CN114895476A - Method for generating diffraction-free Lommel light beam based on super surface - Google Patents

Method for generating diffraction-free Lommel light beam based on super surface Download PDF

Info

Publication number
CN114895476A
CN114895476A CN202210830784.5A CN202210830784A CN114895476A CN 114895476 A CN114895476 A CN 114895476A CN 202210830784 A CN202210830784 A CN 202210830784A CN 114895476 A CN114895476 A CN 114895476A
Authority
CN
China
Prior art keywords
lommel
phase
super
light beam
diffraction
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202210830784.5A
Other languages
Chinese (zh)
Other versions
CN114895476B (en
Inventor
徐弼军
职佳浩
孙志通
林经纬
胡泊
郭运成
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhejiang Lover Health Science and Technology Development Co Ltd
Original Assignee
Zhejiang Lover Health Science and Technology Development Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang Lover Health Science and Technology Development Co Ltd filed Critical Zhejiang Lover Health Science and Technology Development Co Ltd
Priority to CN202210830784.5A priority Critical patent/CN114895476B/en
Publication of CN114895476A publication Critical patent/CN114895476A/en
Application granted granted Critical
Publication of CN114895476B publication Critical patent/CN114895476B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • 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

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Diffracting Gratings Or Hologram Optical Elements (AREA)

Abstract

The invention discloses a method for generating a diffraction-free Lommel beam based on a super surface, which comprises the following steps: a. obtaining a Lommel mode by infinite superposition of Bessel modes, and obtaining a Lommel beam phase; b. acquiring a Dammann grating phase by using the Dammann grating; c. combining the Lommel light beam phase and the Dammann grating phase to generate a Lommel light beam array super surface; d. a Lommel beam array super-surface is used to generate a non-diffracting Lommel beam. The invention can be applied to generate the non-diffraction Lommel beam by the super surface and has potential application in the fields of optical communication, optical tweezers, non-diffraction beam generation and the like.

