CN115394621B - Method and system for generating surge self-focusing electron beam based on vortex circle Airy - Google Patents

Method and system for generating surge self-focusing electron beam based on vortex circle Airy Download PDF

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CN115394621B
CN115394621B CN202211330455.0A CN202211330455A CN115394621B CN 115394621 B CN115394621 B CN 115394621B CN 202211330455 A CN202211330455 A CN 202211330455A CN 115394621 B CN115394621 B CN 115394621B
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邓冬梅
蔡学震
唐惠琳
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South China Normal University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
    • H01J37/02—Details
    • H01J37/21—Means for adjusting the focus
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    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0938—Using specific optical elements
    • G02B27/0944—Diffractive optical elements, e.g. gratings, holograms
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
    • H01J37/02—Details
    • H01J37/04—Arrangements of electrodes and associated parts for generating or controlling the discharge, e.g. electron-optical arrangement, ion-optical arrangement
    • H01J37/06—Electron sources; Electron guns
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
    • H01J37/02—Details
    • H01J37/04—Arrangements of electrodes and associated parts for generating or controlling the discharge, e.g. electron-optical arrangement, ion-optical arrangement
    • H01J37/10—Lenses
    • H01J37/14—Lenses magnetic
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
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    • H01J37/22—Optical or photographic arrangements associated with the tube
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J2237/00—Discharge tubes exposing object to beam, e.g. for analysis treatment, etching, imaging
    • H01J2237/04—Means for controlling the discharge
    • H01J2237/049—Focusing means
    • H—ELECTRICITY
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    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
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    • H01J2237/216—Automatic focusing methods

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Abstract

The invention discloses a method and a system for generating a surge self-focusing electron beam based on vortex circle Airy, wherein an electron gun emits an electron beam; the electron beam transmits a nano holographic diffraction pattern, and the pattern of the nano holographic diffraction pattern is subjected to cubic phase modulation through calculation, so that the transmitted electron beam is modulated into a round Airy electron beam; the circular Airy electron beam passes through a Y-shaped diffraction hologram to generate vortex at the central axis of the circular Airy electron beam to obtain a circular Airy electron beam with central vortex, namely a vortex circular Airy electron beam; the vortex circular Airy electron beams are focused through the magnetic lens, vortex circular Airy wave packets are formed on a focal plane, and the focal plane starts to record the transmission of the vortex circular Airy electron beams; the cross section of the swirling circular airy beam was observed by a transmission electron microscope. The invention can well control the initial field of the round Airy electron beam, and is convenient for regulating and controlling parameters; the generated electron beam has a stronger focusing power than other electron beams and has an orbital angular momentum.

