Method for controlling focusing space-time wave packet to move in three-dimensional space

Abstract

The invention discloses a method for controlling a focusing space-time wave packet to move in a three-dimensional space, and the method comprises the steps: S1, carrying out the theoretical analysis of a primary aberration, obtaining a spherical aberration, enabling a focal field to move in the optical axis direction of a focusing space, and enabling the focal field to shift along the x-axis and y-axis of the focusing space through the distortion; s2, pre-splitting processing is carried out on an incident space-time wave packet, and a spherical aberration function and a distortion function are introduced into the incident wave packet at the same time; s3, focusing the incident space-time wave packet through an objective lens to obtain a focused space-time vortex wave packet capable of moving in a three-dimensional space; and S4, by changing correlation coefficients in the spherical aberration function and the distortion function, the spatial position of the focusing space-time wave packet can be randomly adjusted in the three-dimensional space. According to the invention, the focusing space-time wave packet can move in any direction in a three-dimensional space by comprehensively using spherical aberration and distortion, and the method has potential application in the fields of optical capture, laser processing, light-substance interaction and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of micro-nano optics, and in particular to a method for controlling the movement of a focused space-time wave packet in a three-dimensional space. Background Art

[0002] Photon angular momentum is an important research direction in nanophotonics and can be widely used in large-capacity ultra-high-speed optical communications, quantum information processing, optical tweezers, super-resolution microscopy, spin-orbit coupling and other fields. In the spatial domain, the orbital angular momentum of the light field can be expressed as the vortex wavefront. Indicates that is the azimuth angle in the beam cross section, and l is called the topological charge. With the rapid development of light field control theory and technology, people's understanding of photon angular momentum is also deepening. A large number of theories and experiments have proved the existence of non-zero transverse spin angular momentum, and by introducing phase changes in the time domain, pure transverse orbital angular momentum can be obtained. The resulting vortex beam rotates around an axis perpendicular to its propagation direction.

[0003] In 1856, German mathematician Seidel analyzed the sources of five lens aberrations, which are called Seidel's five aberrations. Spherical aberration refers to the optical phenomenon that when parallel light passes through the edge of the lens, its focal position is closer to the lens, while the focal position of light passing through the center of the lens is farther away from the lens, so that the light cannot converge on an ideal focus. Distortion is the phenomenon that the vertical axis magnification of the main light at the same position is not constant, and the light undergoes refraction, scattering, reflection and other phenomena when passing through optical systems such as lenses, resulting in a decrease in imaging quality. The generation of distortion is related to the field of view of the imaging system. Although it does not affect the clarity of the image, it will cause the image to bend and deform in the focal plane. There is a good correspondence between Zernike polynomials and classical aberrations (such as astigmatism, coma and spherical aberration), which makes it possible to quickly classify and quantify wavefront aberrations. A comprehensive and accurate description of wavefront aberrations can effectively analyze the focused light field affected by aberrations. By adjusting the aberration coefficients in the aberration function, different degrees of aberration can be expressed. MA González-Galicia et al. used the Seidel aberration theory of thin lenses to calculate the phase changes caused by lens aberrations. The effects of aberrations such as spherical aberration, coma, astigmatism, field curvature and distortion on the focusing of ultrashort pulses under uniform illumination were analyzed. Rakesh Kumar Singh et al. used vector Debye integral to study the effect of primary aberrations on the tight focusing of vector Laguerre-Gaussian beams, and presented a series of new phenomena on the changes in polarization singular index and phase of the focusing field of Laguerre-Gaussian beams caused by aberration factors. There are many studies on the effect of aberrations on tightly focused fields, but few studies use aberrations containing phase information as a method to control light fields, and there is a lack of research on using aberrations to move the three-dimensional position of strongly focused space-time wave packets. Summary of the invention

[0004] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a method for controlling the movement of a focused space-time wave packet in three-dimensional space, so as to realize the movement of the three-dimensional spatial position of the focused wave packet in the focusing area, enrich the control method of the space-time light field, and can be widely used in the fields of light-matter interaction, optical information processing, data storage, information encryption, etc. In order to achieve the above-mentioned purpose and other advantages of the present invention, a method for controlling the movement of a focused space-time wave packet in three-dimensional space is provided, comprising:

