CN112287584A - Ultrathin slab waveguide device and design method thereof - Google Patents
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Abstract
The invention relates to elastic fluctuation in an engineering structure, in particular to ultrathin slab waveguide equipment and a design method thereof, the waveguide equipment comprises a slab and a waveguide structure arranged on the slab, the waveguide structure consists of two layers of super surfaces with sub-wavelength thickness, each super surface consists of super cells arranged periodically, each super cell comprises two single cells with gradient indexes, the transmissivity | t | of each single cell is not less than 0.9, the width of each single cell is H, the phase change of elastic waves passing through the two single cells is pi and 2 pi respectively, and the phase gradient of the super surface is
Where L is 2H, L indicates the width of the supercell, and λ/L > 2, where λ indicates a wavelength, must be satisfied in order for the elastic wave to be incident on the super surface and then specularly reflected. The invention can realize elastic wave by designing waveguide equipment with any shapeThe transmission device has the advantages of light and thin structure, small volume, wide working frequency band, strong designability and the like along the purpose of transmission along an expected path.
Description
Technical Field
The invention relates to elastic fluctuation in an engineering structure, in particular to ultrathin slab waveguide equipment and a design method thereof.
Background
In 1842, the Swiss physicist Daniel Colladon used water flow to direct light. In his experiment, the light was totally internally reflected at the interface between water and air, and the water stream made the light travel in a parabolic fashion along this trajectory, a phenomenon known as "light fountain". This experiment was in fact the earliest realization of modern optical waveguide devices. The complete reflection of light at the interface is achieved by using two materials with different refractive indices, typical applications being optical fibers and optical cavities. The optical fiber is mainly composed of two parts, a fiber core and a cladding. The core has a higher refractive index than the cladding. When a light ray is incident on the cladding at an angle greater than a certain angle, the light ray is totally reflected at the interface of the core and the cladding. The light is trapped in the core and is allowed to propagate forward along the core after multiple reflections. The application of optical fibers to communication technology has realized a great revolution in communication technology. Nowadays, optical fiber has become the main transmission mode in world communication due to its wide transmission band, high interference immunity and reduced signal attenuation, which is far superior to the transmission of cable and microwave communication. An optical cavity is a cavity in which light waves are reflected back and forth to control the direction and intensity of the light. The technology greatly expands the application range of the laser equipment, for example, the technology is widely applied to laser scanning and security inspection systems, and even the service life of medical equipment can be prolonged.
If the optical waveguide concept is applied to the slab elastic waveguide, the guide of elastic wave propagation is realized by designing an ultrathin slab waveguide device, which brings huge application prospects in the aspects of vibration reduction and noise reduction of engineering structures, nondestructive detection, energy capture, sensors, even communication and the like. However, elastic waves have more degrees of freedom than light waves. The characteristics of multiple modes, dispersion and the like of the elastic wave bring great challenges to the control of the elastic wave. If two materials are used to achieve complete reflection of the elastic wave at the interface, this would limit the direction of the incident wave and would not be a desirable slab waveguide device, nor would it be convenient to machine and manufacture. How to design an ultra-thin slab waveguide device, can guide the elastic wave of arbitrary direction to propagate along the route of waveguide, use a material simultaneously, simple structure and be convenient for processing, this needs to propose a new design theory.
Disclosure of Invention
In order to solve the problems, the invention provides a light and thin omnibearing mirror reflection super-surface structure, and elastic waves can be transmitted forwards after being reflected for multiple times by utilizing two layers of super-surfaces, so that the aim of waveguide is finally fulfilled.
In order to achieve the purpose, the invention adopts the technical scheme that:
an ultrathin slab waveguide device comprises a slab and a waveguide structure arranged on the slab, wherein the waveguide structure consists of a super surface with two layers of sub-wavelength thicknesses, the super surface consists of periodically arranged supercells, each supercell comprises two unit cells with gradient indexes, the transmissivity | t | of each unit cell is not less than 0.9, the width of each unit cell is H, the phase change of elastic waves passing through the two unit cells is pi and 2 pi respectively, and the phase gradient of the super surface is pi
Where L is 2H, L indicates the width of the supercell, and λ/L > 2, where λ indicates a wavelength, must be satisfied in order for the elastic wave to be incident on the super surface and then specularly reflected.