Description

Method for generating diffraction-free Lommel light beam based on super surface
Technical Field
The invention relates to the technical field of super surfaces, in particular to a method for generating a diffraction-free Lommel beam based on a super surface.
Background
The Lommel beam is a nonparaxial non-diffracted beam proposed in Lommel models, published in the journal of Optics Communications (ISSN: 0030-. Compared to the bezier mode, such a beam has a central spot with a narrow radius, a lateral intensity distribution of the beam has reflection symmetry with respect to two cartesian axes, and has a continuously variable OAM. Qian Zhao et al, in applied optics (ISSN: 1559-128X), first verified using a digital binary amplitude mask and generated a diffraction-free Lommel beam. Belafhal et al, Journal of Quantitative Spectroscopy & radial Transmission (ISSN: 0022) 4073, in an A study of non-diffractive Lommel beams propagating in a medium containing spheres, found that irradiation of rigid spheres by a Lommel beam produces asymmetric scattering. Recently, the Lommel beam has made great progress in the study of communication and turbulence. LIN YU et al published an article entitled "Intensity of vortex modules carried by Lommel beam in wind-to-strandnon-Kolmogorov passage" in the journal of Optics EXPRESS (ISSN: 1094) -4087, studied the effect of atmospheric turbulence on the propagation of vortex modes of Lommel beams, and the results of the study helped to design free-space optical communication links based on orbital angular momentum. The Scintillation and Bit Error Rate of the Lommel Beam are analyzed in the science and Bit Error Analysis of the Lommel Beam published by Mert Bayraktar in the Wireless Personal Communications (ISSN: 0929-6212) journal, and the Lommel Beam has better superiority than the Gaussian Beam.
The super surface is a two-dimensional optical surface formed by periodically arranging sub-wavelength materials, and due to the planarization structure and the excellent characteristics of controlling the phase, amplitude and polarization of light beams, a wide stage is created for the research and development of optical devices. The concept of super-surface is first proposed by Federico Capsos et al in Science (ISSN: 0036-. However, no attempt has been made to apply the Lommel beam to a super-surface.
Disclosure of Invention
The invention aims to provide a method for generating a diffraction-free Lommel light beam based on a super surface. The invention can be applied to generate the non-diffraction Lommel beam by the super surface and has potential application in the fields of optical communication, optical tweezers, non-diffraction beam generation and the like.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: a method for generating a diffraction-free Lommel beam based on a super surface comprises the following steps:
a. obtaining a Lommel mode by infinite superposition of Bessel modes, and obtaining a Lommel beam phase;
b. acquiring a Dammann grating phase by using the Dammann grating;
c. combining the Lommel light beam phase and the Dammann grating phase to generate a Lommel light beam array super surface;
d. and generating a diffraction-free Lommel beam array by using the super surface of the Lommel beam array.
In the method for generating the diffraction-free Lommel beam based on the super surface, the obtaining of the phase of the Lommel beam is that a complex amplitude expression of the Lommel light field along the transmission direction of the optical axis is represented by a Bessel function under a cylindrical coordinate:
Figure DEST_PATH_IMAGE001
；（1）
in the formula (I), the compound is shown in the specification,
Figure 378884DEST_PATH_IMAGE002
represents an electric field;
Figure DEST_PATH_IMAGE003
，
Figure 45489DEST_PATH_IMAGE004
and, represents the position vector, and,
Figure DEST_PATH_IMAGE005
representing position coordinates;
Figure 107991DEST_PATH_IMAGE006
is the azimuth;
Figure DEST_PATH_IMAGE007
represents a transmission distance;
Figure 543652DEST_PATH_IMAGE008
is the propagation factor of the signal that is,
Figure DEST_PATH_IMAGE009
denotes a wavelength of
Figure 502250DEST_PATH_IMAGE010
The wave number of the incident wave of (a);
Figure DEST_PATH_IMAGE011
is an imaginary symbol;
Figure 390571DEST_PATH_IMAGE012
and, the transverse wave component is represented,
Figure DEST_PATH_IMAGE013
is the numerical aperture;
Figure 460027DEST_PATH_IMAGE014
the number of times of superposition;
Figure DEST_PATH_IMAGE015
asymmetric complex parameters;
Figure 750194DEST_PATH_IMAGE016
is the number of angular momentum of the photon orbit;
Figure DEST_PATH_IMAGE017
representing the transverse field distribution of the Lommel beam;
Figure 903131DEST_PATH_IMAGE018
to represent
Figure DEST_PATH_IMAGE019
A first class Bessel function of order;
when asymmetric complex parameter
Figure 278748DEST_PATH_IMAGE015
When =0, all the series terms in equation (1) take zero values, and the Lommel pattern becomes a Bessel pattern:
Figure 168207DEST_PATH_IMAGE020
；（2）
function of Lommel beam
Figure DEST_PATH_IMAGE021
Expressed as:
Figure 827727DEST_PATH_IMAGE022
；（3）
in the formula:
Figure DEST_PATH_IMAGE023
and
Figure 878860DEST_PATH_IMAGE024
is two variables;
using functions
Figure DEST_PATH_IMAGE025
To express equation (1):
Figure 991041DEST_PATH_IMAGE026
；（4）
converting equation (4) from cylindrical coordinates to cartesian coordinates, expressed as:
Figure DEST_PATH_IMAGE027
；（5）
solving the corresponding phase angle obtained by the formula (5) to obtain the phase of the Lommel beam
Figure 153032DEST_PATH_IMAGE028
。
In the method for generating the diffraction-free Lommel light beam based on the super surface, the Dammann grating phase is composed of 6 super cells, each super cell contains 192 × 32 silicon nano columns, the phase change values are set to 0.22057, 0.44563, 0.5, 0.72057 and 0.94563, and the nano columns corresponding to the 7 th, 14 th, 16 th, 23 th and 30 th rows in each super cell can generate 0 or pi phase change.
According to the method for generating the diffraction-free Lommel beam based on the super surface, the fused quartz substrate is adopted as the substrate material of the super surface of the Lommel beam array, the substrate material is provided with the nano columns made of the silicon material, and the nano columns form an array; the Lommel beam array super-surface is provided with periodic boundary conditions in the x direction and the y direction, and a perfect matching layer is arranged in the z direction to absorb an electromagnetic field incident on the perfect matching layer; the height H of the silicon nano-column is 300nm, the length L is 130nm, the width W is 80nm, the interval period P of adjacent unit cells is 250nm, and the rotation angle of the nano-column
Figure DEST_PATH_IMAGE029
And Lommel beam phase
Figure 401480DEST_PATH_IMAGE030
In a relationship of
Figure DEST_PATH_IMAGE031
。
Compared with the prior art, the invention obtains the Lommel mode by infinite superposition of Bessel modes, obtains the Lommel light beam phase, and then introduces the Dammann grating to obtain the Dammann grating phase, the Dammann grating can accurately arrange phase change values to generate random arrangement lattices, the Dammann grating uniformity is not influenced by incident light waves, high-flux light energy is allowed, and the Dammann grating is binary, so that the Dammann grating can be manufactured by using a plane manufacturing technology (such as photoetching and ion beam etching), and the processing and manufacturing difficulty is reduced; then combining the Lommel light beam phase and the Dammann grating phase to generate a Lommel light beam array super surface; and finally, generating a diffraction-free Lommel beam array by using the super surface of the obtained Lommel beam array. The method provides a new idea for generating the Lommel light beam on the super surface, and has potential application in the fields of optical communication, optical tweezers, non-diffraction light beam generation and the like.
Drawings
FIG. 1 is a schematic diagram of the principles of the present invention;
FIG. 2 is a schematic diagram of a super-surface structure of a Lommel beam array of the present invention;
FIG. 3 is a schematic structural diagram of a nanopillar;
FIG. 4a is a Lommel beam array y-z longitudinal field distribution, FIGS. 4b and 4c are x-y transverse field distributions at z =100um and 110um, respectively, in FIG. 4a, and FIGS. 4d and 4e are intensity profiles at heights corresponding to 100um and 110um, respectively, in FIG. 4 a;
FIG. 5 is the polarization conversion efficiency of the cell structure at different wavelengths;
FIG. 6 is a relationship between a change in a rotation angle of a silicon nanopillar and transmission efficiency and phase;
part a of FIG. 7 is a longitudinal field pattern of a Lommel beam at a wavelength of 630 nm; parts b, c and d in fig. 7 are transverse field profiles of the longitudinal position of part a in fig. 7 at z =30 μm,50 μm and 70 μm, respectively; parts e, f and g in fig. 7 are intensity maps of the light beams extracted at the white dotted lines in parts b, c and d in fig. 7, respectively;
parts a, b, c and d in fig. 8 are longitudinal field distributions of the super-surface generated Lommel beam at wavelengths 550nm, 590nm, 670n and 710nm, respectively;
FIG. 9 shows the full width at half maximum values of the x-y focal plane at a height of z =50um at wavelengths of 550nm, 590nm, 630nm, 670nm, 710nm, respectively;
part a in FIG. 10 is the longitudinal field of the Lommel beam y-z generated by the super surface without obstacles (the white arrows in the figure represent the direction of energy flow); parts b and c in fig. 10 represent the Lommel beam y-z longitudinal field when small spheres of perfectly electrically conductive material with a radius of 1um and a radius of 2.5um are placed at a height z =25um, respectively.
Detailed Description