Description

Method and system for generating surge self-focusing electron beam based on vortex circle Airy
Technical Field
The invention relates to the technical field of electron beam surge self-focusing, in particular to a surge self-focusing electron beam generation method and system based on vortex circle Airy.
Background
The effect of the sharp self-focusing first appears in the optical field, describing a beam that is emitted from a laser and then specially modulated so that it can be automatically focused without passing through a lens. Since Berry and Balazs theoretically proposed the airy wave packet for the first time in 1979, the airy beam has attracted a great deal of attention due to its unique properties. In 2010 Nikolaos and Demetrios discovered a novel beam containing the Airy function in the initial planar expression: round Airy beam. This type of beam exhibits a sharp self-focusing characteristic by shifting the lateral self-acceleration characteristic of the airy beam to the radial direction. Based on the same principle, by utilizing the technology of electron beam nano holographic diffraction patterns, vortex circular Airy electron beams can be generated. According to the result of numerical simulation, the electron beam also shows the characteristic of sharp self-focusing in the propagation process. The circular airy can carry orbital angular momentum by loading vortices with centers overlapping the spot center.
The vortex circular Airy electron beam can carry orbital angular momentum, and the characteristics of the sharp self-focusing of the vortex circular Airy electron beam enable the energy density of the vortex circular Airy electron beam to be sharply increased on a focusing plane and the size of a light spot to be sharply reduced. The resolution of the electron microscope can be improved by smaller light spots. It carries orbital angular momentum and has potential application in magnetic chiral dichroism spectroscopy (EMCD).
Disclosure of Invention
In view of the above, the invention provides a method and a system for generating a surge self-focusing electron beam based on vortex circular airy, which can well control the initial field of the circular airy electron beam and facilitate the regulation and control of parameters; the generated electron beam has a stronger focusing power than other electron beams and is provided with orbital angular momentum.
The invention solves the problems through the following technical means:
in one aspect, the invention provides a method for generating a surge self-focusing electron beam based on vortex circle Airy, which comprises the following steps:
the electron gun emits an electron beam;
the electron beam transmits a nano holographic diffraction pattern, and the pattern of the nano holographic diffraction pattern is subjected to cubic phase modulation through calculation, so that the transmitted electron beam is modulated into a round Airy electron beam;
the circular Airy electron beam passes through a Y-shaped diffraction hologram to generate vortex at the central axis of the circular Airy electron beam to obtain a circular Airy electron beam with central vortex, namely a vortex circular Airy electron beam;
focusing the eddy circle Airy electron beam through a magnetic lens, forming an eddy circle Airy wave packet on a focal plane, and recording the propagation of the eddy circle Airy electron beam by the focal plane;
the cross section of the swirling circular airy beam was observed by a transmission electron microscope.
Preferably, the pattern of the nano holographic diffraction pattern is manufactured by performing circular airy modulation calculation on the electron beam after calculation.
Preferably, the fork-shaped diffraction hologram is a grating, i.e., a holographic grating, which is manufactured by using a holographic reconstruction technique, forming interference fringes by interference of a reference beam and a target beam, and then performing an exchange according to the brightness and darkness of the interference fringes, and the purpose of the holographic grating is to increase the eddy in the center of the electron beam in the circle.
Preferably, the resolution of the transmission electron microscope is in the order of micrometers, and the fineness of the diffraction pattern and the interface of the vortex circular airy beam propagation can be observed.
Preferably, the initial field distribution of the circular Airy electron beams is
Figure 347838DEST_PATH_IMAGE001
，
Wherein
Figure 732683DEST_PATH_IMAGE002
For field strength, r is the radius, exp is the natural constant e,
Figure 453514DEST_PATH_IMAGE003
as a function of the number of airy rays,
Figure 743550DEST_PATH_IMAGE004
is the radius of the main ring, and the radius of the main ring,
Figure 247344DEST_PATH_IMAGE005
in order to be the width of the electron beam,
Figure 1542DEST_PATH_IMAGE006
is the attenuation factor.
As a matter of preference, it is preferred that,
Figure 299799DEST_PATH_IMAGE006
the value is 0.1.
Preferably, the initial field distribution of the vortex circular Airy electron beams has more vortex phases than the vortex circular Airy electron beams, and the initial field distribution is
Figure 952497DEST_PATH_IMAGE007
；
Wherein
Figure 523898DEST_PATH_IMAGE008
Is the field strength in a polar coordinate system,
Figure 617756DEST_PATH_IMAGE009
in order to provide a swirl term,
Figure 601761DEST_PATH_IMAGE010
is the azimuth angle in the cylindrical coordinate system.
In another aspect, the present invention provides a system for generating a sharp self-focusing electron beam based on a vortex circle airy, comprising:
an electron gun for emitting an electron beam;
the nano holographic diffraction pattern is used for transmitting the electron beam, and the cubic phase modulation is carried out on the pattern of the nano holographic diffraction pattern through calculation, so that the transmitted electron beam is modulated into a round Airy electron beam;
the Y-shaped diffraction hologram is used for enabling the passing round Airy electron beams to generate vortex at the central axis of the round Airy electron beams to obtain the round Airy electron beams with the central vortex, namely the vortex round Airy electron beams;
a magnetic lens for focusing the passing vortex circular Airy electron beam, wherein a vortex circular Airy wave packet is formed on a focal plane and the focal plane starts to record the propagation of the vortex circular Airy electron beam;
and a transmission electron microscope for observing the cross section of the vortex round Airy electron beam.
Preferably, the initial field distribution of the circular Airy electron beams is
Figure 148280DEST_PATH_IMAGE011
，
Wherein
Figure 711986DEST_PATH_IMAGE012
For field strength, r is the radius, exp is the natural constant e,
Figure 253825DEST_PATH_IMAGE003
as a function of the number of airy rays,
Figure 425044DEST_PATH_IMAGE004
is the radius of the main ring, and the radius of the main ring,
Figure 911389DEST_PATH_IMAGE005
the width of the electron beam is the width of the electron beam,
Figure 826255DEST_PATH_IMAGE013
is the attenuation factor.
Preferably, the initial field distribution of the vortex circular Airy electron beams has more vortex phases than the vortex circular Airy electron beams, and the initial field distribution is
Figure 222601DEST_PATH_IMAGE014
；
Wherein
Figure 551339DEST_PATH_IMAGE015
