CN115047620B - Method for generating space-time wave packet with quasi-supercircular polarization topological structure under strong focusing condition - Google Patents
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Abstract
The invention discloses a method for generating a space-time wave packet with a quasi-supercircular 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 focusing by a high numerical aperture lens, a space-time wave packet with a quasi-super-circular polarization topological structure can be obtained at the lens focal plane, and the intensity distribution of the space-time wave packet forms a yo-yo three-dimensional space-time structure in a space-time domain. The quasi-superannular polarization topological structure formed on the focal plane after the radial polarization two-dimensional space-time vortex is strongly focused is in a transverse magnetic field mode, namely the oscillation direction of a magnetic field in a wave packet surrounds the weft line of the superannular, and the oscillation direction of an electric field surrounds the warp line of the superannular. The quasi-superannular polarization topological structure formed on the focal plane after the angular polarization two-dimensional space-time vortex is strongly focused is in a transverse electric field mode, at the moment, the oscillation direction of an electric field in the wave packet surrounds the weft line of the superannular, and the oscillation direction of a magnetic field surrounds the warp line of the superannular. The invention can be widely applied to the fields of interaction of light and substances, plasma physics, particle acceleration and energy sources, and provides an innovative method for further generating the electromagnetic field with the super-loop structure.
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 with a quasi-super-circular polarization topological structure under a strong focusing condition.
Background
The ring electrodynamics has attracted increasing interest because of the interesting electromagnetic properties of ring topology fields, which enable unconventional light and substance interactions. In electromagnetic metamaterials, resonant ring dipole responses were experimentally observed. The ring mode is also found in plasmons excited in oligomer nanochambers or metal-dielectric-metal sandwich nanostructures excited by radial polarization. In addition, ring modes are also found in the plasma excited in the oligomer nanochamber. 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 ring dipoles. In quantum computing, the insensitivity of the ring dipole to external noise can be exploited to protect the quantum from external interference. The dipole can also be used to measure dielectric constants 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-described local ring dipoles, ring topology wave packets may also exist in free space. Due to the duality of the electric and magnetic fields in free space. The wave packet with the ring topology structure has two forms, namely, a magnetic field oscillation direction surrounds a superloop weft, and an electric field oscillation direction surrounds a transverse magnetic field mode (TM) of the superloop warp; and a transverse electric field mode (TE) in which the electric field oscillation direction surrounds the weft of the superloop and the magnetic field oscillation direction surrounds the warp of the superloop. These two modes can be switched with each other by exchanging only the electric and magnetic fields, which are maxwell's "modified power spectrum" impulse solutions.
Subsequent studies have shown that the Gouy phase shift plays an important role in causing temporal remodeling, temporal inversion and polarity inversion as the monocycle electromagnetic pulse evolves through the focus. 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 dynamic ring dipole modes dominant 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 a ring wave packet 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 utilizing a quantum mechanical method. Despite much research in this emerging field, there is still a lack of methods to generate space-time wave packets in a super-circular polarization-like topology in the focal region of high numerical aperture lenses.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method for generating a space-time wave packet with a quasi-superloop polarization topological structure under a strong focusing condition, which can be widely applied to multiple fields of interaction of light and substances, plasma physics, particle acceleration and energy sources and provides an innovative method for further generating an electromagnetic field with a superloop structure. To achieve the above objects and other advantages and in accordance with the purpose of the invention, there is provided a method for generating a space-time wave packet of a quasi-supercircular polarization topology under a strong focusing condition, comprising:
a column vector two-dimensional spatiotemporal vortex for pretreatment is focused by a high numerical aperture lens comprising the steps of:
s1, taking a column vector two-dimensional space-time vortex as an incident light field of a 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 intensity of the wave packet in the time domain 2 Half pulse width at that point. e, e x Is a unit vector along the x-direction, e y Is a unit vector in the y-direction,
is the azimuth;
s2, carrying out pre-splitting treatment on an incident space-time wave packet to overcome the space-time astigmatism effect of a focusing system, wherein the expression after pre-splitting is as follows:
s21, carrying out pre-splitting treatment on column vector one-dimensional space-time vortex carrying transverse orbital angular momentum in an x-t plane, wherein the splitting method comprises the following steps:
wherein the method comprises the steps of
In order to carry column vector one-dimensional space-time vortex with topological charge number of +1 in the x-t plane,
in order to carry column vector one-dimensional space-time vortex with topological charge number of-1 in an x-t plane, the expressions are 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 column vector, and performing pre-splitting treatment to obtain the column vector two-dimensional space-time vortex with the expression:
s3, taking the preprocessed column vector two-dimensional space-time vortex as an incident field of a strong focusing system, focusing through a high numerical aperture lens, and obtaining a space-time wave packet with a quasi-ultra-circular polarization topological structure on a focal plane.