Further, the super surface can be designed into any shape according to the expected propagation path of the elastic wave, and the elastic wave is incident on the super surface to undergo multiple reflections and finally propagates forwards along the path between the two super surfaces.
Furthermore, the constructed super-surface with sub-wavelength thickness can make incident wave in any direction generate mirror reflection.
Further, the unit cell width H is 7mm, the supercell width L is 14mm, the plate thickness d is 1.5mm, and the wavelength λ of the a0 wave is 30.6mm at the target frequency f of 15 kHz.
The invention also provides a design method of the ultrathin slab waveguide device, which comprises the following steps:
s1, respectively recording the material density, Young modulus and Poisson ratio of the super-surface structure and the flat plate as rho, E and nu;
establishing a finite element model of a unit cell, wherein the finite element model comprises a matrix medium and a unit cell structure, perfect matching layers are arranged in front and at the back of the model, and periodic boundary conditions are arranged on the upper and lower boundaries;
applying simple harmonic force load on one side of the unit cell structure, and calculating the phase change delta phi and the transmissivity | t | of the elastic wave after passing through the unit cell;
s2, calculating the unit cells with different geometric parameters in the step S1, and selecting two unit cells meeting the following conditions: 1) the transmittance | t | is not less than 0.9; 2) the phase change of the elastic wave after passing through the two unit cells is pi and 2 pi respectively, and the changes are used as basic units for forming the super surface;
s3, designing the super surface into a corresponding target shape according to different waveguide paths, and then constructing a slab waveguide device by using two layers of super surfaces to realize propagation of elastic waves along a preset track and meet the waveguide requirements.
The invention has the following beneficial effects:
the invention realizes the omnibearing mirror reflection of elastic waves by designing the super surface with the sub-wavelength thickness, and has the characteristics of simple and light structure, small volume and wide working frequency band.
The waveguide device is composed of two layers of omnidirectional specular reflection super surfaces with sub-wavelength thicknesses, is light and thin in structure, can be designed into any shape according to actual conditions, is good in designability, can guide elastic waves incident in any direction, and is wide in working frequency band and good in environmental adaptability.
The waveguide and the surrounding flat plate are of an integral structure, the same material is adopted, the laser cutting mode is used for processing, the processing precision is high, and the production is convenient.
Drawings
FIG. 1 is a schematic diagram of a super-surface of an omni-directional specular reflection;
FIG. 2 is an enlarged view of a unit cell structure;
FIG. 3 is a displacement field profile of a flat plate containing a super-surface at different incident angles at 15 kHz;
FIG. 4 is a graph of super-surface transmittance amplitude with incident angle θiAnd the variation law of the frequency f;
FIG. 5 is a schematic view of a linear slab waveguide structure;
FIG. 6 is a schematic diagram of an L-shaped slab waveguide structure;
FIG. 7 is a schematic view of a Z-shaped slab waveguide structure;
FIG. 8 is a displacement field distribution diagram of a linear slab waveguide structure under the excitation of a point source at 15 kHz;
FIG. 9 is a displacement field distribution diagram of an L-shaped slab waveguide structure under 15kHz point source excitation;
FIG. 10 is a displacement field distribution diagram of a Z-shaped slab waveguide structure under the excitation of a point source at 15 kHz.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.
The ultra-thin slab waveguide device of the embodiment of the invention realizes the guiding of the propagation of the elastic wave by using the omnibearing mirror reflection super surface with two layers of sub-wavelength thicknesses. The basic principle is that only 0-order modal scattered waves are generated after incident waves in any direction pass through the super surface by the unit cell design of the super surface, and the modal waves are completely reflected, as shown in fig. 1. The conditions for satisfying the above requirements are: 1) λ/L > 2, where λ is the wavelength and L is the width of the supercell; 2) the number of unit cells contained in a supercell is even.
The invention adopts a design method that two single cells form a supercell, the width H of each single cell is 7mm, the width L of the supercell is 14mm, the wavelength lambda is 30.6mm, the total length L of the single cells is 20.5mm, the plate thickness d is 1.5mm, the specific sizes of the two single cells are shown in figure 2, c is 1.5mm, and H is 5.7 mm.