Is the field strength in a polar coordinate system,
Figure 541292DEST_PATH_IMAGE016
in order to provide a swirl term,
Figure 56587DEST_PATH_IMAGE017
is the azimuth angle in the cylindrical coordinate system.
Compared with the prior art, the invention has the beneficial effects that at least:
the electron beam generated by the invention has stronger focusing capability compared with other electron beams and has orbital angular momentum. The invention not only provides a new generation scheme, but also can regulate and control the intensity distribution and the phase of the common electron beam emitted from the electron gun, has the advantages of low manufacturing cost, simple system, convenient operation, wide application and the like, can effectively save the cost and improve the efficiency.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a method for generating a sharp self-focusing electron beam based on a vortex circle Airy according to the present invention;
FIG. 2 is a fork diffraction hologram producing vortices with a number of vortices of 1 and 3, respectively;
FIG. 3 is the initial field of a swirling circular Airy beam with a swirl number of 0,1,2;
fig. 4 is a schematic view of a propagation slice with a vortex number of 1 (n = 1) of the electron beam in a vortex circle airy;
fig. 5 is a propagation diagram of the simulated vortex circle airy beam vortex number of 1 (n = 1) with z =0, z =200 and z = 400.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. It should be noted that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and all other embodiments obtained by those skilled in the art without any inventive work based on the embodiments of the present invention belong to the protection scope of the present invention.
Example 1
As shown in fig. 1, the present invention provides a method for generating a sharp self-focusing electron beam based on a vortex circle airy, comprising the following steps:
s1, emitting an electron beam by an electron gun.
S2, the electron beam transmits a nano holographic diffraction pattern, cubic phase modulation is carried out on the pattern of the nano holographic diffraction pattern through calculation, the transmitted electron beam is modulated into a round Airy electron beam, and the round Airy electron beam is obtained at the moment, wherein the initial field of the round Airy electron beam is distributed into
Figure 697653DEST_PATH_IMAGE018
；
Wherein
Figure 538570DEST_PATH_IMAGE019
For field strength, r is the radius, exp is the natural constant e,
Figure 15818DEST_PATH_IMAGE020
as a function of the number of airy rays,
Figure 600384DEST_PATH_IMAGE004
is the radius of the main ring, and the radius of the main ring,
Figure 361535DEST_PATH_IMAGE005
in order to be the width of the electron beam,
Figure 373353DEST_PATH_IMAGE021
the attenuation factor (defined as 0.1).
S3, generating vortexes at the central axis of the round Airy electron beams through the round Airy electron beams by a fork-shaped diffraction hologram (shown in figure 2), and obtaining the round Airy electron beams with the central vortexes, namely vortex round Airy electron beams; compared with the circular Airy electron beam, the initial field distribution has more vortex phases
Figure 72319DEST_PATH_IMAGE022
；
Wherein
Figure 460575DEST_PATH_IMAGE008
Is the field strength in a polar coordinate system,
Figure 810654DEST_PATH_IMAGE023
in order to be a vortex term, the vortex term,
Figure 993374DEST_PATH_IMAGE010
is the azimuth angle in the cylindrical coordinate system.
Fig. 3 shows the initial field of the vortex circular airy beam, and different nano holographic diffraction patterns can be obtained by adjusting parameters, so that different vortex circular airy beams can be obtained. Shown in fig. 3 are three initial fields with a swirl number of 0,1,2.
S4, focusing the vortex circular Airy electron beams through the magnetic lens, forming vortex circular Airy wave packets on a focal plane, and recording the propagation of the vortex circular Airy electron beams by the focal plane.
And S5, observing the cross section of the vortex round Airy electron beam through a transmission electron microscope.
Fig. 4 is a schematic view of a propagation slice with a vortex number of 1 (n = 1) of the electron beam in a vortex circle airy, the darker the color representing the higher the intensity, and it can be seen that the intensity is gradually focused as the z direction increases. The sharp self-focusing feature is shown in fig. 4.
Fig. 5 is a propagation diagram of the simulated vortex circle airy beam vortex number of 1 (n = 1) with z =0, z =200 and z = 400.
The pattern of the nano holographic diffraction pattern is manufactured by performing circular airy modulation calculation on the electron beam after calculation.
The fork-shaped diffraction hologram is a holographic grating which is made by using a holographic reconstruction technology and forming interference fringes by using a reference beam and a target beam through interference and then performing interchange according to the brightness and darkness of the interference fringes, and aims to increase the vortex in the center of an electron beam in a circle Airy.
The resolution of the transmission electron microscope is higher than that of a common optical microscope, the resolution can reach the micron level, and the fineness of diffraction patterns and the interface of vortex circular Airy electron beam propagation can be observed.
Example 2
As shown in fig. 1, the present invention provides a surge self-focusing electron beam generating system based on vortex circle airy, comprising an electron gun, a nano holographic diffraction pattern, a fork diffraction hologram, a magnetic lens and a transmission electron microscope;
the electron gun is used for emitting electron beams;
the nano holographic diffraction pattern is used for transmitting electron beams, and cubic phase modulation is carried out on the patterns of the nano holographic diffraction pattern through calculation, so that the transmitted electron beams are modulated into round Airy electron beams;
the fork-shaped diffraction hologram is used for enabling the passing round Airy electron beam to generate vortex at the central axis of the round Airy electron beam to obtain the round Airy electron beam with the central vortex, namely the vortex round Airy electron beam;
the magnetic lens is used for focusing the passing vortex circular Airy electron beams, vortex circular Airy wave packets are formed on a focal plane, and the focal plane starts to record the propagation of the vortex circular Airy electron beams;
the transmission electron microscope is used for observing the cross section of the vortex round Airy electron beam.
Other features in this embodiment are the same as those in embodiment 1, and therefore are not described herein again.
The electron beam generated by the invention has stronger focusing capability compared with other electron beams and has orbital angular momentum. The invention not only provides a new generation scheme, but also can regulate and control the intensity distribution and the phase of the common electron beam emitted from the electron gun, has the advantages of low manufacturing cost, simple system, convenient operation, wide application and the like, can effectively save the cost and improve the efficiency.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (8)

