CN113985605A - Design method of super-surface perfect vortex optical beam generator based on geometric phase regulation - Google Patents
Design method of super-surface perfect vortex optical beam generator based on geometric phase regulation Download PDFInfo
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Abstract
The invention relates to a design method of a perfect vortex optical beam generator, in particular to a design method of a super-surface perfect vortex optical beam generator based on geometric phase regulation, which comprises the following steps: step 1, establishing a perfect vortex beam super surface, which comprises a substrate layer (2), wherein a dielectric micro-structure layer (1) is arranged on the substrate layer (2), and the dielectric micro-structure layer (1) is formed by arranging rectangular nano-columns which have the same shape and different rotation angles and are arranged according to a lattice period P; the rectangular nano-columns of the dielectric micro-structure layer (1) have different geometric dimension widths W in the x-direction geometric dimension length L, y direction, and exhibit anisotropy; for incident electromagnetic waves with x polarization and y polarization, the transmitted waves in the two directions have phase differences; and 2, establishing a phase of the perfect vortex beam super surface, linearly superposing the phases of the spiral phase plate, the axicon and the Fourier lens, and adding the phase and the phase into the super surface at the same time in the step 3.
Description
Technical Field
The invention relates to a design method of a perfect vortex optical beam generator, in particular to a design method of a super-surface perfect vortex optical beam generator based on geometric phase regulation.
Background
Vortex Beam (VB) is a special beam with a helical phase front. The vortex beam can be used to manipulate particles or encode information in optical communication systems, and thus it is receiving increasing attention in many key fields such as optical trapping, optical communication, and quantum information processing. However, the annular size of the vortex beam varies with its topological charge, which makes it very difficult to couple and transmit vortex beams with different topological charges in a communication system. To solve this problem, the concept of Perfect Vortex Beam (PVB) is proposed, the annular size of its intensity not varying with the variation of the topological charge. The traditional generation mode of the perfect vortex light beam needs the combined action of a plurality of optical elements such as a spiral phase plate, an axial prism, a Fourier lens and the like, the structure is complex, and the application of the perfect vortex light beam in a miniaturized and integrated optical system is hindered.
The super surface is a plane structure formed by sub-wavelength two-dimensional micro-nano structures according to a specific arrangement mode, and can flexibly regulate and control the amplitude, the phase, the polarization state and the like of electromagnetic waves. The perfect vortex beam can be generated by using a transmission phase type super surface or a geometric phase type super surface. The geometric phase type super surface is composed of anisotropic structures (such as rectangles, ellipses and the like) with the same shape and different in-plane rotation angles, so that the geometric phase type super surface has good tolerance to errors caused by preparation. However, due to the intrinsic symmetry of the geometric phase super-surface, i.e. the incident left-handed circularly polarized light and right-handed circularly polarized light exhibit opposite phase distributions, the multifunctional super-surface device faces many difficulties in design. In order to overcome the above problems, a method of fusing a geometric phase and a transmission phase can be adopted, however, the method needs to perform a large number of parameter scans to obtain various required unit structures, and the design and the processing and preparation are more complicated.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the existing defects and provides a design method of a super-surface perfect vortex optical beam generator based on geometric phase regulation.
In order to solve the technical problems, the invention provides the following technical scheme: a design method of a super-surface perfect vortex optical beam generator based on geometric phase regulation comprises the following steps:
it is formulated as:
wherein,
in the above formula, x and y represent coordinates of the center point of the unit structure in the super-surface plane; equation (2) is the phase equation for a spiral phase plate, where m represents the topological charge; formula (3) is a phase formula of the axicon, wherein d is the period of the axicon, and the phase formula controls the radius of a bright ring of a perfect vortex light beam; formula (4) is a phase formula of the Fourier lens, wherein f is the theoretical focal length of the lens, and lambda is the working wavelength;
step 3, adding phases in the super surface simultaneously
And phase
At this time, the phase distribution of the super-surface that can generate a perfect vortex beam is expressed as:
if two perfectly vortex beams are generated when x-polarization and y-polarization are incident simultaneously, the phase distribution of the super-surface can be expressed by the following formula:
wherein,
respectively generating two different phases corresponding to the perfect vortex light beams; the rotation angle θ (x, y) of the unit structure at different positions has the following relationship with the super-surface phase Φ (x, y): θ (x, y) ═ Φ (x, y)/2.
Preferably, the geometric dimension width W of the rectangular nanopillar in the x direction is different from the geometric dimension width W in the L, y direction, wherein the length L and the width W of the rectangular nanopillar satisfy the following conditions: when the x-polarized electromagnetic wave and the y-polarized electromagnetic wave are incident, the phase difference of the transmitted waves in the two directions is 180 degrees.
