阵,利用理查德沃夫衍射公式可得到紧聚焦焦面处的3×3交叉谱密度函数,如下:It is a 3×3 matrix. Using the Richard Wolf diffraction formula, the 3×3 cross-spectral density function at the tightly focused focal plane can be obtained, as follows:
其中,C(r
1′,r
2′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数;C′(r
1,r
2)为所述紧聚焦透镜后表面的交叉谱密度函数;r
1和r
2分别表示光源处两点的空间坐标,r
1=(x
1,y
1),r
1=(x
2,y
2);r′
1和r′
2分别表示紧聚焦后r
1和r
2两点的空间坐标,r′
1=(x′
1,y′
1),r′
2=(x′
2,y′
2);i表示虚数;f和λ分别表示紧聚焦透镜的焦距和光源发出的部分相干光的波长;k
1和k
2分别表示点r
1和r
2在波数空间中对应的坐标,k
1=(k
1x,k
1y,k
1z),k
2=(k
2x,k
2y,k
2z);dS
1=sinθ
1dθ
1dφ
1和dS
2=sinθ
2dθ
2dφ
2分别表示点r
1和r
2处的积分微元,φ
1和φ
2分别是点r
1和r
2的方位角,且φ
1=arctan(y
1/X
1),φ
2=arctan(y
2/x
2);θ
1是点r
1和紧聚焦透镜焦点的连线与光轴之间的夹角,θ
2是点r
2和紧聚焦透镜焦点的连线与光轴之间的夹角,且满足0≤θ
1≤arcsin(NA/n
t),0≤θ
2≤arcsin(NA/n
t);NA和n
t分别表示紧聚焦透镜的数值孔径和和成像空间的折射率。
Among them, C (r 1 ′, r 2 ′) is the 3×3 cross-spectral density function on the focal plane of the tight focusing lens; C′ (r 1 , r 2 ) is the cross spectrum of the rear surface of the tight focusing lens Density function; r 1 and r 2 respectively represent the spatial coordinates of two points at the light source, r 1 = (x 1 , y 1 ), r 1 = (x 2 , y 2 ); r′ 1 and r′ 2 respectively represent the compact The spatial coordinates of the two points r 1 and r 2 after focusing, r′ 1 = (x′ 1 , y′ 1 ), r′ 2 = (x′ 2 , y′ 2 ); i represents an imaginary number; f and λ represent respectively The focal length of the tight focusing lens and the wavelength of the partially coherent light emitted by the light source; k 1 and k 2 respectively represent the corresponding coordinates of points r 1 and r 2 in the wave number space, k 1 = (k 1x ,k 1y ,k 1z ), k 2 = (k 2x ,k 2y ,k 2z ); dS 1 = sinθ 1 dθ 1 dφ 1 and dS 2 = sinθ 2 dθ 2 dφ 2 represent the integral differential elements at points r 1 and r 2 respectively, φ 1 and φ 2 are the azimuth angles of points r 1 and r 2 respectively, and φ 1 =arctan(y 1 /X 1 ), φ 2 =arctan(y 2 /x 2 ); θ 1 is the point r 1 and the focus of the tight focusing lens The angle between the line connecting point r 2 and the focus of the tight focusing lens and the optical axis, θ 2 is the angle between the line connecting point r 2 and the focus of the tight focusing lens and the optical axis, and satisfies 0 ≤ θ 1 ≤ arcsin (NA/n t ), 0≤θ 2 ≤arcsin(NA/n t ); NA and n t respectively represent the numerical aperture of the tight focusing lens and the refractive index of the imaging space.
