A method for generating asymmetric acoustic vortices using a double-layer metasurface

Abstract

The present invention discloses a method for generating an asymmetric acoustic vortex by using a double-layer metasurface. The maximum-order topological core for transmitting an acoustic vortex in a cylindrical waveguide is l<supgt;M< / supgt>. Two layers of metasurfaces are designed in the cylindrical waveguide such that the "intrinsic topological core" and relationship are satisfied and it is ensured that the number of sub-units designed in the metasurface with the "intrinsic topological core" is even, thereby realizing the generation of an asymmetric acoustic vortex. When an incident plane wave is incident from one side of the waveguide, the two layers of metasurfaces ensure the effective conversion of the acoustic vortex topological core, generating an efficient acoustic vortex field. When the incident plane wave is incident from the other side of the waveguide, due to the acoustic vortex diffraction effect in the metasurface with the "intrinsic topological core", it has an "extrinsic topological core" with reflection characteristics, which hinders the effective conversion of the acoustic vortex topological core and generates an inefficient acoustic vortex field. The present invention provides a feasible technical means for realizing the asymmetric generation and propagation of an acoustic vortex field, and has certain application prospects in particle manipulation and information communication of acoustic orbital angular momentum.

Description

Technical Field

[0001] The present invention belongs to the technical field of vortex field generation and propagation, and particularly relates to a method for generating an asymmetric acoustic vortex by using a double-layer metasurface. Background Art

[0002] The asymmetric propagation of waves has attracted great interest among researchers due to its important value in unidirectional functional applications. In recent years, many technical solutions for realizing the optical / acoustic asymmetric effect have been proposed, including magneto-optical materials, nonlinearity, non-Hermitian modulation, topological insulators, and metasurfaces, leading to the discovery of many novel phenomena, such as unidirectional waveguide mode conversion, asymmetric diffraction, and unidirectional surface plasmon excitation. However, these technical solutions mainly utilize the plane wave field with low degrees of freedom (e.g., plane waves), and it is very challenging to manipulate the structural wave field with higher degrees of freedom, such as the vortex field with orbital angular momentum (OAM).

[0003] Since the discovery that waves can carry OAM, the vortex field with OAM can be used to realize more interesting phenomena and applications than traditional plane waves, including vortex tweezers, optical microscopy imaging, and high-capacity communication, etc. In the research of the vortex field, the generation of the vortex field is a fundamental problem and has been widely studied, especially in the field of phase gradient metasurfaces (PGMs). PGMs are associated with the "intrinsic topological charge" (ITC) and are used to realize the phase twisting effect, which is essentially a common topological charge conservation law. Although great progress has been made in the research on generating optical and acoustic vortices by using metasurfaces, how to achieve asymmetric vortex generation and propagation remains unresolved, which is of great significance for realizing new asymmetric effects and further developing the applications of the vortex field. Summary of the Invention

[0004] Object of the Invention: The present invention proposes a method for generating an asymmetric acoustic vortex by using a double-layer metasurface, which is an effective method for realizing the generation and propagation of asymmetric vortices.

[0005] Technical Solution: A method for generating an asymmetric acoustic vortex by using a double-layer metasurface according to the present invention includes the following steps:

[0006] (1) Construct two phase-gradient metasurfaces, namely PGM-1 and PGM-2, in a cylindrical waveguide with a radius of R, and the distance between PGM-1 and PGM-2 is greater than or equal to one working wavelength;

[0007] (2) PGM-1 carries the "intrinsic topological charge" Within the range of the maximum-order topological core supported by the waveguide, that is PGM-2 carries an "intrinsic topological core" Outside the range of the maximum-order topological core supported by the waveguide, that is ; the difference between the "intrinsic topological cores" of the two metasurfaces is within the support range of the waveguide, that is where l M is determined by the working wavelength λ and the radius R;

[0008] (3) PGM-1 and PGM-2 respectively have l1 ξ and l2 ξ sector-shaped supercells, and each supercell is composed of m1 and m2 sector-shaped subunits respectively; the angular width of each sector-shaped subunit is θ i = 2π / (m i l i ξ )(i = 1, 2), and the phase difference between adjacent subunits is guaranteed to be ΔΦ i = 2π / m i (i = 1, 2) to achieve the required phase gradient;

[0009] (4) When the incident plane wave is incident from one side of the waveguide, the two-layer metasurface ensures the effective conversion of the acoustic vortex topological core, thus generating an efficient acoustic vortex field; when the incident plane wave is incident from the other side of the waveguide, based on the acoustic vortex diffraction effect in the metasurface with an "intrinsic topological core" it has an "extrinsic topological core" with reflection characteristics, which hinders the effective conversion of the acoustic vortex topological core, thus generating an inefficient acoustic vortex field.

[0010] Furthermore, the number of subunits of PGM-2 described in step (1) is an even number.

[0011] Furthermore, the vortex field diffracted by PGM-2 described in step (1) follows the following diffraction law:

[0012]

[0013] where l r and l t are the topological cores of the reflected and transmitted acoustic vortices respectively, n is the diffraction order, and the number of propagation times satisfies L = m2 + n.

[0014] Furthermore, the two metasurfaces PGM-1 and PGM-2 described in step (3) are both composed of four sector-shaped subunits, the angular width of each sector-shaped subunit is θ = 45°, and each sector-shaped subunit is realized by a spatially folded artificial structure design to achieve the required phase delays: 0, π / 2, π, 3π / 2.

[0015] Furthermore, the subunit described in step (3) is a spatial folding structure or a Helmholtz resonator.

[0016] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: The asymmetric effect in the present invention is not only reflected in the unidirectional transmission efficiency, but also in that the generated OAM has different orders; by making full use of the regulation characteristics of ITC and ETC in the double-layer metasurface on the vortex field in the waveguide, the proposed asymmetric characteristics have good robustness. Description of the Drawings

[0017] Figure 1 Schematic diagram of generating a low-efficiency vortex field by incident plane waves from the right side into a cylindrical waveguide with a double-layer metasurface;

[0018] Figure 2 Schematic diagram of generating a high-efficiency vortex field by incident plane waves from the left side into a cylindrical waveguide with a double-layer metasurface;

[0019] Figure 3 Schematic diagram of the generation principle of an asymmetric acoustic vortex with opposite helicities of the double-layer metasurface;

[0020] Figure 4 Schematic diagram of the generation principle of an asymmetric acoustic vortex with the same helicities of the double-layer metasurface;

[0021] Figure 5 Schematic diagram of the design principle of the fan-shaped substructure in the waveguide;

[0022] Figure 6 Cross-sectional view of the fan-shaped substructure;

[0023] Figure 7 PGM-2 constructed using the fan-shaped substructure;

[0024] Figure 8 PGM-1 constructed using the fan-shaped substructure;

[0025] Figure 9 Total sound pressure field diagram of plane sound waves incident from the left side onto a double-layer metasurface with opposite helicities;

[0026] Figure 10 Total sound pressure field diagram of plane sound waves incident from the right side onto a double-layer metasurface with opposite helicities;

[0027] Figure 11 For Figure 9 Sound field amplitude diagram of the right circular cross-section in

[0028] Figure 12 For Figure 9 Sound field phase diagram of the right circular cross-section in

[0029] Figure 13is Figure 10 The sound field amplitude diagram on the left circular cross-section in

[0030] Figure 14 is Figure 10 The sound field phase diagram on the left circular cross-section in

[0031] Figure 15 is the total sound pressure field diagram after a plane sound wave is incident from the left on a double-layer metasurface with the same helicity;

[0032] Figure 16 is the total sound pressure field diagram after a plane sound wave is incident from the right on a double-layer metasurface with the same helicity;

[0033] Figure 17 is Figure 15 The sound field amplitude diagram on the right circular cross-section in

[0034] Figure 18 is Figure 15 The sound field phase diagram on the right circular cross-section in

[0035] Figure 19 is Figure 16 The sound field amplitude diagram on the left circular cross-section in

[0036] Figure 20 is Figure 16 The sound field phase diagram on the left circular cross-section in Detailed implementation mode

[0037] The present invention will be further described in detail below with reference to the accompanying drawings.

[0038] The present invention proposes a method for generating an asymmetric acoustic vortex using a double-layer metasurface. The method for generating an asymmetric acoustic vortex is realized by using double-layer PGMs with different ITCs. Specifically, based on the acoustic vortex diffraction law of PGMs in a cylindrical waveguide, and making full use of the "extrinsic topological charge" (ETC, external topologic charge) caused by the multiple reflection effect in PGMs, a double-layer PGMs (PGM-1 and PGM-2) is constructed to break the traditional topological charge conservation law and realize the generation of an extremely asymmetric acoustic vortex field. The asymmetric effect in the present invention is not only reflected in the unidirectional transmission efficiency, but also in the different orders of the generated OAM. Due to the special combination of ITC and ETC in PGMs, the invented asymmetric characteristics have good robustness, which is difficult to achieve in technical methods that usually only involve the twisted phase, such as the spiral phase plate. The specific steps are as follows:

[0039] Construct two phase-gradient metasurfaces, namely PGM-1 and PGM-2, in a cylindrical waveguide with a radius of R, and the distance between PGM-1 and PGM-2 is greater than or equal to one working wavelength.

[0040] Figure 1 and Figure 2 Briefly shows the schematic diagram of the asymmetric generation of acoustic vortices proposed in the present invention. In a cylindrical waveguide with a radius of R, two PGMs with the same thickness but different ITCs are placed: PGM-1 and PGM-2. At a fixed operating wavelength (or frequency), the vortex modes in the cylindrical waveguide are limited. Assuming that the maximum topological core of the supported propagating vortex modes is l M , then the topological core range of the propagating vortex field modes in the waveguide is [-l M , l M , where the "+" and "-" signs define the clockwise and counterclockwise helicities of the propagating vortex field. The acoustic pressure field of each propagating vortex mode in the waveguide is expressed as:

[0041] p = J l (k l,v r) / J l (k l,v R) exp(ilθ + ik z z), (-l M < l < l M )

[0042] where k z and k l,v are the wave vectors in the propagation direction and perpendicular to the propagation direction respectively, l is the topological core carried by the sound wave, k0 = 2π / λ is the wave vector of the sound wave in air, 1 / J l (k l,v R) is the normalization factor, and k l,v needs to satisfy That is, the radial propagation velocity should be cut off at the waveguide boundary, and the relationship between the wave vectors is For the k z of the vortex mode propagating in the waveguide to be real, it is necessary to require k l,v < k0. Therefore, the waveguide has the maximum topological core of the propagating vortex field.

[0043] PGM-1 carries the "intrinsic topological core" within the range of the maximum order topological core supported by the waveguide, that is PGM-2 carries the "intrinsic topological core" outside the range of the maximum order topological core supported by the waveguide, that is The difference between the "intrinsic topological cores" of the two metasurfaces is within the support range of the waveguide, that is where the magnitude of l M is determined by the operating wavelength λ and the radius R.

[0044] PGM-1 and PGM-2 have l1 ξ and l2ξ A fan-shaped supercell, each supercell is composed of m1 and m2 fan-shaped sub-units respectively; the angular width of each fan-shaped sub-unit is θ i = 2π / (m i l i ξ )(i = 1, 2), and ensure that the phase difference between adjacent sub-units is ΔΦ i = 2π / m i (i = 1, 2) is used to achieve the required phase gradient.

[0045] When an incident plane wave is incident from one side of the waveguide, the two-layer metasurface ensures the effective conversion of the acoustic vortex topological core, thus generating an efficient acoustic vortex field; when the incident plane wave is incident from the other side of the waveguide, based on the acoustic vortex diffraction effect in the metasurface with an "intrinsic topological core" The metasurface has an "extrinsic topological core" with reflection characteristics, which hinders the effective conversion of the acoustic vortex topological core, thus generating an inefficient acoustic vortex field.

[0046] Assume First, the physical conditions for generating an inefficient acoustic vortex field when incident from the right side of the waveguide. Consider the incident wave l in = 0 is incident from the right side of the waveguide and carries the topological core after passing through PGM-2 If This is a prohibited mode in the waveguide because its corresponding propagation constant is imaginary. Therefore, a multiple reflection effect with a propagation number of L appears in PGM-2, and the vortex field diffracted from PGM-2 follows the following diffraction law:

[0047]

[0048] In the formula, l r(t) are the topological cores of the reflected wave (transmitted) acoustic vortex respectively, n is the diffraction order, and the propagation number satisfies L = m2 + n. Due to the introduced phase gradient, n = 1 is the minimum diffraction order, corresponding to the ITC twisted phase. If the scattered vortex field follows other diffraction orders (n ≤ 0), PGM-2 can provide an equivalent ETC, and its magnitude is When and l in = 0, only the diffraction order n = 0 is the vortex mode that can be propagated. If the number of sub-structural units in PGM-2 is set to an even number, the number of multiple reflections L in it is also an even number. Then, the incident wave is blocked back, Figure 3 and Figure 4 In the process marked "incident from the right side", only a very weak or even no transmitted plane wave enters PGM-1. Then, under the action of PGM-1, an inefficient acoustic vortex field can be obtained on the left side of the waveguide.

[0049] In Under the condition that m2 is even, the present invention discloses the conditions for generating high-efficiency vortices from a plane sound wave incident from the left. Two different cases are considered, namely, the helicities of the two PGMs are the same or opposite. For PGMs with opposite helicities, the ITCs provided by PGM-1 and PGM-2 are respectively and The method of twisting the phase is the most convenient way to generate an efficient vortex field. The left-incident beam carries an angular momentum l in = 0 is twisted by PGM-1 into a vortex field carrying a topological core and then twisted again by PGM-2 into another vortex field carrying a topological core If these vortex field modes can all propagate in the waveguide ( and ), finally, the topological core of the high-efficiency vortex field generated on the right is Figure 3 The process marked "left incidence". For PGMs with the same helicity ( and ), its physical mechanism for generating high-efficiency vortices is somewhat different from that in the case of PGMs with opposite helicities. When the plane wave incident from the left is twisted by PGM-1 into a vortex field with a topological core of , this vortex field cannot be twisted again by PGM-2 because However, through the high-order diffraction order n = -1, PGM-2 can also provide an ETC with a value of Since the number of unit cells m2 of PGM-2 is even, the number of propagation times L = m2 - 1 of this diffraction order is odd, so a transmitted vortex field with a topological core of can be obtained, Figure 4 The process marked "left incidence", and ensure that it is within the range supported by the waveguide, that is, |l t | ≤ l M .

[0050] Therefore, by designing two layers of metasurfaces in a cylindrical waveguide, making the relationship between its "intrinsic topological cores" and satisfy and ensuring that the number of structural units designed in PGM-2 is even, the generation of asymmetric acoustic vortices is realized. When the incident plane wave is incident from one side of the waveguide, the two layers of metasurfaces ensure the effective conversion of the topological core of the acoustic vortex, thus generating an efficient acoustic vortex field; when the incident plane wave is incident from the other side of the waveguide, due to the acoustic vortex diffraction effect in the metasurface, it has a reflective "extrinsic topological core", which hinders the effective conversion of the topological charge of the acoustic vortex, thus generating an inefficient acoustic vortex field

[0051] In this embodiment, the parameters of a double-layer metasurface waveguide structure provided by the present invention are as follows: and m2 = 4, and the working wavelength is set to λ = 10 cm and the waveguide radius is R = 0.4λ to achieve l M = 1. For PGM-2, the geometric parameters are m2 = 4 and the angular width of the fan-shaped sub-unit in PGM-2 is By designing a two-dimensional spatially folded artificial structure, such as Figure 6 shown, and rotating it by π / 4 around the z-axis, a three-dimensional structure of the fan-shaped sub-unit can be obtained. Placing the three-dimensional fan-shaped sub-unit in the corresponding fan-shaped waveguide, as Figure 5 shown, by changing the number, length, and spacing of the rectangular blocks in the structural unit, the required transmission and phase parameters can be obtained. Based on this, four three-dimensional fan-shaped sub-units are designed, as Figure 7 labeled #1, #2, #3, #4, which satisfy the required phase difference ΔΦ = π / 4 and almost 100% transmission efficiency. For a wave incident along the +z direction, this PGM-2 can provide the ITC of. For PGM-1, the angular width of the fan-shaped sub-unit is Using a similar design process, the corresponding PGM-1 can be constructed by designing m1 groups of three-dimensional fan-shaped sub-units. Since if the number of sub-units for constructing PGM-1 is m1 = 4, then θ1 = 2θ2. PGM-1 can be constructed by placing the corresponding sub-units of PGM-2 twice, as Figure 8 shown, and this PGM-1 can provide the ITC of.

[0052] Based on the designed metasurface, COMSOL numerical simulation is used to verify the asymmetric generation of the acoustic vortex field. When the double-layer metasurface has opposite helicities, for the left-incident plane wave, the simulation results of the asymmetric generation of the acoustic vortex field are shown in Figure Figure 9 as follows: The incident plane wave is twisted into an acoustic vortex with a topological core of l = -1, and after propagating in the air gap (Δ = λ) between the PGMs, it is twisted again by PGM-2 into a high-intensity acoustic vortex field with a topological core of l t = -1 + 2 = 1. However, in the case of right-side incidence, as Figure 10 shown, the incident plane wave is almost completely blocked by PGM-2, and some weak acoustic plane waves mainly composed of l = 0 leak out from PGM-2 and are twisted by PGM-1 into a weak acoustic vortex field with a topological core of l t = 1. The asymmetric generation of the acoustic vortex can be clearly seen from the corresponding amplitudes and phases at the transmission end under the two incidences. When incident from the left, the high-amplitude hollow field amplitude information detected at the right transmission end, as Figure 11as shown; and a perfect spiral phase distribution, such as Figure 12 as shown; which indicates that the left incidence generates a high-efficiency acoustic vortex field with a topological core of l t = 1. When the incidence is on the right side, a weak amplitude distribution is found on the left transmission end face, such as Figure 13 , and a broken spiral phase distribution, such as Figure 14 , which means that a very inefficient and imperfect acoustic vortex field is generated (with a topological core of l t = 1). Through numerical calculation, the transmission efficiencies in the cases of left incidence and right incidence are 98.1% and 5.9% respectively, proving that the device nearly perfectly realizes the unidirectional generation of the acoustic vortex field.