[0005] S1. Through theoretical analysis of primary aberrations, it is found that spherical aberration causes the focal field to move in the direction of the optical axis of the focusing space, and distortion causes the focal field to shift along the x-axis and y-axis of the focusing space;

[0006] S2, by pre-splitting the incident space-time wave packet, and introducing the spherical aberration function and the distortion function into the incident wave packet;

[0007] S3, focusing the incident space-time wave packet through the objective lens to obtain a focused space-time vortex wave packet that can move in three-dimensional space;

[0008] S4. By changing the correlation coefficients in the spherical aberration function and the distortion function, the spatial position of the focused space-time wave packet can be arbitrarily adjusted in three-dimensional space.

[0009] That is, under the focus of the objective lens, a method is used to realize the movement of the focused space-time wave packet in three-dimensional space. Based on the influence of optical aberration on the spatial position of the focused wave packet, by introducing spherical aberration and distortion, the three-dimensional movement of the space-time wave packet with transverse orbital angular momentum in the focusing space of the tight focusing system is realized. Spherical aberration is used to realize the movement of the focused space-time wave packet along the optical axis, and distortion is used to move the focused space-time wave packet in the x-axis and y-axis directions.

[0010] Compared with the prior art, the present invention has the following beneficial effects: it provides a three-dimensional spatial position movement method for highly localized space-time vortices generated under strong focusing conditions. There is a good correlation between the three aberration coefficients and the corresponding offsets, and they are independent of each other, providing a convenient and efficient method for position control of space-time vortex light fields with pure transverse orbital angular momentum. It has great application potential in the fields of microscopic imaging, optical tweezers, laser processing, etc.

[0011] The present invention has little effect on the space-time spiral phase of the space-time focal field, and the aberration factor does not affect the topological charge of the focused vortex wave packet, and the space-time spiral phase can be retained while the space-time wave packet is moved.

[0012] The invention has strong scalability and the method proposed by the invention can be applied to the full-band space-time light field. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A schematic diagram of a method for moving a focused space-time vortex wave packet in a three-dimensional space in the present invention;

[0014] Figure 2 The intensity (a1)-(c1) and phase distribution (a2)-(c2) of the space-time wave packet focused to different positions on the optical axis under different spherical aberration coefficients in the present invention, as well as the fitting curve diagram (d) of the spherical aberration coefficient and the offset Δz; the spherical aberration coefficients in (a)-(c) are 0.3λ, 0λ, -0.3λ, respectively, (a1)-(c1) also give the isosurface diagram of the focused space-time wave packet at 0.3 times the peak intensity, and (d) also gives the enlarged diagram of the nonlinear part in the relationship between the displacement and the spherical aberration coefficient;

[0015] Figure 3The intensity (a1)-(b1) and phase distribution (a2)-(b2) of the space-time wave packet focused to different positions on the focal plane under different x-distortion coefficients in the present invention, and the fitting curve diagram (c) of the x-distortion coefficient and the offset Δx; the x-distortion coefficients in (a) and (b) are 0.5λ and 1λ respectively, and the isosurface diagram of the focused space-time wave packet at 0.3 times the peak intensity is given in (a1) and (b1);

[0016] Figure 4 The intensity (a1)-(b1) and phase distribution (a2)-(b2) of the space-time wave packet focused to different positions on the focal plane under different y distortion coefficients in the present invention, and the fitting curve diagram (c) of the y distortion coefficient and the offset Δy; the y distortion coefficients in (a) and (b) are 0.5λ and 1λ respectively, and the isosurface diagram of the focused space-time wave packet at 0.3 times the peak intensity is given in (a1) and (b1);

[0017] Figure 5 This is the relationship between the aberration coefficient and the three-dimensional displacement Δx, Δy and Δz of the focused wave packet when the three aberrations act together. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] Reference Figure 1 , a method for controlling the movement of a focused space-time wave packet in three-dimensional space, comprising the following steps:

[0020] S1. Through theoretical analysis of primary aberrations, it is found that spherical aberration causes the focal field to move in the direction of the optical axis of the focusing space, and distortion causes the focal field to shift along the x-axis and y-axis of the focusing space.