其中:in:
sinθ
1=k
1z/k
0,x
1=-f k
1x/k
0,y
1=-f k
1y/k
0
sinθ 1 =k 1z /k 0 , x 1 =-f k 1x /k 0 , y 1 =-f k 1y /k 0
sinθ
2=k
2z/k
0,x
2=-f k
1x/k
0,y
1=-f k
1y/k
0
sinθ 2 =k 2z /k 0 , x 2 =-f k 1x /k 0 , y 1 =-f k 1y /k 0
其中,
表示光源发出的部分相干光的波数;代入公式(7),得到:
in, Represents the wave number of partially coherent light emitted by the light source; substituted into formula (7), we get:
令r′
1=r′
2=r′,此时,C(r
1′,r
2′)表示为:
Let r′ 1 =r′ 2 =r′. At this time, C(r 1 ′, r 2 ′) is expressed as:
令:make:
q
2(r′,k
1,k
2)=C(k
1,k
2)h
*(r′,k
1)h(r′,k
2)
q 2 (r′, k 1 , k 2 )=C (k 1 , k 2 )h * (r′, k 1 )h (r′, k 2 )
此时,公式(9)表示为:At this time, formula (9) is expressed as:
其中,q
2(r′,k
1,k
2)是非线性光学***的脉冲函数,是输出点r′对点k
1和k
2两点脉冲的响应。因此也可以把这种非线性光学***称为双线性***。
Among them, q 2 (r′, k 1 , k 2 ) is the pulse function of the nonlinear optical system, and is the response of the output point r′ to the pulses of points k 1 and k 2 . Therefore, this nonlinear optical system can also be called a bilinear system.
S3、利用模式分解理论将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加;具体包括:S3. Use mode decomposition theory to convert the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems; specifically including:
S31、将光源处的交叉谱密度函数表示为模式分解的形式,如下:S31. Express the cross-spectral density function at the light source in the form of mode decomposition, as follows:
其中,C(k
1,k
2)表示光源处的交叉谱密度函数;k
1和k
2分别表示光源处两点在波数空间中对应的坐标;
和
分别表示点k
1和k
2的交叉谱密度函数分解的第n个完全相干模式,n=1,2,……,N,N为完全相干模式总数;β
n表示第n个完全相干模式的权重,T表示转置;
Among them, C (k 1 , k 2 ) represents the cross-spectral density function at the light source; k 1 and k 2 respectively represent the corresponding coordinates of the two points at the light source in the wave number space; and Represents the n-th completely coherent mode decomposed by the cross-spectral density function of points k 1 and k 2 respectively, n=1, 2,...,N, N is the total number of completely coherent modes; β n represents the n-th completely coherent mode Weight, T represents transpose;
S32、将光源处的交叉谱密度函数的模式分解形式代入所述紧聚焦透镜焦 平面上3×3的交叉谱密度函数,以将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加。S32. Substitute the mode decomposition form of the cross-spectral density function at the light source into the 3×3 cross-spectral density function on the focal plane of the tight focusing lens to convert the output signal of the nonlinear optical system into a series of linear optical systems incoherent superposition of the output signals.
具体地,将公式(11)代入所述紧聚焦透镜焦平面上3×3的交叉谱密度函数,得到:Specifically, formula (11) is substituted into the 3×3 cross-spectral density function on the focal plane of the tight focusing lens to obtain:
其中,C(r′,r′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数;
表示输出点r′对输入点k的单脉冲的响应,公式(12)中绝对值中的积分项:
Among them, C(r′, r′) is the 3×3 cross-spectral density function on the focal plane of the tight focusing lens; Represents the response of output point r′ to a single pulse of input point k. The integral term in the absolute value in formula (12):
等效于线性***的输出信号,即模式***。因此,公式(12)可认为是一系列的脉冲响应为
的模式***的模平方的叠加。
Equivalent to the output signal of a linear system, that is, a pattern system. Therefore, formula (12) can be considered as a series of impulse responses as The superposition of modular squares of a system of modes.
S4、根据自旋角动量的定义,计算得到由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。S4. According to the definition of spin angular momentum, calculate the three-dimensional spin density represented by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens.