The present invention will be further described with reference to the following examples and drawings, but the present invention is not limited thereto.
Example (b): a method for generating a diffraction-free Lommel beam based on a super surface comprises the following steps:
a. obtaining a Lommel mode (also called a Lommel beam) by infinite superposition of Bessel modes (also called Bessel beams), and obtaining a Lommel beam phase; the Lommel beam is essentially a linear superposition of Bessel beams, so the complex amplitude expression of the Lommel optical field along the optical axis transmission direction can be expressed by a Bessel function under a cylindrical coordinate:
Figure 76044DEST_PATH_IMAGE032
；（1）
in the formula (I), the compound is shown in the specification,
Figure 957412DEST_PATH_IMAGE002
represents an electric field;
Figure 454252DEST_PATH_IMAGE003
，
Figure 104677DEST_PATH_IMAGE004
and, represents the position vector, and,
Figure 12459DEST_PATH_IMAGE005
representing position coordinates;
Figure 381123DEST_PATH_IMAGE006
is the azimuth;
Figure 416075DEST_PATH_IMAGE007
represents a transmission distance;
Figure 186585DEST_PATH_IMAGE008
is the propagation factor of the signal that is,
Figure 265268DEST_PATH_IMAGE009
denotes a wavelength of
Figure 121229DEST_PATH_IMAGE010
The wave number of the incident wave of (a);
Figure 959872DEST_PATH_IMAGE011
is an imaginary symbol;
Figure 319309DEST_PATH_IMAGE012
and, the transverse wave component is represented,
Figure 834473DEST_PATH_IMAGE013
is the numerical aperture;
Figure 912150DEST_PATH_IMAGE014
the number of times of superposition;
Figure 554484DEST_PATH_IMAGE015
asymmetric complex parameters;
Figure 34007DEST_PATH_IMAGE016
is the number of angular momentum of the photon orbit;
Figure 720072DEST_PATH_IMAGE017
representing the transverse field distribution of the Lommel beam;
Figure 285046DEST_PATH_IMAGE018
to represent
Figure 465492DEST_PATH_IMAGE019
A first class Bessel function of order;
as can be seen from equation (1), to ensure the convergence of equation (1), it is necessary to make
Figure DEST_PATH_IMAGE033
When is coming into contact with
Figure 517630DEST_PATH_IMAGE015
When real number is taken, the light intensity of the cross section of the Lommel light beam is symmetrical relative to the longitudinal axis when the real number is taken
Figure 125329DEST_PATH_IMAGE015
When taking an imaginary number, the light intensity of the cross section of the Lommel light beam is symmetrical relative to the horizontal axis. When in use
Figure 177599DEST_PATH_IMAGE015
When the module value of (A) is closer to 1, the fracture of the concentric circle of the cross section of the light beam is more obvious; when in use
Figure 896156DEST_PATH_IMAGE015
When =0, the Lommel mode is converted to the Bessel mode, so the Bessel beam can be regarded as a special solution for the Lommel beam:
Figure 147009DEST_PATH_IMAGE034
；（2）
function of Lommel beam
Figure 378139DEST_PATH_IMAGE021
Expressed as:
Figure 714442DEST_PATH_IMAGE022
；（3）
in the formula:
Figure 439953DEST_PATH_IMAGE023
and
Figure 545312DEST_PATH_IMAGE024
is two variables;
using functions
Figure 744081DEST_PATH_IMAGE025
To express the equation (1）：
Figure 505364DEST_PATH_IMAGE026
；（4）
Converting equation (4) from cylindrical coordinates to cartesian coordinates, expressed as:
Figure DEST_PATH_IMAGE035
；（5）
obtaining the phase angle corresponding to the solution obtained by the formula (5) to obtain the phase of the Lommel beam
Figure 300144DEST_PATH_IMAGE028
。
b. Acquiring a Dammann grating phase by using the Dammann grating; in order to generate the super surface of the Lommel beam array, an optical diffraction element of Dammann grating is introduced, the Dammann grating is a binary phase grating and can be used for generating a one-dimensional or two-dimensional light spot array with equal intensity, the Dammann grating phase is composed of 6 super units, each super unit comprises 192 multiplied by 32 silicon nano columns, the phase change values are set to be 0.22057, 0.44563, 0.5, 0.72057 and 0.94563, and the phase change of 0 or pi can occur on the nano columns corresponding to the 7 th, 14 th, 16 th, 23 th and 30 th rows in each super unit.
c. Combining the phase of the Lommel beam with the phase of the Dammann grating to generate the super surface of the Lommel beam array, as shown in FIG. 3, the phase of the Dammann grating
Figure 712540DEST_PATH_IMAGE036
And Lommel beam phase
Figure DEST_PATH_IMAGE037
The phase of the synthesis is expressed as:
Figure 301784DEST_PATH_IMAGE038
；（6）
the design of the Lommel beam array super-surface is finite difference time domain (FDT) under the flag of the Lumerical Solutions companyD Solutions) simulation software for optimization simulation. As shown in fig. 2, the super surface of the Lommel beam array adopts a fused quartz substrate as a substrate material, the substrate material is provided with nano columns made of silicon material, and the nano columns form an array; the Lommel beam array super-surface is provided with periodic boundary conditions in the x direction and the y direction, and a perfect matching layer is arranged in the z direction to absorb an electromagnetic field incident on the perfect matching layer; as shown in FIG. 3, the height H of the silicon nanopillar is 300nm, the length L is 130nm, the width W is 80nm, the interval period P between adjacent unit cells is 250nm, and the rotation angle of the nanopillar