The super surface unit cell can realize the change of the elastic wave phase, and the phase change is pi and 2 pi respectively. The transmission of each unit cell is greater than 0.9, so that the elastic wave cannot be completely reflected but is completely transmitted by using one unit cell alone. If two unit cells are arranged in a staggered mode to form the super surface, the elastic waves are subjected to specular reflection when being incident to the super surface along any direction. The planar waveguide with any shape can be designed by adopting two layers of omnibearing specular reflection super surfaces.
The design method of the ultrathin slab waveguide equipment comprises the following steps:
s1, respectively recording the material density, Young modulus and Poisson ratio of the super-surface structure and the flat plate as rho, E and nu;
establishing a finite element model of a unit cell, wherein the finite element model comprises a matrix medium and a unit cell structure, perfect matching layers are arranged in front and at the back of the model, and periodic boundary conditions are arranged on the upper and lower boundaries;
applying simple harmonic force load on one side of the unit cell structure, and calculating the phase change delta phi and the transmissivity | t | of the elastic wave after passing through the unit cell;
s2, calculating the unit cells with different geometric parameters in the step S1, and selecting two unit cells meeting the following conditions: 1) the transmittance | t | is not less than 0.9; 2) the phase change of the elastic wave after passing through the two unit cells is pi and 2 pi respectively, and the changes are used as basic units for forming the super surface;
s3, designing the super surface into a corresponding target shape according to different waveguide paths, and then constructing a slab waveguide device by using two layers of super surfaces to realize propagation of elastic waves along a preset track and meet the waveguide requirements.
The ultra-thin slab waveguide device of the embodiment comprises three parts, including a slab, a waveguide composed of two layers of ultra-surfaces, a wave source and a material304 stainless steel, and a density, Young's modulus and Poisson's ratio of 7930kg/m3200Gpa, 0.3. In order to verify the influence of different incidence angles and frequencies on the vibration isolation effect of the super-surface, the super-surface with the supercells arranged along a straight line is designed, a COMSOL Multiphysics finite element analysis software is adopted to establish a whole finite element model, and the model comprises a flat plate, a waveguide, a wave source and a perfect matching layer. The flat plate and the super surface are divided by adopting a free triangular grid and a swept grid in a combined mode, and the perfect matching layer is divided by adopting a mapping grid and a swept grid in a combined mode. And (3) researching in a frequency domain by adopting a solid mechanics module, giving the material property of the whole model, and setting parameters of a perfect matching layer. Generating 15kHz at the interface of the incident area and the perfect matching layer and having amplitude of 1e-7N/m2The displacement amplitude fields for different incident angles of the gaussian beam are shown in fig. 3. The angle of incidence and frequency were parametrically scanned to obtain the transmission as a function of angle of incidence and frequency, as shown in fig. 4. The result shows that the super-surface can completely reflect incident waves in any direction within the frequency range of 8-18 kHz.
According to the invention, firstly, a linear waveguide (figure 5) is adopted to verify the guiding effect of the elastic wave, a wave source is positioned in the middle of a waveguide channel, the wave source is incident from one end, and the displacement amplitude field distribution of the whole flat plate is observed under the frequency of 15kHz, as shown in figure 8, the elastic wave generated from the wave source almost completely linearly propagates along the path of the waveguide, and the displacement amplitude outside the waveguide is very small compared with the displacement amplitude inside the waveguide, which indicates that the elastic wave can effectively propagate along the linear waveguide.
Further, the present invention verifies the effect of the slab waveguide device of "L" type (fig. 6) and "Z" type (fig. 7), in which the wave source is located in the middle of the waveguide channel, and the displacement amplitude field distribution of the whole slab is observed at a frequency of 15kHz incident from one end, as shown in fig. 9 and 10. For the L-shaped waveguide and the Z-shaped waveguide, the elastic wave from the wave source is well transmitted to the other end along the path of the waveguide, and the displacement amplitude of the outer part of the waveguide is very small compared with that of the inner part of the waveguide, which shows that the elastic wave can be effectively transmitted along the waveguide device with any shape, thereby proving that the slab waveguide device has very good designability and can be designed into different shapes according to actual conditions.