对于角频率为ω=kc(c为真空光速)的任意时域谐波光场,其在空间ρ点的自旋密度可定义为:For any time domain harmonic light field with an angular frequency of ω = kc (c is the speed of light in vacuum), its spin density at the ρ point in space can be defined as:
其中,ε
0表示真空中的介电常数;ω是光源的角频率。利用模式分解理论,焦平面处的r′点的自旋密度可表示为:
Among them, ε 0 represents the dielectric constant in vacuum; ω is the angular frequency of the light source. Using mode decomposition theory, the spin density of point r′ at the focal plane can be expressed as:
其中,ψ
n(r′)表示焦面处的交叉谱密度函数的展开模式。自旋密度的在空间x,y,z三个方向上的分量表示为:
Among them, ψ n (r′) represents the expansion mode of the cross-spectral density function at the focal plane. The components of the spin density in the three directions of space x, y, and z are expressed as:
三维自旋密度由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示为:The three-dimensional spin density is expressed by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens as:
其中,S
x(r′),S
y(r′),S
z(r′)分别表示自旋密度的在空间x,y,z三个方向上的分量;双引号表示取虚部;C
yz(r′,r′),C
zy(r′,r′),C
zx(r′,r′),C
xz(r′,r′),C
xy(r′,r′)和C
yx(r′,r′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数中的元素。
Among them, S x (r′), S y (r′), and S z (r′) respectively represent the components of the spin density in the three directions of space x, y, and z; double quotes indicate taking the imaginary part; C yz (r′, r′), C zy (r′, r′), C zx (r′, r′), C xz (r′, r′), C xy (r′, r′) and C yx (r′, r′) is the element in the 3×3 cross-spectral density function on the focal plane of the tight focusing lens.
在其中一实施例中,采用本发明中利用光学***的模式分解计算紧聚焦三维自旋密度的方法计算径向偏振的高斯谢尔模光束经过紧聚焦后的三维自旋密度,具体计算过程如下:In one embodiment, the method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in the present invention is used to calculate the three-dimensional spin density of a radially polarized Gaussian Scher mode beam after being tightly focused. The specific calculation process is as follows:
沿z轴传播的径向偏振的高斯谢尔模光束的交叉谱密度函数的系综平均表示为:The ensemble average of the cross-spectral density function of a radially polarized Gaussian Scher mode beam propagating along the z-axis is expressed as:
其中,
和
分别是紧聚焦透镜前的入射光在r
1和r
2两点的光谱强度,
为径向偏振单位矢量,
是r
1和r
2两点之间的相干度分布,*表示复共轭,T表示矩阵的转置。r
1和r
2两点在紧聚焦透镜前后表面的光场振幅的关系分别为:
in, and are the spectral intensities of the incident light in front of the tight focusing lens at points r 1 and r 2 respectively, is the radial polarization unit vector, is the coherence distribution between the two points r 1 and r 2 , * represents the complex conjugate, and T represents the transpose of the matrix. The relationship between the light field amplitudes of the two points r 1 and r 2 on the front and rear surfaces of the tight focusing lens is:
其中,t
0(r
1)和t
0(r
2)分别表示紧聚焦透镜对光源在r
1和r
2两点的透过率函数,已知入射光的偏振态是径向偏振的,t
0(r
1)和t
0(r
2)可表示为:
Among them, t 0 (r 1 ) and t 0 (r 2 ) respectively represent the transmittance function of the tight focusing lens to the light source at two points r 1 and r 2 . It is known that the polarization state of the incident light is radially polarized, t 0 (r 1 ) and t 0 (r 2 ) can be expressed as:
和
分别表示紧聚焦透镜在θ
1和θ