Figure 815942DEST_PATH_IMAGE040
And Lommel beam phase
Figure DEST_PATH_IMAGE041
In a relationship of
Figure 866944DEST_PATH_IMAGE042
. In the present embodiment, a numerical aperture is provided here based on the synthetic phase principle of equation (6)
Figure 884578DEST_PATH_IMAGE013
=0.167, asymmetric complex parameter
Figure 425150DEST_PATH_IMAGE015
=0.8, topological charge number n = 3.
d. And generating a diffraction-free Lommel beam array by using the super surface of the Lommel beam array. The y-z longitudinal field distribution of the 1X 4Lommel beam array generated by 630nm levorotatory circularly polarized incidence is shown in FIG. 4a, where 4 sets of Lommel beams with complete shape and uniform intensity are clearly observed, and the measured average depth of focus is 124.3um (197. mu.m)
Figure DEST_PATH_IMAGE043
). FIGS. 4b and 4c are x-y transverse field distributions of 100um and 110um, respectively, at the white-line dashed positions in FIG. 4a, 4 uniformly sized, uniformly energetic spots can be seen, and FIGS. 4d and 4e are intensity profiles of corresponding heights calculated by averaging the full width at half maximum at 100um3.62um, the full width at half maximum at 110um is 3.82um, has embodied the even characteristic of beam energy. The characteristics prove that the superior performance of the Lommel beam array super-surface generated by the combination of the Lommel beam phase designed by the invention and the optimized Dammann grating phase is excellent.
The Lommel beam array super-surface (called super-surface for short) in the implementation meets the Nyquist sampling standard (P)<λ/2NA) sufficient to generate a Lommel beam in the wavelength range of 550-710 nm. For incident circularly polarized light, Pancharatnam-Berry (PB) or geometric phase, a local phase shift is produced by rotating an anisotropic rectangular nanopillar acting as a half-wave plate
Figure 629866DEST_PATH_IMAGE044
Wherein
Figure DEST_PATH_IMAGE045
Is the rotation angle of the nanopillar. The PB phase depends only on the geometry of the nanopillars and is therefore not sensitive to wavelength. The Polarization Conversion Efficiency (PCE) of the cell is an important condition, and fig. 5 shows that the polarization conversion efficiency of the cell at the incidence of left-handed circularly polarized light with a wavelength of 550nm to 710nm reaches 82% at 600nm and reaches more than 60% between 550 and 630 nm. FIG. 6 is a black curve fitted at 630nm wavelength incidence showing abrupt phase change and rotation angle of transmitted light
Figure 15717DEST_PATH_IMAGE045
The linear relation between the nano columns and the nano columns can realize 0-2 through the abrupt phase generated by rotation
Figure 887858DEST_PATH_IMAGE046
Is continuously varied. At the same time, with the angle
Figure 615643DEST_PATH_IMAGE045
In variation, the transmission efficiency of the nanopillars is approximately the same, with an average transmission efficiency of 88%, as shown by the upper curve in fig. 5.
In FIG. 7, a is the wavelength
Figure 838814DEST_PATH_IMAGE043
Incident numerical aperture of 630nm for left-handed polarized light
Figure 293935DEST_PATH_IMAGE013
Is 0.25, asymmetric complex parameter
Figure 286161DEST_PATH_IMAGE015
With a super-surface generated Lommel beam (longitudinal y-z plane) with a topological charge value of n =4, =0.8, two main lobes with very strong energy and side lobes on both sides can be clearly seen, and the focal depth of the two main lobes is measured to be 75um (119 um)
Figure 184847DEST_PATH_IMAGE043
) In fig. 7, the focal planes at different white dotted lines (z =30um, z =50um and z =70 um) in the longitudinal y-z plane are shown in part b and part c, two central spots with very symmetry and strong energy can be seen, and by calculating the intensity of the optical field distribution in the transverse x-y plane, the full width at half maximum (FWHM) values at different heights are obtained, as shown in part e to part g in fig. 7, the full width at half maximum values at 30um,50um and 70um are 0.48um, 0.51um and 0.55um, respectively, (where the full width at half maximum is the distance between two peaks), which means that the variation of the full width at half maximum is small, the energy variation during the transmission of the beam along the z axis is uniform and highly concentrated, and the Lommel beam has asymmetric complex parameters compared to the central ring of the first order bessel beam
Figure 629735DEST_PATH_IMAGE015
