CN115047620A - Method for generating time-space wave packet of quasi-toroidal polarization topological structure under strong focusing condition - Google Patents
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Abstract
The invention discloses a method for generating a time-space wave packet of a quasi-toroidal polarization topological structure under a strong focusing condition, which comprises the following steps: by pre-splitting the column vector two-dimensional space-time vortex, after the column vector two-dimensional space-time vortex is focused by a high numerical aperture lens, a space-time wave packet with a super-ring-like polarization topological structure can be obtained at a lens focal plane, and the intensity of the space-time wave packet is distributed in a time-space domain to form a yo-yo spherical three-dimensional space-time structure. A radial polarization two-dimensional space-time vortex is focused strongly, and then a super-ring-like polarization topological structure formed on a focal plane is in a transverse magnetic field mode, namely the oscillation direction of a magnetic field in a wave packet surrounds the latitude lines of a super-ring, and the oscillation direction of an electric field surrounds the longitude lines of the super-ring. The angular polarization two-dimensional space-time vortex is focused strongly, then a super-ring-like polarization topological structure formed on a focal plane is in a transverse electric field mode, at the moment, the oscillation direction of an electric field in a wave packet surrounds the latitude lines of the super-ring, and the oscillation direction of a magnetic field surrounds the longitude lines of the super-ring. The method can be widely applied to the fields of light and substance interaction, plasma physics, particle acceleration and energy sources, and provides an innovative method for further generating the super-ring structure electromagnetic field.
Description
Technical Field
The invention relates to the technical field of electromagnetic wave information transmission, in particular to a method for generating a space-time wave packet of a quasi-toroidal polarization topological structure under a strong focusing condition.
Background
Circular electrodynamics is of increasing interest because the interesting electromagnetic properties of the circular topological fields allow for unconventional light-to-substance interactions. In electromagnetic metamaterials, a resonant ring dipole response is experimentally observed. Circular modes are also found in plasmons excited in oligomer nanocavities or metal-dielectric-metal sandwich nanostructures excited by radial polarization. In addition, a toroidal mode is also found in the plasma excited in the oligomer nanocavity. The scientific community also proposes a novel spectroscopy method based on standing wave illumination for analyzing optical transitions of different materials under the action of a ring dipole. In quantum computing, the insensitivity of the ring dipole to external noise can be used to protect the quantum from external interference. A dipole can also be used to measure dielectric constant because it can directionally deposit energy in a material with a higher polarization rate at the interface of two media.
In addition to the above-mentioned local ring dipoles, ring topology wave packets may also exist in free space. Due to the duality of an electric field and a magnetic field in a free space, the wave packet of the ring topological structure has two forms, namely a transverse magnetic field mode (TM) that the oscillation direction of the magnetic field surrounds the latitude line of the super ring and the oscillation direction of the electric field surrounds the longitude line of the super ring; and a transverse electric field mode (TE) in which the electric field oscillation direction surrounds the latitude lines of the supercycle and the magnetic field oscillation direction surrounds the longitude lines of the supercycle. These two modes can be switched to each other by merely exchanging the electric and magnetic fields, which are maxwell's "modified power spectrum" pulse solutions.
Subsequent studies have shown that the Gouy phase shift plays an important role in causing temporal remodeling, time reversal and polarity reversal when monocycle electromagnetic pulses evolve through a focal point. In recent years, studies have shown that ring pulses undergo complex polarization sensitive transformations in isotropic media under reflection and refraction, and can excite the dominant dynamic ring dipole modes in spherical dielectric particles. The TM ring pulse can be used as a diagnostic and spectroscopic analysis tool for dynamic anapole excitation in dielectric materials. Later researchers designed a metamaterial converter that generated ring packets by controlling the spatial and spectral structure of the incident pulse. In addition, the singular points in the electromagnetic ring pulse are subjected to numerical analysis, and the space-time inseparability in the electromagnetic ring pulse is quantitatively analyzed by using a quantum mechanical method. Despite the extensive research in this emerging field, there is still a lack of methods for generating space-time wave packets in a super-ring-like polarization topology at the focal zone of a high numerical aperture lens.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for generating a space-time wave packet of a quasi-toroidal polarization topological structure under a strong focusing condition, which can be widely applied to the fields of light and substance interaction, plasma physics, particle acceleration and energy and provides a pioneering method for further generating a super-ring structured electromagnetic field. To achieve the above objects and other advantages in accordance with the present invention, there is provided a method for generating a space-time wave packet of a super-ring polarization-like topology under strong focusing conditions, comprising:
focusing the preprocessed column vector two-dimensional space-time vortex through a high numerical aperture lens, and the method comprises the following steps:
s1, taking the column vector two-dimensional space-time vortex as an incident light field of the focusing system, wherein the expression is as follows:
where w is the beam waist radius of the wave packet in the spatial domain, w t Is 1/e of the maximum strength of the wave packet in the time domain 2 Half pulse width of (d). e.g. of the type x Is a unit vector in the x direction, e y Is a unit vector in the y direction;
s2, pre-splitting the incident space-time wave packet to overcome the space-time astigmatism effect of the focusing system, the detailed pre-splitting process is as follows:
s21, pre-splitting the column vector one-dimensional space-time vortex carrying the transverse orbital angular momentum in the x-t plane, wherein the splitting method comprises the following steps:
wherein
Is a one-dimensional space-time vortex carrying a column vector with topological charge number of +1 in an x-t plane,
in order to carry the column vector one-dimensional space-time vortex with topological charge number of-1 in an x-t plane, the expressions are respectively as follows:
s22, on the basis of the formula (2) in the step S21, applying a space-time spiral phase in a y-t plane to the pre-splitting column, and performing pre-splitting treatment to obtain a pre-split column vector two-dimensional space-time vortex expression as follows:
and S3, taking the preprocessed column vector two-dimensional space-time vortex as an incident field of a strong focusing system, and focusing the incident field through a high-numerical-aperture lens to obtain a space-time wave packet with a quasi-toroidal polarization topological structure on a focal plane.
Preferably, in step S1, β is used to control the polarization state of the incident spatio-temporal vortex, and when β is 0, the incident field is radial polarization; the incident field is angularly polarized when β is 90 °.
Preferably, the field distribution of the time-space wave packet of the super-ring-like polarization topology in the focal plane in step S3 can be calculated according to Richards-Wolf vector diffraction formula:
wherein B (θ) describes the apodization function of the lens, for a sinusoidal lens
Describing the complex amplitude distribution of the refracted field on the sphere omega,
can be expressed as:
preferably, the
The polarization change of the polarization distribution of the incident field after refraction by the high numerical aperture lens is described as follows:
when the beta is equal to 0, the beta value,
when β is equal to 90 °,
compared with the prior art, the invention has the beneficial effects that:
(1) the method for generating the space-time wave packet with the super-ring-like polarization topological structure at the focal plane of the lens by focusing the preprocessed column vector two-dimensional space-time vortex through the high-numerical-aperture lens provides a feasible technical path for generating the pulse wave packet with the super-ring topological structure experimentally, and has important application prospects in the fields of energy, particle acceleration and the like.
(2) The space-time wave packet of the super-ring-like polarization topological structure generated by the invention simultaneously carries transverse orbital angular momentum and polarization singularity in a spatial domain, and has potential application value in the field of orbital angular momentum and singularity optics.
(3) The invention can control the polarization state of the incident field to select the mode of the generated super-ring-like polarization topological structure.
(4) The method has wide application range, and the method can be suitable for the space-time light field of the full wave band.
Drawings
FIG. 1 is a schematic diagram of the principle of focusing a preprocessed column vector two-dimensional space-time vortex through a high numerical aperture lens according to the method for generating a super-ring-like polarization topological structure space-time wave packet under a strong focusing condition of the present invention;
FIG. 2 is an unpreprocessed radially polarized incident wave packet and its horizontal and vertical polarization components of a method of generating a super-ring-like polarization topology space-time wave packet under strong focusing conditions according to the present invention;
FIG. 3 is a diagram of a preprocessed radially polarized incident wave packet and its horizontal and vertical polarization components of a method of generating a super-ring-like polarization topology space-time wave packet under strong focusing conditions according to the present invention;
FIG. 4 is a diagram of intensity and phase distribution of three polarization components in a space-time wave packet with a super-ring-like polarization topology structure obtained at a lens focal plane after a pre-processed radial polarization two-dimensional space-time vortex is focused by a high numerical aperture lens according to the method for generating the super-ring-like polarization topology structure space-time wave packet under a strong focusing condition of the present invention;
FIG. 5 shows the space-time wave packet with super-ring-like polarization topology and its polarization distribution obtained at the lens focal plane after the pre-processed radial polarization two-dimensional space-time vortex is focused by a high numerical aperture lens according to the method for generating the super-ring-like polarization topology space-time wave packet under the strong focusing condition of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Referring to fig. 1-5, a method for generating a time-space wave packet of a super-ring polarization-like topology under a strong focusing condition includes: focusing the preprocessed column vector two-dimensional space-time vortex through a high numerical aperture lens, and is characterized by comprising the following steps of:
s1, taking the column vector two-dimensional space-time vortex as an incident light field of the focusing system, wherein the expression is as follows:
where w is the beam waist radius of the wave packet in the spatial domain, w t Is 1/e of the maximum strength of the wave packet in the time domain 2 Half pulse width of (d). e.g. of the type x Is a unit vector in the x direction, e y Is a unit vector in the y-direction;
s2, pre-splitting the incident space-time wave packet to overcome the space-time astigmatism effect of the focusing system, the detailed pre-splitting process is as follows:
s21, pre-splitting the column vector one-dimensional space-time vortex carrying the transverse orbital angular momentum in the x-t plane, wherein the splitting method comprises the following steps:
wherein
Is a one-dimensional space-time vortex carrying a column vector with topological charge number of +1 in an x-t plane,
to carry in the x-t planeThe column vector one-dimensional space-time vortex with topological charge number of-1 has the following expressions:
s22, on the basis of the formula (2) in the step S21, applying a space-time spiral phase in a y-t plane to the pre-splitting column, and performing pre-splitting treatment to obtain a pre-split column vector two-dimensional space-time vortex expression as follows:
s3, taking the preprocessed column vector two-dimensional space-time vortex as an incident field of a strong focusing system, focusing the incident field through a high-numerical-aperture lens, obtaining a space-time wave packet with a quasi-toroidal polarization topological structure on a focal plane, and strongly focusing the radial polarization two-dimensional space-time vortex to form the quasi-toroidal polarization topological structure on the focal plane as a transverse magnetic field mode; the two-dimensional space-time vortex of angular polarization is focused strongly, and then a super-ring-like polarization topological structure formed on a focal plane is in a transverse electric field mode.
Further, in step S1, β is used to control the polarization state of the incident spatio-temporal vortex, and when β is equal to 0, the incident field is radial polarization; the incident field is angularly polarized when β is 90 °.
Further, the field distribution of the time-space wave packet of the super-ring-like polarization topology structure in the focal plane in step S3 can be calculated according to Richards-Wolf vector diffraction formula:
wherein B (θ) describes the apodization function of the lens, for a sinusoidal lens
Describing the complex amplitude distribution of the refracted field on the sphere omega,
can be expressed as:
further, the
The polarization change of the polarization distribution of the incident field after refraction by the high numerical aperture lens is described as follows:
when the beta is equal to 0, the beta value,
when β is equal to 90 °,
as shown in fig. 1, after the preprocessed column vector two-dimensional space-time vortex is focused by a high numerical aperture lens, a space-time wave packet with a super-ring-like polarization topological structure can be obtained on a focal plane. The specific implementation of the technical solution is illustrated here by taking as an example the generation of a space-time wave packet with a transverse magnetic field pattern of a super-ring-like polarization topology, comprising the following steps:
the method comprises the following steps: the radial polarization two-dimensional space-time vortex is taken as an incident field of a strong focusing system, and can be expressed as follows:
the field distribution of the uncleaved radial polarization two-dimensional space-time vortex in the space-time domain is shown in fig. 2, and it can be seen from fig. 2(a) and 2(b) that the x-polarization component carries the transverse OAM of the topological charge +1 in the y-t plane, and it can be seen from fig. 2(c) and 2(d) that the y-polarization component carries the transverse OAM of the topological charge +1 in the x-t plane. It can be seen from fig. 2(e) that the uncleaved radially polarized incident space-time wave packet contains both one spatial polarization singularity and two space-time OAM singularities, which are orthogonal to each other. FIG. 2(f) shows that the polarization distribution in the x-y plane remains radially polarized, with a polarization singularity present. For the x-polarization component, the factor is due to the x-coordinate
The sign of (2) is changed, the transverse OAM in the x-t plane is destroyed; whereas for the y-polarization component, the factor is due to the y-coordinate
The transverse OAM in the y-t plane is destroyed.
Step two: collapse of the spatio-temporal helical phase distribution occurs during focusing of high numerical aperture lenses due to the effect of spatio-temporal astigmatism. In order to overcome the space-time astigmatism effect, pre-splitting processing needs to be performed on an incident space-time wave packet, and the processed wave packet can be represented as follows:
the field distribution of the pre-cleaved incident spatiotemporal wave packet is shown in fig. 3, and it can be seen from fig. 3(a), 3(c) and 3(e) that the x and y polarization component wave packets and the whole incident spatiotemporal wave packet are cleaved into four parts. The intensity of the x-polarized component is distributed mainly in the x-t plane and the intensity of the y-polarized component is distributed mainly in the y-t plane. The phase distributions of the x-polarization component and the y-polarization component are dispersed as 0.5 pi (light gray region), -0.5 pi (black region), and 0 (dark gray region) as shown in fig. 3(b) and 3 (d). The pre-cleave processed wave packet is radially polarized in the spatial domain as shown in fig. 3 (f).
Step three: focusing the preprocessed radial polarization two-dimensional space-time vortex through a high-numerical-aperture lens, and generating a super-ring-like polarization topological structure space-time wave packet with a transverse magnetic field mode at a lens focal plane.
According to the Richards-Wolf vector diffraction formula, the calculated field distribution of each component of the strongly focused space-time wave packet on the focal plane and the polarization distribution of the total focused wave packet in the spatial domain are respectively shown in FIGS. 4 and 5. As shown in fig. 4(a) and 4(c), the wave packet of the x-polarization component is orthogonal to the wave packet of the y-polarization component; as shown in fig. 4(b), the phase distribution of the x-polarized component changes counterclockwise from-pi to pi on the y-t plane, indicating that the x-polarized component carries a transverse OAM with a topological charge of +1 on the y-t plane; as shown in fig. 4(d), the phase distribution of the y-polarized component changes counterclockwise from-pi to pi on the x-t plane, indicating that the y-polarized component carries a transverse OAM with a topological charge of +1 on the x-t plane; as shown in fig. 4(e) and 4(f), the z-polarization component has transverse OAM in both the x-t and y-t planes, resulting in phase singularity traces in the wave packet along the x-axis and y-axis, respectively. As shown in fig. 5, the polarization distribution of the strongly focused wave packet in the spatial domain is symmetrical about the coordinate plane where t is 0, so that several typical slices are taken in the range of [ -2, 0] of t to analyze the polarization evolution, and it can be seen that the polarization distribution in the x-y plane is substantially maintained as a radial distribution when the slices scan the wave packet from front to back along the t axis. When the slice is close to the middle of the wave packet, the polarization performance is more complicated, the polarization distribution becomes a quasi-quadrupole polarization distribution when t is close to 0, and the polarization distribution around each polarization singularity is still radial polarization. Therefore, after radial polarization two-dimensional space-time vortex is focused strongly, a super-ring-like polarization topological structure formed on a focal plane is in a transverse magnetic field mode, namely the oscillation direction of a magnetic field in a wave packet surrounds the latitude line of a super-ring, and the oscillation direction of an electric field surrounds the longitude line of the super-ring.
The number of devices and the scale of the processes described herein are intended to simplify the description of the invention, and applications, modifications and variations of the invention will be apparent to those skilled in the art.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.
Claims (5)
1. A method for generating a space-time wave packet of a quasi-toroidal polarization topological structure under a strong focusing condition is used for focusing a preprocessed column vector two-dimensional space-time vortex through a high-numerical-aperture lens, and is characterized by comprising the following steps of:
s1, taking the column vector two-dimensional space-time vortex as an incident light field of the focusing system, wherein the expression is as follows:
where w is the beam waist radius of the wave packet in the spatial domain, w t Is 1/e of the maximum strength of the wave packet in the time domain 2 Half pulse width of (d). e.g. of the type x Is a unit vector in the x direction, e y Is a unit vector in the y-direction;
s2, pre-splitting the incident space-time wave packet to overcome the space-time astigmatism effect of the focusing system, wherein the pre-splitting expression is as follows:
and S3, taking the preprocessed column vector two-dimensional space-time vortex as an incident field of a strong focusing system, and focusing the incident field through a high-numerical-aperture lens to obtain a space-time wave packet with a quasi-toroidal polarization topological structure on a focal plane.
2. The method for generating space-time wave packet of super ring polarization-like topology under strong focusing condition as claimed in claim 1, wherein β is used to control polarization state of incident space-time vortex in step S1, and incident field is radial polarization when β is 0; the incident field is angularly polarized when β is 90 °.
3. The method for generating super ring polarization-like topological structure space-time wave packet under strong focusing condition according to claim 2, wherein the field distribution of super ring polarization-like topological structure space-time wave packet in the focal plane in step S3 can be calculated according to Richards-Wolf vector diffraction formula:
wherein B (θ) describes the apodization function of the lens, for a sinusoidal lens
Describing the complex amplitude distribution of the refracted field on the sphere omega,
can be expressed as:
4. the method for generating super-ring polarization-like topology space-time wave packet under strong focusing condition according to claim 3, wherein said method is characterized in that
The polarization change of the polarization distribution of the incident field after refraction by the high numerical aperture lens is described as follows:
when the beta is equal to 0, the beta value,
when β is equal to 90 °,
5. the method for generating the super-ring-like polarization topological structure space-time wave packet under the strong focusing condition according to claim 4, wherein the obtaining of the space-time wave with the super-ring-like polarization topological structure on the focal plane through the focusing of the high numerical aperture lens includes that the radial polarization two-dimensional space-time vortex is strongly focused and the angular polarization two-dimensional space-time vortex is strongly focused, wherein the super-ring-like polarization topological structure formed on the focal plane after the radial polarization two-dimensional space-time vortex is strongly focused is a transverse magnetic field mode, and the super-ring-like polarization topological structure formed on the focal plane after the angular polarization two-dimensional space-time vortex is strongly focused is a transverse electric field mode.
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