Preferably, β in step S1 is used to control the polarization state of the incident spatiotemporal vortex, and the incident field is radial polarized when β=0; the incident field is angularly polarized when β=90°.
Preferably, the field distribution of the space-time wave packet of the quasi-supercircular polarization topological structure in the focal plane in the step S3 can be calculated according to a 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 refractive field on sphere Ω, < >>
Can be expressed as:
θ is the angle between the refracted ray and the z axis; Φ is the azimuth in the focal plane; r is (r) f Is the observation point Q (r) on the focal plane f Phi) from the origin; z f Is the z-axis of the Cartesian coordinate system at the focal plane; alpha is the cone angle determined by the numerical aperture of the focusing lens.
Preferably, the said
The polarization change of the incident field after the polarization distribution is refracted by the high numerical aperture lens is described as follows:
when the value of beta is to be taken as 0,
when the angle beta is equal to 90 deg.,
compared with the prior art, the invention has the beneficial effects that:
(1) The method for generating the space-time wave packet with the quasi-superloop polarization topological structure at the lens focal plane by the pretreated column vector two-dimensional space-time vortex through high numerical aperture lens focusing provides a feasible technical path for experimentally generating the pulse wave packet with the superloop topological structure, and has important application prospects in the fields of energy, particle acceleration and the like.
(2) The space-time wave packet with the quasi-supercircular polarization topological structure generated by the invention carries the transverse orbital angular momentum and the polarization singular point in the space domain, and has potential application value in the field of orbital angular momentum and singular point optics.
(3) The invention can control the polarization state of the incident field to select the mode of the generated quasi-super-circular polarization topological structure.
(4) The method has wide application range, and can be suitable for space-time light fields in all wave bands.
Drawings
FIG. 1 is a schematic diagram of the principle of the pre-processed column vector two-dimensional spatio-temporal vortex focusing through a high numerical aperture lens according to the method of generating a spatio-temporal wave packet of a quasi-supercircular polarization topology under strong focusing conditions;
FIG. 2 is a diagram of three non-pretreated radially polarized incident wave packets and their horizontal and vertical polarization components of a method for generating a space-time wave packet of a quasi-supercircular polarization topology under strong focusing conditions according to the present invention;
FIG. 3 is a pre-processed radially polarized incident wave packet and its horizontal and vertical polarization components for a method of generating a space-time wave packet of a quasi-supercircular polarization topology under strong focusing conditions in accordance with the present invention;
FIG. 4 is a graph showing the intensity and phase distribution of three polarization components in a space-time wave packet with a super-circular polarization-like topology 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 a space-time wave packet with a super-circular polarization-like topology under strong focusing conditions;
fig. 5 is a view of a pre-processed radial polarized two-dimensional spatiotemporal vortex of a method of generating a spatiotemporal wave packet of a quasi-toroidal polarization topology under strong focusing conditions according to the present invention after focusing by a high numerical aperture lens to obtain a spatiotemporal wave packet of a quasi-toroidal polarization topology at the lens focal plane.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1-5, a method for generating space-time wave packets of a quasi-supercircular polarization topology under strong focusing conditions, comprising: a column vector two-dimensional spatiotemporal vortex for pretreatment focused by a high numerical aperture lens comprising the steps of:
s1, taking a column vector two-dimensional space-time vortex as an incident light field of a 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 intensity of the wave packet in the time domain 2 Half pulse width at that point. e, e x Is a unit vector along the x-direction, e y Is a unit vector in the y-direction,
is the azimuth;
s2, carrying out pre-splitting treatment on an incident space-time wave packet to overcome the space-time astigmatism effect of a focusing system, wherein the detailed pre-splitting process is as follows:
s21, carrying out pre-splitting treatment on column vector one-dimensional space-time vortex carrying transverse orbital angular momentum in an x-t plane, wherein the splitting method comprises the following steps:
wherein the method comprises the steps of
In order to carry column vector one-dimensional space-time vortex with topological charge number of +1 in the x-t plane,
to carry topology charges in x-t plane of-1Column vector one-dimensional spatiotemporal vortices of which 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 column vector, and performing pre-splitting treatment to obtain the column vector two-dimensional space-time vortex with the expression:
s3, taking the preprocessed column vector two-dimensional space-time vortex as an incident field of a strong focusing system, focusing through a high numerical aperture lens, and obtaining a space-time wave packet with a quasi-super-circular polarization topological structure on a focal plane, wherein the quasi-super-circular 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; the super-circular polarization-like 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.