The effect of (2) is that the ring is broken obviously and is split into two light spots with concentrated energy.
Furthermore, the characteristics of the designed super-surface device in a broadband range are researched, and the incident wavelengths of the super-surface device are respectively incident to the super-surface
Figure 888547DEST_PATH_IMAGE043
Left-handed circularly polarized light of 550nm, 590nm, 670nm, 710nm, and parts a, b, c, and d in fig. 8The longitudinal field distributions of the ultra-surface generated Lommel light beam at the wavelengths of 550nm, 590nm, 670n and 710nm (the generated Lommel light beams are set to have the same light intensity here) are respectively divided, and as the ultra-surface device can have some dispersion phenomena at different wavelengths, the focal length of the Lommel light beams generated under the incidence of different wavelengths can be reduced along with the increase of the wavelengths. Although the super-surface generated Lommel beam is affected by the dispersion, the full width at half maximum value of the generated Lommel beam does not change significantly, as shown in fig. 9. FIG. 9 shows the wavelengths respectively
Figure 859DEST_PATH_IMAGE043
At 550nm, 590nm, 630nm, 670nm and 710nm, the half-height width values of the x-y focal plane at the height of z =50um are respectively 0.53um, 0.55um, 0.51um, 0.50um and 0.52um, which proves the broadband characteristics of the super-surface device of the invention at the wavelength of 550-710 nm.
The Lommel light beam has good self-healing property in the space transmission process, namely the intensity distribution of the Lommel light beam is basically consistent with the intensity distribution of the Lommel light beam which is not influenced by the obstacle and transmitted for the same distance after the Lommel light beam meets the obstacle and passes through a certain propagation distance. The self-healing capability of the Lommel light beam generated by the super surface is researched, and the self-healing performance of the generated Lommel light beam is verified by placing obstacles with different radiuses on the main lobe of the light beam and calculating the energy flux density of the obstacles. Part a in fig. 10 is the longitudinal field of the Lommel beam y-z generated by the super surface without obstacles, and the white arrows in the figure represent the direction of energy flow. Part b of fig. 10 and part c of fig. 10 show the longitudinal field of the Lommel beam y-z when pellets of Perfect Electrical Conductor material (PEC) with a radius of 1um and a radius of 2.5um are placed at a height z =25um, respectively, and it can be seen from an observation that the main lobe intensity in part b of fig. 10 passes a short distance through the pellet and a significant self-healing phenomenon starts to occur at a height of 29um, i.e. the main lobe intensity returns to the same value as it would without the influence of obstacles. After the PEC pellets are further increased in size, as shown in part c of fig. 10, when PEC pellets with a radius of 2.5um are placed on the main lobe propagation path at the same height, it can be observed that the transmission distance required for self-healing becomes longer as the size of the obstacle increases, and a significant self-healing phenomenon starts to occur at the height of 34.5um, which shows that the super-surface generated Lommel beam of the present invention has good self-healing performance.
In summary, in the Lommel beam super-surface of the present invention, the focal depth of the main lobe of the Lommel beam generated when the 630nm wavelength left-handed polarized light is incident on the super-surface can reach 75um (119 um)
Figure 804867DEST_PATH_IMAGE043
) Meanwhile, the broadband characteristic of the designed super surface between 550nm and 710nm is verified, and the variation amplitude of a full width at half maximum (FWHM) at the height of 50um is 0.05 um. And then, the good self-healing property of the Lommel light beam is verified, PEC material balls with different sizes are placed on the propagation path of the generated Lommel light beam, the self-healing performance of the Lommel light beam after passing through a certain transmission distance is found, and the light intensity distribution of the healed light beam is almost the same as that of the Lommel light beam without a barrier. Finally, a super-surface is generated that produces a 1 x 4 array of Lommel beams, the Lommel beams generated by the super-surface having a composite phase generated by combining the Lommel beam phase and the optimized Dammann grating phase, and the average depth of focus measured is 124.3um (197)
Figure 2631DEST_PATH_IMAGE043
) Meanwhile, 4 light spots with uniform sizes and uniform energy can be clearly observed. The method provides a new idea for generating the Lommel light beam on the super surface, and has potential application in the fields of optical communication, optical tweezers, non-diffraction light beam generation and the like.