The invention has the advantages of light and thin volume, simple structure, convenient processing, wide working frequency band and strong designability of structure, and can generate ideal guide effect on elastic waves in any direction. The design does not consider the damping characteristic, and the defects of damping materials are avoided. The unit cell has small size, does not need external energy supply, can be designed into any shape according to actual conditions, and has high economical efficiency and environmental adaptability.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (5)
1. The utility model provides an ultra-thin slab waveguide equipment, includes the flat board and sets up the waveguide structure on the flat board which characterized in that: the waveguide structure is composed of two layers of super surfaces with sub-wavelength thickness, the super surfaces are composed of super cells arranged periodically, each super cell comprises two unit cells with gradient indexes, the transmissivity | t | of the unit cells is not less than 0.9, the width of the unit cells is H, the phase change of elastic waves after passing through the two unit cells is pi and 2 pi respectively, and the phase gradient of the super surfaces is
Where L is 2H, L indicates the width of the supercell, and λ/L > 2, where λ indicates a wavelength, must be satisfied in order for the elastic wave to be incident on the super surface and then specularly reflected.
2. An ultra-thin slab waveguide device as claimed in claim 1 wherein: the super-surface may be designed in any shape according to the expected path of propagation of the elastic wave.
3. An ultra-thin slab waveguide device as claimed in claim 1 wherein: the super-surface with the sub-wavelength thickness can cause the incident wave in any direction to generate mirror reflection.
4. An ultra-thin slab waveguide device as claimed in claim 1 wherein: the unit cell width H is 7mm, the supercell width L is 14mm, the plate thickness d is 1.5mm, and the wavelength lambda of A0 wave is 30.6mm when the target frequency f is 15 kHz.
5. The method of designing a structure of an ultra-thin slab waveguide device as claimed in any one of claims 1 to 4, wherein: the method comprises the following steps:
s1, respectively recording the material density, Young modulus and Poisson ratio of the super-surface structure and the flat plate as rho, E and nu;
establishing a finite element model of a unit cell, wherein the finite element model comprises a matrix medium and a unit cell structure, perfect matching layers are arranged in front and at the back of the model, and periodic boundary conditions are arranged on the upper and lower boundaries;
applying simple harmonic force load on one side of the unit cell structure, and calculating the phase change delta phi and the transmissivity | t | of the elastic wave after passing through the unit cell;
s2, calculating the unit cells with different geometric parameters in the step S1, and selecting two unit cells meeting the following conditions: 1) the transmittance | t | is not less than 0.9; 2) the phase change of the elastic wave after passing through the two unit cells is pi and 2 pi respectively, and the changes are used as basic units for forming the super surface;
s3, designing the super surface into a corresponding target shape according to different waveguide paths, and then constructing a slab waveguide device by using two layers of super surfaces to realize propagation of elastic waves along a preset track and meet the waveguide requirements.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113162611A (en) * | 2021-03-25 | 2021-07-23 | 北京无线电测量研究所 | Broadband shifter for elastomer waves and manufacturing method thereof |
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| US20180159494A1 (en) * | 2016-10-20 | 2018-06-07 | Skyworks Solutions, Inc. | Elastic wave device with sub-wavelength thick piezoelectric layer |
| US20190278086A1 (en) * | 2016-05-18 | 2019-09-12 | Lumus Ltd. | Head-mounted imaging device |
| CN111723496A (en) * | 2020-07-23 | 2020-09-29 | 西北工业大学 | Ultrathin omnibearing vibration isolation super-surface structure and design method thereof |
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| US20190278086A1 (en) * | 2016-05-18 | 2019-09-12 | Lumus Ltd. | Head-mounted imaging device |
| US20180159494A1 (en) * | 2016-10-20 | 2018-06-07 | Skyworks Solutions, Inc. | Elastic wave device with sub-wavelength thick piezoelectric layer |
| CN111723496A (en) * | 2020-07-23 | 2020-09-29 | 西北工业大学 | Ultrathin omnibearing vibration isolation super-surface structure and design method thereof |
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| CN113162611A (en) * | 2021-03-25 | 2021-07-23 | 北京无线电测量研究所 | Broadband shifter for elastomer waves and manufacturing method thereof |
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