2两点的透过率函数,等式(20)右边的矩阵表示径向偏振(RP)高斯谢尔模光束经过透镜后的x,y,z三个方向的分量大小。将上式带入公式(6)可得紧聚焦透镜后表面的交叉谱密度函数:
and represent the transmittance functions of the tightly focused lens at θ 1 and θ 2 respectively. The matrix on the right side of equation (20) represents the x, y, and z directions of the radially polarized (RP) Gaussian Scher mode beam after passing through the lens. Portion size. Putting the above formula into formula (6), we can get the cross-spectral density function of the back surface of the tight focusing lens:
将公式(21)简写成:Abbreviate formula (21) as:
它是一个3×3的矩阵,其中:It is a 3×3 matrix, where:
其中:in:
sinθ
1=k
1z/k
0,x
1=-f k
1x/k
0,y
1=-f k
1y/k
0
sinθ 1 =k 1z /k 0 , x 1 =-f k 1x /k 0 , y 1 =-f k 1y /k 0
sinθ
2=k
2z/k
0,x
2=-f k
1x/k
0,y
1=-f k
1y/k
0
sinθ 2 =k 2z /k 0 , x 2 =-f k 1x /k 0 , y 1 =-f k 1y /k 0
其中,
表示光源发出的部分相干光的波数;则公式(23)式可表示为:
in, Represents the wave number of the partially coherent light emitted by the light source; then formula (23) can be expressed as:
将公式(23)代入公式(8)可得到紧聚焦焦面处的交叉谱密度:Substituting formula (23) into formula (8), the cross-spectral density at the tightly focused focal plane can be obtained:
令r′
1=r′
2=r′,此时,C
xx(r
1′,r
2′)表示为:
Let r′ 1 =r′ 2 =r′, at this time, C xx (r 1 ′, r 2 ′) is expressed as:
令:make:
则公式(24)可写成:Then formula (24) can be written as:
其中,C
xx(r′,r′)是非线性光学***后的输出信号,即场的3×3交叉谱 密度函数矩阵中的第一项。
Among them, C xx (r′, r′) is the output signal after the nonlinear optical system, that is, the first item in the 3×3 cross-spectral density function matrix of the field.
将光源处的交叉谱密度函数用模式分解的形式表示为:The cross-spectral density function at the light source is expressed in the form of mode decomposition as:
其中,
和β
n分别表示入射光的展开模式和它对应的权重。将公式(28)代入公式(27)可得:
in, and β n respectively represent the expansion mode of the incident light and its corresponding weight. Substituting formula (28) into formula (27) we can get:
其中,C
nxx(r′,r′)是C
xx(r′,r′)分解的第n个完全相干模式,F是傅里叶变换符号,C
nxx(r′,r′)可以用傅里叶变换快速计算。公式(29)绝对值里面的积分项是完全相干光入射的线性***的输出信号,即模式***,公式(29)可认为是一系列的脉冲响应为
的模式***的模平方的相干叠加。类似地,交叉谱密度函数矩阵的其它8项C
xy(r
1′,r
1′)、C
xz(r
1′,r
1′)、C
yx(r
1′,r
1′)、C
yy(r
1′,r
1′)、C
yz(r
1′,r
1′)、C
zx(r
1′,r
1′)、C
zy(r
1′,r
1′)、C
zz(r
1′,r
1′)可以用同样的方法求出。利用这9项交叉谱密度公式便可得到自旋密度分量:
Among them, C nxx (r′, r′) is the n-th completely coherent mode decomposed by C xx (r′, r′), F is the Fourier transform symbol, and C nxx (r′, r′) can be Fast calculation of Lieye transform. The integral term in the absolute value of formula (29) is the output signal of the linear system with completely coherent light incident, that is, the mode system. Formula (29) can be considered as a series of impulse responses as Coherent superposition of modular squares of a system of modes. Similarly, the other eight items of the cross-spectral density function matrix are C xy (r 1 ′, r 1 ′), C xz (r 1 ′, r 1 ′), C yx (r 1 ′, r 1 ′), C yy (r 1 ′, r 1 ′), C yz (r 1 ′, r 1 ′), C zx (r 1 ′, r 1 ′), C zy (r 1 ′, r 1 ′), C zz (r 1 ′, r 1 ′) can be obtained in the same way. Using these 9 cross-spectral density formulas, the spin density component can be obtained:
即公式(17)。That is formula (17).