Preferably, the height of the rectangular nano-pillar is 600nm, the material is titanium dioxide, the length L of the geometric dimension in the x direction is 274nm, the width W of the geometric dimension in the y direction is 82nm, and the lattice period P is 350 nm.
Preferably, the thickness of the base layer is 2um, and the material is glass.
The invention has the beneficial effects that: the invention relates to a method for preparing a high-performance composite material.
Drawings
FIG. 1 is a schematic diagram of a super-surface three-dimensional structure of a perfect vortex optical beam generator of the present invention;
FIG. 2 is a schematic cross-sectional view of the electromagnetic wave propagation direction of the super-surface perfect vortex optical beam generator of the present invention;
fig. 3 is a top view of a simulated structure of the super-surface perfect vortex optical beam generator of the present invention.
Description of the drawings: 1. a dielectric microstructure layer; 2. a base layer.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
In particular implementations, the inventive super-surface structure is comprised of a two-layer structure. The upper layer is a dielectric medium microstructure layer 1 and is formed by arranging rectangular nano columns which are identical in shape and different in rotation angle theta according to a certain lattice period P; the lower layer is a base layer 2. The upper rectangular nano-pillars have different widths W in the direction of the length L, y of the geometric dimension in the x direction, and exhibit anisotropy; for an incident electromagnetic wave with x-polarization and y-polarization, the transmitted waves in these two directions will have a phase difference. The length L and the width W of the rectangular nano-column meet the following conditions: when the x-polarization electromagnetic wave and the y-polarization electromagnetic wave are incident, the phase difference of the transmitted waves in the two directions is 180 degrees, namely the rectangular nano-pillar is equivalent to a half-wave plate.
The thickness of the dielectric micro-structure layer 1, namely the height of the rectangular nano-column is 600nm, the material is titanium dioxide, the length L of the geometric dimension in the x direction is 274nm, the width W of the geometric dimension in the y direction is 82nm, the lattice period P is 350nm, and the rotation angle theta is related to the position of the rotation angle theta in the plane of the micro-structure layer 1; the thickness of the base layer 2 is 2um, and the material is glass.
The working wavelength of the super-surface structure is 532 nm.
The designed phase of the super surface of the perfect vortex beam is formed by linearly superposing the phases of a spiral phase plate, an axial prism and a Fourier lens, and is expressed by a formula as follows:
wherein,
in the above formula, x and y represent coordinates of the center point of the unit structure in the super-surface plane. Equation (2) is the phase equation for a spiral phase plate, where m represents the topological charge. Equation (3) is the phase equation of the axicon, where d is the axicon period, which controls the size of the bright ring radius of a perfect vortex beam. Equation (4) is the phase equation for a fourier lens, where f is the theoretical focal length of the lens and λ is the operating wavelength.
According to the principle of geometric phase regulation and control, when circularly polarized light passes through a super-surface unit array with a rotation angle theta, the transmission field comprises circularly polarized light with the same chirality as the incident light and also comprises circularly polarized light with the opposite chirality to the incident light, and the circularly polarized light has a phase mutation +/-2 theta, wherein +/-depends on the chirality of the incident circularly polarized light. When the super-surface cell array is a half-wave plate, the conversion efficiency of the polarization state is highest, namely the ratio of circularly polarized light opposite to the incident light chirality in the transmission field is the largest. Linearly polarized light can be seen as a superposition of a left-handed circular polarized component and a right-handed circular polarized component, and thus, when linearly polarized light is incident, the transmission field can still be seen as a superposition of the corresponding right-handed circular polarized component and left-handed circular polarized component.
Adding a perfect vortex phase in a half-wave plate super-surface array
The phase enables the incident levorotatory circular polarization component to generate a perfect vortex light beam after passing through the super surface, and simultaneously enables the incident dextrorotatory circular polarization component to be dispersed after passing through the super surface. On the contrary, if a perfect vortex phase is added to the half-wave plate super-surface array
The phase enables the incident right-handed circularly polarized component to generate a perfect vortex beam after passing through the super-surface, while the incident left-handed circularly polarized component is dispersed after passing through the super-surface. Therefore, in order to obtain a perfectly vortex beam with a linear polarization state, phase is added to the super-surface simultaneously
And phase
At this time, the phase distribution of the super-surface that can generate a perfect vortex beam is expressed as:
if two perfectly vortex beams are generated when x-polarization and y-polarization are incident simultaneously, the phase distribution of the super-surface can be expressed by the following formula:
wherein,
respectively, to produce two different phases of a perfect vortex beam. The design selects the rectangular nano-pillars as the unit structure of the super-surface structure. The rotation angle θ (x, y) of the unit structure at different positions has the following relationship with the super-surface phase Φ (x, y): θ (x, y) ═ Φ (x, y)/2.