[0053] When the double-layer metasurface has the same helicity, a similar phenomenon of unidirectional generation of the acoustic vortex field is also verified by numerical simulation. Figure 15 Shows the simulated field pattern of the generation of a high-efficiency acoustic vortex field with a topological core of l = -1 when a plane wave is incident from the left side, Figure 16 Shows the simulated field pattern of the generation of a low-efficiency and imperfect acoustic vortex field with a topological core of l = -1 when a plane wave is incident from the right side. Such as Figure 17 and Figure 18 By detecting the high-amplitude hollow field amplitude information and the perfect spiral phase distribution at the right port corresponding to the left incidence, the generation of this high-efficiency acoustic vortex field is further confirmed, and its efficiency is 96.2%. Such as Figure 19 and Figure 20 as shown. By detecting the weak amplitude distribution and the imperfect spiral phase distribution at the left port corresponding to the right incidence, the generation of this low-efficiency and imperfect acoustic vortex field is confirmed, and its efficiency is 6.1%. The numerical simulation well verifies the asymmetric generation of the acoustic vortex field proposed by the present invention.

[0054] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, in any regard, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0055] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for generating an asymmetric acoustic vortex using a double-layer metasurface, characterized in that It includes the following steps: (1) Construct two phase-gradient metasurfaces, namely PGM-1 and PGM-2, in a cylindrical waveguide with a radius of R. The distance between PGM-1 and PGM-2 is greater than or equal to one working wavelength; (2) PGM-1 carries the "intrinsic topological core" Within the range of the maximum order topological core supported by the waveguide, that is PGM-2 carries the "intrinsic topological core" Outside the range of the maximum order topological core supported by the waveguide, that is The difference between the "intrinsic topological cores" of the two metasurfaces is within the support range of the waveguide, that is where l M is determined by the working wavelength λ and the radius R; (3) PGM-1 and PGM-2 each have and sector supercells, and each supercell is composed of m1 and m2 sector subunits respectively; the angular width of each sector subunit is and the phase difference between adjacent subunits is guaranteed to be ΔΦ i = 2π / m i (i = 1, 2) for realizing the required phase gradient; (4) When the incident plane wave is incident from one side of the waveguide, the two-layer metasurface ensures the effective conversion of the acoustic vortex topological core, thereby generating an efficient acoustic vortex field; while when the incident plane wave is incident from the other side of the waveguide, based on the acoustic vortex diffraction effect in the metasurface with an "intrinsic topological core" the "extrinsic topological core" with reflection characteristics is formed, which hinders the effective conversion of the acoustic vortex topological core, thereby generating an inefficient acoustic vortex field.

2. A method for generating an asymmetric acoustic vortex using a double-layer metasurface according to claim 1, characterized in that, The number of sub-units of PGM-2 in step (1) is an even number.

3. A method for generating an asymmetric acoustic vortex using a double-layer metasurface according to claim 1, characterized in that, The vortex field diffracted by PGM-2 in step (1) follows the following diffraction law: where l r and l t are the topological cores of the reflected and transmitted acoustic vortices respectively, n is the diffraction order, and the propagation number satisfies L = m2 + n.

4. A method for generating an asymmetric acoustic vortex using a double-layer metasurface according to claim 1, characterized in that Both of the two metasurfaces PGM-1 and PGM-2 in step (3) are composed of four sector sub-units. The angular width of each sector sub-unit is θ = 45°. Each sector sub-unit realizes the required phase delays: 0, π / 2, π, 3π / 2 through the design of a space-folded artificial structure.

5. A method for generating an asymmetric acoustic vortex using a double-layer metasurface according to claim 1, characterized in that The sub-unit described in step (3) is a space-folded structure or a Helmholtz resonator.

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