Claims (4)

1. A method for generating a diffraction-free Lommel beam based on a super surface is characterized by comprising the following steps: the method comprises the following steps:
a. obtaining a Lommel mode by infinite superposition of Bessel modes, and obtaining a Lommel beam phase;
b. acquiring a Dammann grating phase by using the Dammann grating;
c. combining the Lommel light beam phase and the Dammann grating phase to generate a Lommel light beam array super surface;
d. a Lommel beam array super-surface is used to generate a non-diffracting Lommel beam.
2. The method for generating a non-diffracting Lommel beam based on a super surface as claimed in claim 1, wherein: the Lommel light beam phase is obtained by expressing a Lommel light field complex amplitude expression along the optical axis transmission direction by a Bessel function under a cylindrical coordinate:
Figure 723721DEST_PATH_IMAGE001
；（1）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE002
represents an electric field;
Figure 827812DEST_PATH_IMAGE003
，
Figure DEST_PATH_IMAGE004
and, represents the position vector, and,
Figure 545232DEST_PATH_IMAGE005
representing position coordinates;
Figure DEST_PATH_IMAGE006
is the azimuth;
Figure 127392DEST_PATH_IMAGE007
represents a transmission distance;
Figure DEST_PATH_IMAGE008
is the propagation factor of the signal that is,
Figure 879447DEST_PATH_IMAGE009
denotes a wavelength of
Figure DEST_PATH_IMAGE010
The wave number of the incident wave of (a);
Figure 888861DEST_PATH_IMAGE011
is an imaginary symbol;
Figure DEST_PATH_IMAGE012
and, the transverse wave component is represented,
Figure 93577DEST_PATH_IMAGE013
is the numerical aperture;
Figure DEST_PATH_IMAGE014
the number of times of superposition;
Figure 479428DEST_PATH_IMAGE015
asymmetric complex parameters;
Figure DEST_PATH_IMAGE016
is the number of angular momentum of the photon orbit;
Figure 85990DEST_PATH_IMAGE017
representing the transverse field distribution of the Lommel beam;
Figure DEST_PATH_IMAGE018
to represent
Figure 266304DEST_PATH_IMAGE019
A first class Bessel function of order;
when asymmetric complex parameter
Figure 489475DEST_PATH_IMAGE015
When =0, all the series terms in equation (1) assume zero values, and the Lommel pattern becomes a Bessel pattern:
Figure DEST_PATH_IMAGE020
；（2）
function of Lommel beam
Figure 164170DEST_PATH_IMAGE021
Expressed as:
Figure DEST_PATH_IMAGE022
；（3）
in the formula:
Figure 343347DEST_PATH_IMAGE023
and
Figure DEST_PATH_IMAGE024
is two variables;
using functions
Figure 960142DEST_PATH_IMAGE025
To express equation (1):
Figure DEST_PATH_IMAGE026
；（4）
converting equation (4) from cylindrical coordinates to cartesian coordinates, expressed as:
Figure 139451DEST_PATH_IMAGE027
；（5）
obtaining the phase angle corresponding to the solution obtained by the formula (5) to obtain the phase of the Lommel beam
Figure DEST_PATH_IMAGE028
。
3. The method for generating a non-diffracting Lommel beam based on a super surface as claimed in claim 1, wherein: the Dammann grating phase is composed of 6 super cells, each super cell comprises 192 × 32 silicon nano columns, the phase change values are set to 0.22057, 0.44563, 0.5, 0.72057 and 0.94563, and the nano columns corresponding to 7 th, 14 th, 16 th, 23 th and 30 th rows in each super cell can generate 0 or pi phase change.
4. The method for generating a diffraction-free Lommel beam based on a super surface according to any one of claims 1-3, wherein: the ultra-surface of the Lommel beam array adopts a fused quartz substrate as a base material, the base material is provided with nano columns made of silicon materials, and the nano columns form an array; the Lommel beam array super-surface is provided with periodic boundary conditions in the x direction and the y direction, and a perfect matching layer is arranged in the z direction to absorb an electromagnetic field incident on the perfect matching layer; the height H of the silicon nano-column is 300nm, the length L is 130nm, the width W is 80nm, the interval period P of adjacent unit cells is 250nm, and the rotation angle of the nano-column
Figure 601525DEST_PATH_IMAGE029
And Lommel beam phase
Figure DEST_PATH_IMAGE030
In a relationship of
Figure 182679DEST_PATH_IMAGE031
。
CN202210830784.5A 2022-07-15 2022-07-15 Method for generating diffraction-free Lommel light beam based on super surface Active CN114895476B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210830784.5A CN114895476B (en) 2022-07-15 2022-07-15 Method for generating diffraction-free Lommel light beam based on super surface