Further, β in step S1 is used to control the polarization state of the incident space-time vortex, and when β=0, the incident field is radial polarization; the incident field is angularly polarized when β=90°.
Further, the field distribution of the space-time wave packet of the quasi-supercircular polarization topological structure in the focal plane in the step S3 can be calculated according to the richard-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 refractive field on sphere Ω, < >>
Can be expressed as:
θ is the angle between the refracted ray and the z axis; Φ is the azimuth in the focal plane;
the complex amplitude distribution of the refractive field on the sphere Ω is described.
Further, the said
The polarization change of the incident field after the polarization distribution is refracted by the high numerical aperture lens is described as follows:
when the value of beta is to be taken as 0,
when the angle beta is equal to 90 deg.,
as shown in FIG. 1, after the pretreated column vector two-dimensional space-time vortex is focused by a high numerical aperture lens, a space-time wave packet with a quasi-supercircular polarization topological structure can be obtained on a focal plane. The specific implementation of the technical scheme is described herein by taking the space-time wave packet with a transverse magnetic field mode and similar to a super-circular polarization topological structure as an example, and the method comprises the following steps:
step one: 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, it can be seen from fig. 2 (a) and 2 (b) that the x-polarization component carries the transverse OAM with the topology charge +1 in the y-t plane, and from fig. 2 (c) and 2 (d) that the y-polarization component carries the transverse OAM with the topology charge +1 in the x-t plane. From fig. 2 (e) it can be seen that the uncracked radially polarized incident space-time wave packet contains both one 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-polarized component, a factor is caused by the x-coordinate
The sign change of (a), the transverse OAM in the x-t plane is destroyed; whereas for the y-polarized component the factor +_ is due to the y-coordinate>
The sign change of (c) and the transverse OAM in the y-t plane is destroyed.
Step two: collapse of the spatio-temporal spiral phase distribution occurs due to the effect of spatio-temporal astigmatism upon focusing of the high numerical aperture lens. In order to overcome the space-time astigmatism effect, the incident space-time wave packet needs to be subjected to pre-splitting treatment, and the wave packet after treatment can be expressed as:
the field distribution of the incident space-time wave packet after pre-splitting is shown in fig. 3, and the x-polarized component wave packet, the y-polarized component wave packet and the whole incident space-time wave packet can be seen from fig. 3 (a), 3 (c) and 3 (e), and split into four parts. The intensity of the x-polarized component is mainly distributed in the x-t plane and the intensity of the y-polarized component is mainly distributed in the y-t plane. The phase distribution of the x-polarized component and the y-polarized component as shown in fig. 3 (b) and 3 (d) is discretized into 0.5 pi (light gray area), -0.5 pi (black area), and 0 (dark gray area). The pre-split wave packet is radially polarized in the spatial domain as shown in fig. 3 (f).
Step three: the pretreated radial polarization two-dimensional space-time vortex is focused by a high numerical aperture lens, and a space-time wave packet with a cross magnetic field mode and similar to a super-circular polarization topological structure is generated at the focal plane of the lens.