The above embodiments are preferred embodiments of the present invention, and those skilled in the art can make variations and modifications to the above embodiments, therefore, the present invention is not limited to the above embodiments, and any obvious improvements, substitutions or modifications made by those skilled in the art based on the present invention are within the protection scope of the present invention.
Claims (4)
1. A design method of a super-surface perfect vortex optical beam generator based on geometric phase regulation is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a perfect vortex beam super surface, which comprises a substrate layer (2), wherein a dielectric micro-structure layer (1) is arranged on the substrate layer (2), and the dielectric micro-structure layer (1) is formed by arranging rectangular nano-columns which have the same shape and different rotation angles theta according to a lattice period P; the rectangular nano-pillars of the dielectric micro-structure layer 1 have different widths W in the direction of the length L, y in the x direction, and exhibit anisotropy; for incident electromagnetic waves with x polarization and y polarization, the transmitted waves in the two directions have phase differences;
step 2, establishing a phase of a perfect vortex beam super surface, linearly superposing the phases of a spiral phase plate, an axial prism and a Fourier lens,
it is formulated as:
wherein,
in the above formula, x and y represent coordinates of the center point of the unit structure in the super-surface plane; equation (2) is the phase equation for a spiral phase plate, where m represents the topological charge; formula (3) is a phase formula of the axicon, wherein d is the period of the axicon, and the phase formula controls the radius of a bright ring of a perfect vortex light beam; formula (4) is a phase formula of the Fourier lens, wherein f is the theoretical focal length of the lens, and lambda is the working wavelength;
step 3, adding phases in the super surface simultaneously
And phase
At this time, the phase distribution of the super-surface that can generate a perfect vortex beam is expressed as:
if two perfectly vortex beams are generated when x-polarization and y-polarization are incident simultaneously, the phase distribution of the super-surface can be expressed by the following formula:
wherein,
respectively generating two different phases corresponding to the perfect vortex light beams; the rotation angle θ (x, y) of the unit structure at different positions has the following relationship with the super-surface phase Φ (x, y): θ (x, y) ═ Φ (x, y)/2.
2. The design method of a super-surface perfect vortex optical beam generator based on geometric phase control as claimed in claim 1, wherein: the geometric dimension width W of the rectangular nano-column in the x direction is different from that in the L, y direction, wherein the length L and the width W of the rectangular nano-column meet the following conditions: when the x-polarized electromagnetic wave and the y-polarized electromagnetic wave are incident, the phase difference of the transmitted waves in the two directions is 180 degrees.
3. The design method of a super-surface perfect vortex optical beam generator based on geometric phase control as claimed in claim 1, wherein: the height of the rectangular nano-column is 600nm, the material is titanium dioxide, the length L of the geometric dimension in the x direction is 274nm, the width W of the geometric dimension in the y direction is 82nm, and the lattice period P of the rectangular nano-column is 350 nm.
4. The design method of a super-surface perfect vortex optical beam generator based on geometric phase control as claimed in claim 1, wherein: the thickness of stratum basale (2) is 2um, and the material is glass.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115236786A (en) * | 2022-08-02 | 2022-10-25 | 西北工业大学 | Liquid crystal phase plate, preparation method and double-sided vortex light beam generation system |
| CN115561915A (en) * | 2022-09-20 | 2023-01-03 | 昆明理工大学 | Manufacturing method of super surface capable of generating annular vortex light beam array and display system |
| CN117870883A (en) * | 2024-03-08 | 2024-04-12 | 中国航天三江集团有限公司 | Circular polarization Hartmann wave front detection design method based on geometric phase super surface |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115236786A (en) * | 2022-08-02 | 2022-10-25 | 西北工业大学 | Liquid crystal phase plate, preparation method and double-sided vortex light beam generation system |
| CN115236786B (en) * | 2022-08-02 | 2024-02-02 | 西北工业大学 | Liquid crystal phase plate, preparation method and double-sided vortex light beam generation system |
| CN115561915A (en) * | 2022-09-20 | 2023-01-03 | 昆明理工大学 | Manufacturing method of super surface capable of generating annular vortex light beam array and display system |
| CN117870883A (en) * | 2024-03-08 | 2024-04-12 | 中国航天三江集团有限公司 | Circular polarization Hartmann wave front detection design method based on geometric phase super surface |
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