本发明通过将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***,计算非线性光学***的输出信号,表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数,再利用模式分解理论将非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加,最终得到由紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。本发明降低了紧聚焦自旋密度的计算难度和计算时间,促进了对光学自旋轨道相互作用的研究。The present invention equates the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system, and calculates the output signal of the nonlinear optical system, which is expressed as a 3×3 signal on the focal plane of the tight focusing lens. Cross spectral density function, and then use mode decomposition theory to convert the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems, and finally obtain a 3×3 cross spectral density function on the focal plane of the tight focusing lens represents the three-dimensional spin density. The invention reduces the calculation difficulty and calculation time of tightly focused spin density and promotes research on optical spin-orbit interaction.
本发明优选实施例还公开了一种电子设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,所述处理器执行所述程序时实现上述实施例中所述方法的步骤。A preferred embodiment of the present invention also discloses an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements what is described in the above embodiment. Method steps.
本发明优选实施例还公开了一种计算机可读存储介质,其上存储有计算机程序,该程序被处理器执行时实现上述实施例中所述方法的步骤。A preferred embodiment of the present invention also discloses a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the method described in the above embodiment are implemented.
本发明优选实施例还公开了一种利用光学***的模式分解计算紧聚焦三维自旋密度的***,其包括以下模块:The preferred embodiment of the present invention also discloses a system for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, which includes the following modules:
等效模块,用于将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***;The equivalent module is used to equate the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system;
输出信号计算模块,用于根据非线性***理论和理查德沃夫衍射理论,利用所述非线性光学***的输入信号和脉冲函数计算出所述非线性光学***的输出信号,所述非线性光学***的输出信号表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数;The output signal calculation module is used to calculate the output signal of the nonlinear optical system using the input signal and pulse function of the nonlinear optical system according to the nonlinear system theory and Richard Wolf diffraction theory. The output signal of the optical system is expressed as a 3×3 cross-spectral density function on the focal plane of the tight focusing lens;
模式分解模块,用于利用模式分解理论将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加;A mode decomposition module for converting the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems using mode decomposition theory;
三维自旋密度计算模块,用于根据自旋角动量的定义,计算得到由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。The three-dimensional spin density calculation module is used to calculate the three-dimensional spin density represented by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens according to the definition of spin angular momentum.
本发明实施例中的利用光学***的模式分解计算紧聚焦三维自旋密度的***用于实现前述的利用光学***的模式分解计算紧聚焦三维自旋密度的方法,因此该***的具体实施方式可见前文中的利用光学***的模式分解计算紧聚焦三维自旋密度的方法的实施例部分,所以,其具体实施方式可以参照相应的上 述方法实施例的描述,在此不再展开介绍。The system for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in the embodiment of the present invention is used to implement the aforementioned method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system. Therefore, the specific implementation of the system can be seen The foregoing embodiments of a method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, therefore, for its specific implementation, refer to the corresponding description of the above method embodiments and will not be introduced here.
另外,由于本实施例的利用光学***的模式分解计算紧聚焦三维自旋密度的***用于实现前述的利用光学***的模式分解计算紧聚焦三维自旋密度的方法,因此其作用与上述方法的作用相对应,这里不再赘述。In addition, since the system for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system in this embodiment is used to implement the aforementioned method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, its function is the same as that of the above method. The functions correspond to each other and will not be described again here.
以上实施例仅是为充分说明本发明而所举的较佳的实施例,本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换,均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。The above embodiments are only preferred embodiments to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be determined by the claims.
Claims (9)
- 利用光学***的模式分解计算紧聚焦三维自旋密度的方法,其特征在于,包括以下步骤:A method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system, which is characterized by including the following steps:S1、将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***;S1. Equivalent the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens to a nonlinear optical system;S2、根据非线性***理论和理查德沃夫衍射理论,利用所述非线性光学***的输入信号和脉冲函数计算出所述非线性光学***的输出信号,所述非线性光学***的输出信号表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数;S2. According to the nonlinear system theory and Richard Wolf diffraction theory, use the input signal and pulse function of the nonlinear optical system to calculate the output signal of the nonlinear optical system. The output signal of the nonlinear optical system Expressed as a 3×3 cross-spectral density function on the focal plane of a tightly focused lens;S3、利用模式分解理论将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加;S3. Use mode decomposition theory to convert the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems;S4、根据自旋角动量的定义,计算得到由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。S4. According to the definition of spin angular momentum, calculate the three-dimensional spin density represented by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens.
- 如权利要求1所述的利用光学***的模式分解计算紧聚焦三维自旋密度的方法,其特征在于,所述紧聚焦透镜焦平面上3×3的交叉谱密度函数为:The method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system as claimed in claim 1, characterized in that the 3×3 cross-spectral density function on the focal plane of the tightly focused lens is:其中,C(r 1′,r 2′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数;C′(r 1,r 2)为所述紧聚焦透镜后表面的交叉谱密度函数;r 1和r 2分别表示光源处两点的空间坐标,r 1=(x 1,y 1),r 1=(x 2,y 2);r′ 1和r′ 2分别表示紧聚焦后r 1和r 2两点的空间坐标,r′ 1=(x′ 1,y′ 1),r′ 2=(x′ 2,y′ 2);i表示虚数;f和λ分别表示紧聚焦透镜的焦距和光源发出的部分相干光的波长;k 1和k 2分别表示点r 1和r 2在波数空间中对应的坐标,k 1=(k 1x,k 1y,k 1z),k 2=(k 2x,k 2y,k 2z);dS 1=sinθ 1dθ 1dφ 1和dS 2=sinθ 2dθ 2dφ 2分别表示点r 1和r 2处的积分微元,φ 1和φ 2分别是点r 1和r 2的方位角,且φ 1=arctan(y 1/x 1),φ 2=arctan(y 2/x 2);θ 1是点r 1和紧聚焦透镜焦点的连线与光轴之间的夹角,θ 2是点r 2和紧聚焦透镜焦点的连线与光轴之间的夹角,且满足0≤θ 1≤arcsin(NA/n t),0≤θ 2≤arcsin(NA/n t);NA和n t分别表示紧聚焦透镜的数值孔径和和成像空间的折射率。 Among them, C (r 1 ′, r 2 ′) is the 3×3 cross-spectral density function on the focal plane of the tight focusing lens; C′ (r 1 , r 2 ) is the cross spectrum of the rear surface of the tight focusing lens Density function; r 1 and r 2 respectively represent the spatial coordinates of two points at the light source, r 1 = (x 1 , y 1 ), r 1 = (x 2 , y 2 ); r′ 1 and r′ 2 respectively represent the compact The spatial coordinates of the two points r 1 and r 2 after focusing, r′ 1 = (x′ 1 , y′ 1 ), r′ 2 = (x′ 2 , y′ 2 ); i represents an imaginary number; f and λ represent respectively The focal length of the tight focusing lens and the wavelength of the partially coherent light emitted by the light source; k 1 and k 2 respectively represent the corresponding coordinates of points r 1 and r 2 in the wave number space, k 1 = (k 1x , k 1y , k 1z ), k 2 = (k 2x , k 2y , k 2z ); dS 1 = sinθ 1 dθ 1 dφ 1 and dS 2 = sinθ 2 dθ 2 dφ 2 respectively represent the integral differential elements at points r 1 and r 2 , φ 1 and φ 2 are the azimuth angles of points r 1 and r 2 respectively, and φ 1 =arctan(y 1 /x 1 ), φ 2 =arctan(y 2 /x 2 ); θ 1 is the point r 1 and the focus of the tight focusing lens The angle between the line connecting point r 2 and the focus of the tight focusing lens and the optical axis, θ 2 is the angle between the line connecting point r 2 and the focus of the tight focusing lens and the optical axis, and satisfies 0 ≤ θ 1 ≤ arcsin (NA/n t ), 0≤θ 2 ≤arcsin(NA/n t ); NA and n t respectively represent the numerical aperture of the tight focusing lens and the refractive index of the imaging space.
- 如权利要求2所述的利用光学***的模式分解计算紧聚焦三维自旋密度的方法,其特征在于,The method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system as claimed in claim 2, characterized in that:sinθ 1=k 1z/k 0,x 1=-fk 1x/k 0,y 1=-fk 1y/k 0 sinθ 1 =k 1z /k 0 , x 1 =-fk 1x /k 0 , y 1 =-fk 1y /k 0sinθ 2=k 2z/k 0,x 2=-fk 1x/k 0,y 1=-fk 1y/k 0 sinθ 2 =k 2z /k 0 , x 2 =-fk 1x /k 0 , y 1 =-fk 1y /k 0其中, 表示光源发出的部分相干光的波数;代入公式(7),得到: in, Represents the wave number of partially coherent light emitted by the light source; substituted into formula (7), we get:令r′ 1=r′ 2=r′,此时,C(r 1′,r 2′)表示为: Let r′ 1 =r′ 2 =r′. At this time, C(r 1 ′, r 2 ′) is expressed as:令:make:q 2(r′,k 1,k 2)=C(k 1,k 2)h *(r′,k 1)h(r′,k 2) q 2 (r′, k 1 , k 2 )=C (k 1 , k 2 )h * (r′, k 1 )h (r′, k 2 )此时,公式(9)表示为:At this time, formula (9) is expressed as:其中,q 2(r′,k 1,k 2)是非线性光学***的脉冲函数,是输出点r′对点k 1和k 2两点脉冲的响应。 Among them, q 2 (r′, k 1 , k 2 ) is the pulse function of the nonlinear optical system, and is the response of the output point r′ to the pulses of points k 1 and k 2 .
- 如权利要求1所述的利用光学***的模式分解计算紧聚焦三维自旋密度的方法,其特征在于,步骤S3包括:The method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system as claimed in claim 1, wherein step S3 includes:S31、将光源处的交叉谱密度函数表示为模式分解的形式;S31. Express the cross-spectral density function at the light source in the form of mode decomposition;S32、将光源处的交叉谱密度函数的模式分解形式代入所述紧聚焦透镜焦平面上3×3的交叉谱密度函数,以将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加。S32. Substitute the mode decomposition form of the cross-spectral density function at the light source into the 3×3 cross-spectral density function on the focal plane of the tight focusing lens to convert the output signal of the nonlinear optical system into a series of linear optical systems incoherent superposition of the output signals.
- 如权利要求4所述的利用光学***的模式分解计算紧聚焦三维自旋密度的方法,其特征在于,光源处的交叉谱密度函数表示为模式分解的形式,如下:The method of calculating tightly focused three-dimensional spin density using mode decomposition of an optical system as claimed in claim 4, characterized in that the cross-spectral density function at the light source is expressed in the form of mode decomposition, as follows:其中,C(k 1,k 2)表示光源处的交叉谱密度函数;k 1和k 2分别表示光源处两点在波数空间中对应的坐标; 和 分别表示点k 1和k 2的交叉谱密度函数分解的第n个完全相干模式,n=1,2,……,N,N为完全相干模式总数;β n表示第n个完全相干模式的权重,T表示转置; Among them, C (k 1 , k 2 ) represents the cross-spectral density function at the light source; k 1 and k 2 respectively represent the corresponding coordinates of the two points at the light source in the wave number space; and Represents the n-th completely coherent mode decomposed by the cross-spectral density function of points k 1 and k 2 respectively, n=1, 2,...,N, N is the total number of completely coherent modes; β n represents the n-th completely coherent mode Weight, T represents transpose;S32、将公式(11)代入所述紧聚焦透镜焦平面上3×3的交叉谱密度函数,得到:S32. Substitute formula (11) into the 3×3 cross-spectral density function on the focal plane of the tight focusing lens to obtain:其中,C(r′,r′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数; 表示输出点r′对输入点k的单脉冲的响应,公式(12)中绝对值中的积分项等效于线性***的输出信号。 Among them, C(r′, r′) is the 3×3 cross-spectral density function on the focal plane of the tight focusing lens; Represents the response of output point r′ to a single pulse of input point k. The integral term in the absolute value in formula (12) is equivalent to the output signal of the linear system.
- 如权利要求5所述的利用光学***的模式分解计算紧聚焦三维自旋密度的方法,其特征在于,三维自旋密度由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示为:The method for calculating tightly focused three-dimensional spin density using mode decomposition of an optical system as claimed in claim 5, characterized in that the three-dimensional spin density is represented by a 3×3 cross-spectral density function on the focal plane of the tightly focused lens as :其中,S x(r′),S y(r′),S z(r′)分别表示自旋密度的在空间x,y,z三个方向上的分量;双引号表示取虚部;ε 0表示真空中的介电常数;ω是光源的角频率;C yz(r′,r′),C zy(r′,r′),C zx(r′,r′),C xz(r′,r′),C xy(r′,r′)和C yx(r′,r′)为所述紧聚焦透镜焦平面上3×3的交叉谱密度函数中的元素。 Among them, S x (r′), S y (r′), and S z (r′) respectively represent the components of the spin density in the three directions of space x, y, and z; double quotes indicate taking the imaginary part; ε 0 represents the dielectric constant in vacuum; ω is the angular frequency of the light source; C yz (r′, r′), C zy (r′, r′), C zx (r′, r′), C xz (r ′, r′), C xy (r′, r′) and C yx (r′, r′) are elements in the 3×3 cross-spectral density function on the focal plane of the tight focusing lens.
- 一种电子设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,其特征在于,所述处理器执行所述程序时实现权利要求1-6中任意一项所述方法的步骤。An electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that when the processor executes the program, it implements any one of claims 1-6. Describe the steps of the method.
- 一种计算机可读存储介质,其上存储有计算机程序,其特征在于,该程序被处理器执行时实现权利要求1-6任意一项所述方法的步骤。A computer-readable storage medium on which a computer program is stored, characterized in that when the program is executed by a processor, the steps of the method described in any one of claims 1-6 are implemented.
- 利用光学***的模式分解计算紧聚焦三维自旋密度的***,其特征在于,包括以下模块:A system for calculating tightly focused three-dimensional spin density using mode decomposition of optical systems, which is characterized by including the following modules:等效模块,用于将光源发出的部分相干光、紧聚焦透镜和紧聚焦透镜后的空间等效为非线性光学***;The equivalent module is used to equate the partially coherent light emitted by the light source, the tight focusing lens and the space behind the tight focusing lens into a nonlinear optical system;输出信号计算模块,用于根据非线性***理论和理查德沃夫衍射理论,利用所述非线性光学***的输入信号和脉冲函数计算出所述非线性光学***的输出信号,所述非线性光学***的输出信号表示为紧聚焦透镜焦平面上3×3的交叉谱密度函数;The output signal calculation module is used to calculate the output signal of the nonlinear optical system using the input signal and pulse function of the nonlinear optical system according to the nonlinear system theory and Richard Wolf diffraction theory. The output signal of the optical system is expressed as a 3×3 cross-spectral density function on the focal plane of the tight focusing lens;模式分解模块,用于利用模式分解理论将所述非线性光学***的输出信号转化为一系列线性光学***的输出信号的非相干叠加;A mode decomposition module for converting the output signal of the nonlinear optical system into an incoherent superposition of the output signals of a series of linear optical systems using mode decomposition theory;三维自旋密度计算模块,用于根据自旋角动量的定义,计算得到由所述紧聚焦透镜焦平面上3×3的交叉谱密度函数表示的三维自旋密度。The three-dimensional spin density calculation module is used to calculate the three-dimensional spin density represented by the 3×3 cross-spectral density function on the focal plane of the tight focusing lens according to the definition of spin angular momentum.
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CN110531530A (en) * | 2019-08-30 | 2019-12-03 | 苏州大学 | A kind of quick calculation method for realizing partially coherent light tightly focused |
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