According to the richard-Wolf vector diffraction formula, the 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 calculated as shown in fig. 4 and 5, respectively. As shown in fig. 4 (a) and 4 (c), the wave packet of the x-polarized component is orthogonal to the wave packet of the y-polarized component; as shown in fig. 4 (b), the phase distribution of the x-polarized component changes anticlockwise from-pi to pi in the y-t plane, which indicates that the x-polarized component carries a transverse OAM with a topological charge of +1 in the y-t plane; as shown in fig. 4 (d), the phase distribution of the y-polarized component changes anticlockwise from-pi to pi in the x-t plane, which indicates that the y-polarized component carries a transverse OAM with a topological charge of +1 in the x-t plane; as shown in fig. 4 (e) and 4 (f), the z-polarized component presents transverse OAM in both the x-t and y-t planes, resulting in the presence of phase singularities trajectories 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 symmetrically distributed about the coordinate plane of t=0, so that several typical slices are taken in the interval of t [ -2,0] to analyze the polarization evolution condition, and as can be seen from the above, the polarization distribution in the x-y plane remains substantially radial when the slices scan the wave packet from front to back along the t-axis. When the slice is near the middle of the wave packet, the polarization behavior is more complex, and the polarization distribution becomes a quadrupole-like polarization distribution near t=0, and the polarization distribution around each polarization singular point is still radial polarization. Therefore, after radial polarization two-dimensional space-time vortex is strongly focused, the quasi-superannular polarization topological structure formed on the focal plane is in a transverse magnetic field mode, namely the oscillation direction of a magnetic field in a wave packet surrounds the weft line of the superannular, and the oscillation direction of an electric field surrounds the warp line of the superannular.
The number of devices and the scale of processing 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. Although embodiments of the present invention have been disclosed above, it is not limited to the details and embodiments shown and described, it is well suited to various fields of use for which the invention would be readily apparent to those skilled in the art, and accordingly, the invention is not limited to the specific details and illustrations shown and described herein, without departing from the general concepts defined in the claims and their equivalents.
Claims (3)
1. The method for generating the space-time wave packet with the quasi-supercircular polarization topological structure under the strong focusing condition is used for 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 a column vector two-dimensional space-time vortex as an incident light field of a 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 intensity of the wave packet in the time domain 2 Half pulse width at; e, e x Is a unit vector along the x-direction, e y Is a unit vector along the y-direction; wherein β is used to control the polarization state of the incident spatiotemporal vortex, the incident field is radially polarized when β=0; the incident field is angularly polarized when β=90°,
is the azimuth;
s2, carrying out pre-splitting treatment on an incident space-time wave packet to overcome the space-time astigmatism effect of a focusing system, wherein the expression after pre-splitting is as follows:
s3, taking the preprocessed column vector two-dimensional space-time vortex as an incident field of a strong focusing system, focusing through a high numerical aperture lens, and obtaining a space-time wave packet with a quasi-ultra-circular polarization topological structure on a focal plane.
2. The method for generating a space-time wave packet with a quasi-supercircular polarization topology according to claim 1, wherein the field distribution of the space-time wave packet with a quasi-supercircular polarization topology in the focal plane in step S3 can be calculated according to the richard-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 refractive field on sphere Ω, < >>
Can be expressed as:
θ is the angle between the refracted ray and the z axis; phi is the azimuth angle in the focal plane, r f Is the observation point Q (r) on the focal plane f Phi) from the origin; z f Is the z-axis of the Cartesian coordinate system at the focal plane; α is the cone angle determined by the numerical aperture of the focusing lens;
the said
The polarization change of the incident field after the polarization distribution is refracted by the high numerical aperture lens is described as follows:
when the value of beta is to be taken as 0,
when the angle beta is equal to 90 deg.,
3. the method of generating a space-time wave packet of a quasi-supercircular polarization topology according to claim 2, wherein the obtaining of the space-time wave of the quasi-supercircular polarization topology in the focal plane through the focusing of the high numerical aperture lens comprises the strong focusing of the radial polarization two-dimensional space-time vortex and the strong focusing of the angular polarization two-dimensional space-time vortex, wherein the quasi-supercircular polarization topology formed in the focal plane after the radial polarization two-dimensional space-time vortex is strongly focused is a transverse magnetic field mode, and the quasi-supercircular polarization topology formed in 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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