1. A method for generating a sharp self-focusing electron beam based on vortex circle Airy is characterized by comprising the following steps:
the electron gun emits an electron beam;
the electron beam transmits a nano holographic diffraction pattern, and the pattern of the nano holographic diffraction pattern is subjected to cubic phase modulation through calculation, so that the transmitted electron beam is modulated into a round Airy electron beam;
the circular Airy electron beam passes through a Y-shaped diffraction hologram to generate vortex at the central axis of the circular Airy electron beam to obtain a circular Airy electron beam with central vortex, namely a vortex circular Airy electron beam;
focusing the eddy circle Airy electron beam through a magnetic lens, forming an eddy circle Airy wave packet on a focal plane, and recording the propagation of the eddy circle Airy electron beam by the focal plane;
observing the cross section of the vortex round Airy electron beam through a transmission electron microscope;
the initial field distribution of the round Airy electron beams is
Figure FDA0003999315970000011
Wherein E (r) is field strength, r is radius, exp is natural constant E, air (·) is Airy function, r is field intensity, r is radius, and 0 is the major ring radius, w o Is the electron beam width, a is the attenuation factor.
2. The method of claim 1, wherein the pattern of the nano holographic diffraction pattern is calculated by performing a circular airy modulation on the electron beam.
3. The method as claimed in claim 1, wherein the fork-shaped diffraction hologram is a holographic grating, which is formed by using a holographic reconstruction technique to form interference fringes by interfering a reference beam and a target beam, and then performing an interchange according to the brightness and darkness of the interference fringes, so as to increase the vortex in the center of the electron beam in the circle.
4. The method of claim 1, wherein the resolution of the transmission electron microscope is in the order of micron, and the fine degree of the diffraction pattern and the interface of the vortex circular Airy beam propagation can be observed.
5. The method of claim 1, wherein a is 0.1.
6. The method according to claim 1, wherein the initial field distribution of the vortex round Airy electron beams has more vortex phases than the round Airy electron beams, and the initial field distribution is
Figure FDA0003999315970000021
Wherein E (r, phi) is the field strength in a polar coordinate system, exp (il phi) is the vortex term, and phi is the azimuth angle in a cylindrical coordinate system.
7. A surge self-focusing electron beam generation system based on vortex circle Airy is characterized by comprising:
an electron gun for emitting an electron beam;
the nano holographic diffraction pattern is used for transmitting the electron beam, and the cubic phase modulation is carried out on the pattern of the nano holographic diffraction pattern through calculation, so that the transmitted electron beam is modulated into a round Airy electron beam;
the Y-shaped diffraction hologram is used for enabling the passing round Airy electron beams to generate vortex at the central axis of the round Airy electron beams to obtain the round Airy electron beams with the central vortex, namely the vortex round Airy electron beams;
a magnetic lens for focusing the passing eddy circular airy beam, the eddy circular airy wave packet being formed on a focal plane and the focal plane starting to record propagation of the eddy circular airy beam;
a transmission electron microscope for observing the cross section of the vortex round Airy electron beam;
the initial field distribution of the round Airy electron beams is
Figure FDA0003999315970000022
Wherein E (r) is field strength, r is radius, exp is natural constant E, air (·) is Airy function, r is field intensity, r is radius, and 0 is the major ring radius, w o Is the electron beam width, a is the attenuation factor.
8. The system of claim 7, wherein the vortex circular Airy beam has an initial field distribution with more vortex phases than the circular Airy beam, the initial field distribution being
Figure FDA0003999315970000031
Wherein E (r, phi) is the field strength in a polar coordinate system, exp (il phi) is the vortex term, and phi is the azimuth angle in a cylindrical coordinate system.
CN202211330455.0A 2022-10-28 2022-10-28 Method and system for generating surge self-focusing electron beam based on vortex circle Airy Active CN115394621B (en)

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