[0021] Furthermore, the aberration function described by Zernike polynomials is adopted. The Zernike polynomials under Born and Wolf indices can be written as:

[0022]

[0023] Where n and m represent the degree of the radial polynomial and the frequency of the angular function, respectively. The area radius ρ is defined as ρ = sinθ / sinα, where θ is the light cone angle during focusing, α is the maximum light cone angle, and α = sin -1(NA), NA is the numerical aperture of the objective lens. Radial polynomial It is expressed as:

[0024]

[0025] In the aberration represented by Zernike polynomials, the functional expressions of primary spherical aberration, x-distortion and y-distortion can be obtained as follows:

[0026]

[0027] It can be seen that the x distortion and y distortion are orthogonal to each other, and the real number A s , A dx and A dy The intensity of the aberration is called the aberration coefficient. Spherical aberration and distortion affect the wavefront of the incident wave packet, and the additional phase factor brought to the incident wave packet is:

[0028]

[0029] Since spherical aberration will cause focal shift at the focal point, the spherical aberration function can be used to The focal field is moved in the direction of the optical axis of the focusing space; at the same time, the x-distortion function can be used and the y distortion function The focal field is shifted along the x-axis and y-axis directions of the focusing space.

[0030] S2, by pre-splitting the incident space-time wave packet, and at the same time introducing the spherical aberration function and the distortion function into the incident wave packet. Further, the incident space-time wave packet needs to be pre-splited to overcome the space-time astigmatism effect in the focusing process, and then the additional phase factor Applied to the pre-processed incident wave packet.

[0031] S3. Focus the incident space-time wave packet through the objective lens to obtain a focused space-time vortex wave packet that can move in three-dimensional space; establish a three-dimensional coordinate system in the focusing space by taking the focal position of the incident space-time wave packet after being focused by the objective lens when there is no aberration as the origin, the light field propagation direction is the z direction, and the plane passing through the focusing point and orthogonal to the optical axis is the xy plane.

[0032] S4. By changing the correlation coefficients in the spherical aberration function and the distortion function, the spatial position of the focused space-time wave packet can be adjusted arbitrarily in the three-dimensional space. In the three-dimensional focusing space, the relationship between the spherical aberration coefficient and the displacement of the focused space-time wave packet along the z direction is determined, the relationship between the x distortion coefficient and the displacement of the focused space-time wave packet along the x direction is determined, and the relationship between the y distortion coefficient and the displacement of the focused space-time wave packet along the y direction is determined. The method for determining the above relationship is: when the incident space-time wave packet is only affected by spherical aberration, the position of the focused vortex in the propagation direction is found, and its distance value from the origin of the focusing space is the corresponding offset Δz under the spherical aberration coefficient; under the influence of only the x distortion or y distortion factor, the focused wave packet is offset along the x-axis or y-axis, and the offset Δx or Δy generated by the focused wave packet along the x-axis or y-axis under different distortion coefficients is analyzed.

[0033] Example 1

[0034] like Figure 1 As shown, after the incident space-time wave packet containing aberration is focused by the objective lens, the three-dimensional spatial position of the focused space-time wave packet can be moved in the focusing space by changing the corresponding aberration coefficient. The intensity and phase distribution of the focused space-time wave packet in the space-time domain can be calculated using the Richard Wolf vector diffraction integral. Here, the specific implementation method of the technical solution is explained by taking the movement of the focused space-time wave packet in the xyz direction as an example, which includes the following steps:

[0035] Step 1: Using primary spherical aberration x-distortion and y distortion To control the three-dimensional spatial position of the focused space-time wave packet, their functional expressions are shown in equations (3)-(5) respectively. The additional phase brought by these three aberrations to the incident space-time wave packet is shown in equation (6).

[0036] Step 2: Taking the generation of a spacetime vortex with a transverse orbital angular momentum of a topological charge of +1 in the focusing space as an example, the preprocessed incident spacetime wave packet required at this time is

[0037]

[0038] Among them, w p is the waist radius of the incident space-time wave packet in the spatial domain, w t The intensity of the incident space-time wave packet drops to 1 / e of its peak intensity in the time domain 2 The half pulse width at this time. Spherical aberration function and distortion function are introduced into the incident wave packet, and the incident wave packet becomes

[0039] Step 3: In order to obtain a focused space-time wave packet with a three-dimensional position movement in the focusing space, the field distribution of the focused wave packet is calculated by the Richard Wolf vector diffraction integral:

[0040]

[0041] Where B(θ) is the apodization function of the objective lens. Here we use a sinusoidal objective lens. k = 2π / λ is the wave number, λ is the central wavelength of the incident wave packet. α = a sin (NA) is the angle between the focused light and the optical axis, NA is the numerical aperture of the objective lens. In this embodiment, NA is 0.9.

[0042] The x-distortion coefficient and the y-distortion coefficient are set to 0λ, and the movement of the focused wave packet is analyzed when only spherical aberration exists. Figure 2 (a) shows that when the spherical aberration coefficient is 0.3λ, the focused wave packet moves -0.5λ along the z-axis compared to the coordinate origin in the focusing space; Figure 2 (b) is the focused wave packet without spherical aberration (i.e., the spherical aberration coefficient is 0λ), and the wave packet has no offset in the focusing space; Figure 2 (c) shows that when the spherical aberration coefficient is -0.3λ, the focused wave packet moves 0.5λ along the z-axis compared to the coordinate origin in the focusing space. Figure 2 (a2)-2(c2) show the phase distribution of the focused wave packet in the time and space domain under three conditions. It can be seen that in the process of moving along the z-axis, the focused wave packet always carries a transverse orbital angular momentum with a topological charge of +1 in its xt plane. Further, the spherical aberration coefficients are summarized and analyzed to obtain Figure 2 (d) The offset Δz and the spherical aberration coefficient A s When the spherical aberration coefficient |A s |When it is greater than 0.1λ, the offset Δz and the spherical aberration coefficient A s Has a good linear relationship. Specifically, Δz = -1.5A s +0.05, A s ∈[-1,-0.1); Δz=-1.5A s -0.05, A s ∈(0.1,1]. When the spherical aberration coefficient is in the range of [-0.1λ,0.1λ], the above linear relationship no longer holds and instead exhibits nonlinear characteristics.

[0043] The spherical aberration coefficient and the y-distortion coefficient are set to 0λ, and the movement of the focused wave packet is analyzed when only the x-distortion exists. Figure 3 (a) shows that when the x-distortion coefficient is 0.5λ, the focused wave packet moves 0.56λ in the positive direction along the x-axis in the focusing space; Figure 3 (b) shows that when the x-distortion coefficient is 1λ, the focused wave packet moves 1.12λ in the positive direction along the x-axis in the focusing space. Figure 3(a2) and 3(b2) show the phase distribution of the focused wave packet in the space-time domain in these two cases. It can be seen that in the process of moving along the x-axis, the focused wave packet always carries a transverse orbital angular momentum with a topological charge of +1 in its xt plane. Further, the analysis of more x-distortion coefficients yields Figure 3 (c) The offset Δx and the x-distortion coefficient A dx It can be seen from the figure that the offset distance Δx of the focused wave packet changes with the x distortion coefficient A. dx The relationship between them is approximately linear, satisfying Δx=p1A dx +p2, where p1 = 1.107, p2 = 1.994 × 10 -17 .

[0044] The spherical aberration coefficient and the x-distortion coefficient are set to 0λ, and the movement of the focused wave packet is analyzed when only the y-distortion exists. Figure 4 (a) shows that when the y-distortion coefficient is 0.5λ, the focused wave packet moves 0.56λ in the positive direction along the y-axis in the focusing space; Figure 4 (b) shows that when the y-distortion coefficient is 1λ, the focused wave packet moves 1.12λ along the positive y-axis in the focusing space. Figure 4 (a2) and 4(b2) show the phase distribution of the focused wave packet in the space-time domain in these two cases. It can be seen that in the process of moving along the y-axis, the focused wave packet always carries a transverse orbital angular momentum with a topological charge of +1 in its xt plane. Further, the analysis of more y distortion coefficients yields Figure 4 (c) Offset Δy and y distortion coefficient A dy At this time, the offset Δy and the y distortion coefficient A dy The relationship is also approximately linear. Specifically, we can get Δy = p3A dy +p4, where p3=1.107, p4=1.994×10 -17 .

[0045] According to the correspondence between the single aberration and the offset of the focused wave packet obtained above, in order to make the focused wave packet offset simultaneously in the x, y and z directions in the focusing space, the three aberrations need to work together. Figure (5) shows the correspondence between the three-dimensional spatial offset of the focused wave packet and each coefficient when the three aberrations exist at the same time, indicating that the focused wave packet has offsets in the x, y and z directions.

[0046] In summary, after the incident space-time wave packet with additional spherical aberration, x distortion and y distortion is focused by the objective lens, the focused space-time wave packet can be arbitrarily moved in the three-dimensional position in the focusing space, and the transverse orbital angular momentum topological charge of the focused space-time wave packet can be kept unchanged during the movement.

[0047] The number of devices and processing scales described here are used to simplify the description of the present invention, and the application, modification and variation of the present invention will be obvious to those skilled in the art.

[0048] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and implementation modes. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for controlling the movement of a focused space-time wave packet in three-dimensional space, characterized in that: include: S1. Through theoretical analysis of primary aberrations, it is found that spherical aberration causes the focal field to move in the direction of the optical axis of the focusing space, and distortion causes the focal field to shift along the x-axis and y-axis of the focusing space; S2, by pre-splitting the incident space-time wave packet, and introducing the spherical aberration function and the distortion function into the incident wave packet; S3, focusing the incident space-time wave packet through the objective lens to obtain a focused space-time vortex wave packet that can move in three-dimensional space; S4. By changing the correlation coefficients in the spherical aberration function and the distortion function, the spatial position of the focused space-time wave packet can be arbitrarily adjusted in three-dimensional space.

2. A method for controlling the movement of a focused space-time wave packet in three-dimensional space as claimed in claim 1, characterized in that: In step S1, the aberration function is described by Zernike polynomials, and the Zernike polynomials expressed by Born and Wolf indices are used to obtain the functions of primary spherical aberration, x distortion and y distortion in the aberrations expressed by the Zernike polynomials.

3. A method for controlling the movement of a focused space-time wave packet in three-dimensional space as claimed in claim 2, characterized in that: By expressing the aberration under Zernike polynomials, it is found that the x-distortion and the y-distortion are orthogonal to each other, and the spherical aberration and the distortion affect the wavefront of the incident wave packet, thereby bringing an additional phase factor to the incident wave packet.

4. A method for controlling the movement of a focused space-time wave packet in three-dimensional space as claimed in claim 1, characterized in that: In step S2, the incident space-time wave packet needs to be pre-splitting processed, and then the additional phase factor is applied to the pre-processed incident wave packet.

5. A method for controlling the movement of a focused space-time wave packet in three-dimensional space as claimed in claim 1, characterized in that: In step S3, a three-dimensional coordinate system in the focusing space is established with the focal position of the incident space-time wave packet after being focused by the objective lens when there is no aberration as the origin, the light field propagation direction is the z direction, and the plane passing through the focusing point and orthogonal to the optical axis is the xy plane.

6. A method for controlling the movement of a focused space-time wave packet in three-dimensional space as claimed in claim 1, characterized in that: In step S4, in the three-dimensional focusing space, the relationship between the spherical aberration coefficient and the displacement of the focused space-time wave packet along the z direction is determined, the relationship between the x distortion coefficient and the displacement of the focused space-time wave packet along the x direction is determined, and the relationship between the y distortion coefficient and the displacement of the focused space-time wave packet along the y direction is determined.

7. A method for controlling the movement of a focused space-time wave packet in three-dimensional space as claimed in claim 6, characterized in that: When the incident space-time wave packet is only affected by spherical aberration, the position of the focused vortex in the propagation direction is found, and its distance from the origin of the focusing space is the corresponding offset Δz under the spherical aberration coefficient.

8. A method for controlling the movement of a focused space-time wave packet in three-dimensional space as claimed in claim 7, characterized in that: Under the influence of only x-distortion or y-distortion factors, the focused wave packet will be offset along the x-axis or y-axis. The offset Δx or Δy of the focused wave packet along the x-axis or y-axis under different distortion coefficients is obtained by analysis.

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