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210830784.5A CN114895476B (en) 2022-07-15 2022-07-15 Method for generating diffraction-free Lommel light beam based on super surface

Publications (2)

Publication Number Publication Date
CN114895476A true CN114895476A (en) 2022-08-12
CN114895476B CN114895476B (en) 2022-09-30

Family

ID=82729953

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210830784.5A Active CN114895476B (en) 2022-07-15 2022-07-15 Method for generating diffraction-free Lommel light beam based on super surface

Country Status (1)

Country Link
CN (1) CN114895476B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117806033A (en) * 2023-11-29 2024-04-02 深圳博升光电科技有限公司 Optical unit geometric parameter determining method of super-surface optical device and optical device

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090185274A1 (en) * 2008-01-21 2009-07-23 Prime Sense Ltd. Optical designs for zero order reduction
CN102495472A (en) * 2011-11-29 2012-06-13 中国科学院上海光学精密机械研究所 Bessel beam generator based on annular Dammann gratings
CN110361864A (en) * 2019-04-11 2019-10-22 北京理工大学 The method for generating bessel beam array based on the super clever surface of Huygens
CN111766647A (en) * 2020-06-30 2020-10-13 上海理工大学 Airy beam generator based on super surface
CN113193349A (en) * 2021-04-26 2021-07-30 北京理工大学 Method for generating real space and K space Airy beam array based on metasurface

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090185274A1 (en) * 2008-01-21 2009-07-23 Prime Sense Ltd. Optical designs for zero order reduction
CN102495472A (en) * 2011-11-29 2012-06-13 中国科学院上海光学精密机械研究所 Bessel beam generator based on annular Dammann gratings
CN110361864A (en) * 2019-04-11 2019-10-22 北京理工大学 The method for generating bessel beam array based on the super clever surface of Huygens
CN111766647A (en) * 2020-06-30 2020-10-13 上海理工大学 Airy beam generator based on super surface
CN113193349A (en) * 2021-04-26 2021-07-30 北京理工大学 Method for generating real space and K space Airy beam array based on metasurface

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
QIAN ZHAO,LEI GONG,YIN-MEI LI: "《Shaping diffraction-free Lommel beams with digital binary amplitude masks》", 《APPLIED OPTICS》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117806033A (en) * 2023-11-29 2024-04-02 深圳博升光电科技有限公司 Optical unit geometric parameter determining method of super-surface optical device and optical device

Also Published As

Publication number Publication date
CN114895476B (en) 2022-09-30

Similar Documents

Publication Publication Date Title
CN105676314B (en) A kind of super surface device of multispectral phase-type
CN105629364B (en) A kind of super surface device of wavelength selective
AU2011281097B2 (en) Nano-optic refractive optics
KR101905444B1 (en) Active metasurface, optical device including the same and manufacturing method thereof
US20140340732A1 (en) A planar optical component and its design method
CN113378372B (en) Design method of terahertz vortex processor, product obtained by design method and application of terahertz vortex processor
Minin et al. Basic principles of Fresnel antenna arrays
CN112882133B (en) Geometric phase type super lens for generating Airy beam
CN107728236B (en) The manufacturing method of super structure surface element and its method for generating nanoscale longitudinal direction hot spot chain
CN114895476A (en) Method for generating diffraction-free Lommel light beam based on super surface
Liu et al. Terahertz beam steering using a MEMS-based reflectarray configured by a genetic algorithm
CN109709630B (en) Sub-wavelength vortex light beam array generation method based on metal nano super surface
Lin et al. Single-layer re-organizable all-dielectric meta-lens platform for arbitrary transmissive phase manipulation at millimeter-wave frequencies
Yu et al. Synthesis for OAM vortex electromagnetic waves based on Fourier–Bessel expansion
Sun et al. All-dielectric metasurface for linear-polarization conversion with an arbitrary polarization rotating angle
Soltani et al. Multifunctional automatic metasurface design using deep learning approach
Elwi et al. Theory of gain enhancement of UC-PBG antenna structures without invoking Maxwell's equations: An array signal processing approach
Li et al. Phase Change Materials‐Based Bilayer Metasurfaces for Near‐Infrared Photonic Routing
CN214470399U (en) Full-polarization stealth carpet based on graphene phase gradient super-surface
Xue et al. Wideband directional-fed holographic metasurface with integrated monopole and parabolic reflector for far-/near-field beams manipulations
Su et al. Construction of Three-Dimensional Microwave Helical Beams Using Huygens’ Metasurface
Zhang et al. Sensitivity analysis of faceted reflector antennas and a contour beam synthesis technology
Fan et al. Ka-band quasi-nondiffraction beam generation through a broadband Bessel lens antenna
Lu et al. Polarization-multiplexing graphene-based coding metasurface for flexible terahertz wavefront control
Gong et al. High‐Throughput Fabrication of Curved Plasmonic Metasurfaces for Switchable Beam Focusing and Thermal Infrared Cloaking

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant