Construction method of photonic crystal and one-dimensional coupling resonant cavity chain based on photonic crystal

Abstract

The invention relates to the field of acoustics, and discloses a construction method of a phononic crystal and a one-dimensional coupled resonant cavity chain based on the phononic crystal, and the construction method of the phononic crystal based on a non-Hermite induction topological insulator specifically comprises the following steps: constructing a plurality of acoustic resonant cavities; every two acoustic resonant cavities are connected through a coupling pipe; additional loss is introduced to at least one coupling tube. The method solves the problem that the effect of a coupling rod between cavities is not considered in the prior art, and has the characteristic of being capable of inducing a topological edge state.

Description

Technical Field

[0001] The present invention relates to the field of acoustics, and more specifically, to a method for constructing a phononic crystal and a one-dimensional coupled resonant cavity chain based thereon. Background Art

[0002] Phononic crystals are a medium composed of periodic composites of materials with different elastic properties. They are a new type of acoustic functional material with phonon energy bands and band gaps.

[0003] Hermitian properties are the basis of quantum systems. They effectively guarantee real eigenvalues ​​and orthogonal eigenstates. These Hermitian properties are usually used to define various quantum topological structures and accurately classify the topological phases of matter. Generally speaking, the way phononic crystals manipulate electromagnetic waves can achieve zero gain and loss through the real parameters of the phononic crystals, which falls into the category of Hermitian properties.

[0004] Most of the existing topologies are studied based on Hermitian systems. Although these classical topological systems follow Hermitian properties, since it is impossible for the system to have no energy exchange with the outside world, there must be losses and / or gains, so they are essentially non-Hermitian in nature. Therefore, research under Hermitian systems is ideal and too limited. When considering a non-conservative system that interacts with the outside world, its energy conservation is violated, and the concept of non-Hermitian dynamics is naturally introduced. Non-Hermitian physics flourishes in non-conservative systems, because in physical systems that exist in nature, it is difficult to have no energy exchange with the outside world. The system has more or less coupling with the outside world, so there is energy gain or loss. Since its proposal, non-Hermitian physics has been widely studied, and new principles, phenomena and applications have been shown in open quantum systems, interacting electronic systems, and classical systems with added gains and losses. For example, by introducing gains and losses, under the condition of satisfying space-time symmetry, the system has special singular points in the complex energy plane, supporting one-way propagation and abnormal Fermi arcs and other characteristics.

[0005] At present, the traditional introduction of non-Hermitian is through the introduction of imaginary loss. Therefore, non-Hermitian only makes the topological boundary state decay, and has no effect on the real part and eigenstate of dispersion, and the topological properties of the band cannot be determined, because the induced band gap can be topological or mediocre. Whether the introduction of non-Hermitian can induce the acquisition of topological phases and play a more important application is unknown, and it is difficult to further apply it to practical fields such as acoustics and optics. Therefore, it is very important to study the crystal design of inducing topological states under non-Hermitian state, so as to apply it to acoustics and optics to achieve lossless transmission.

[0006] The prior art has a two-dimensional phononic crystal structure based on non-Hermitian induced topological angle states, which relates to the technical field of phononic crystal design. The structure is composed of rectangular acoustic resonant cavities arranged in rows and columns, and every two acoustic resonant cavities are connected by two upper and lower coupling tubes. In addition, virtual in-situ energy γ1 with only background loss and virtual in-situ energy γ2 with additional loss are introduced at different lattice points of the two-dimensional phononic crystal structure. By gradually increasing the additional loss of the virtual in-situ energy γ2, the dispersion relation of the two-dimensional phononic crystal gradually changes from closed to open, and high-order topological angle states appear in the band gap.

[0007] However, the existing technology has the problem of not considering the role of the coupling rods between cavities. Therefore, how to invent a bulk phononic crystal with non-Hermitian acoustic topological insulation considering the coupling rods is a technical problem that urgently needs to be solved in this technical field. Summary of the invention

[0008] In order to solve the problem in the prior art that the role of coupling rods between cavities is not considered, the present invention provides a method for constructing a phononic crystal and a one-dimensional coupled resonant cavity chain based thereon, which has the characteristic of inducing topological edge states.

[0009] In order to achieve the above-mentioned purpose of the present invention, the technical scheme adopted is as follows:

[0010] A method for constructing a phononic crystal based on a non-Hermitian induced topological insulator comprises the following steps:

[0011] Constructing several acoustic resonant cavities;

[0012] Connect every two acoustic resonant cavities via a coupling tube;

[0013] Additional losses are introduced into at least one coupling tube.

[0014] Preferably, the acoustic resonance cavity is a rectangular parallelepiped acoustic resonance cavity.

[0015] Furthermore, the coupling tube is specifically a cylindrical coupling tube.

[0016] Furthermore, the introduction of additional loss into at least one coupling tube is specifically achieved by adding sound absorbing material at the corresponding coupling tube opening to introduce additional loss.

[0017] Furthermore, specifically, the one-dimensional phononic crystal includes four acoustic resonant cavities.

[0018] Furthermore, specifically, the coupling tube between the first acoustic resonant cavity and the second acoustic resonant cavity, and the coupling tube between the second acoustic resonant cavity and the third acoustic resonant cavity both introduce additional losses.

[0019] Furthermore, specifically, the coupling tube between the second acoustic resonant cavity and the third acoustic resonant cavity, and the coupling tube between the third acoustic resonant cavity and the fourth acoustic resonant cavity both introduce additional losses.

[0020] Furthermore, the resonant cavity wall and the coupling tube wall are considered as hard boundaries.

[0021] A one-dimensional coupled resonant cavity chain comprises a plurality of the above-mentioned phononic crystals; additional loss is introduced at the same position in each phononic crystal; and every two phononic crystals are connected via a coupling tube.

[0022] Preferably, specifically, it comprises 5 of the phononic crystals.

[0023] The beneficial effects of the present invention are as follows:

[0024] The present invention discloses a method for constructing a phononic crystal based on a non-Hermitian induced topological insulator. The method constructs a phononic crystal including a plurality of acoustic resonant cavities and coupling tubes, introduces additional loss in at least one coupling tube, designs a one-dimensional phononic crystal structure in a non-Hermitian state, takes into account the role of coupling rods between cavities, and induces topological edge states, thereby laying a foundation for transmission in acoustic devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a schematic flow chart of a method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to the present invention.

[0026] Figure 2 It is a structural schematic diagram of a method for constructing a phononic crystal based on a non-Hermitian induced topological insulator of the present invention in Example 1.

[0027] Figure 3 It is a schematic diagram of a one-dimensional coupled resonant cavity chain of the present invention.

[0028] Figure 4 This is the dispersion relation diagram before the additional loss is introduced in Example 2.

[0029] Figure 5 This is a dispersion relation diagram after additional loss is introduced in Example 2.

[0030] Figure 6 It is the energy state diagram of the one-dimensional coupled resonant cavity chain in Example 3.

[0031] Figure 7 It is the energy state diagram of the one-dimensional coupled resonant cavity chain after the volume of the ninth resonant cavity is reduced in Example 3. DETAILED DESCRIPTION

[0032] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] Example 1

[0034] like Figure 1 As shown, a method for constructing a phononic crystal based on a non-Hermitian induced topological insulator comprises the following steps:

[0035] Constructing several acoustic resonant cavities;

[0036] Connect every two acoustic resonant cavities via a coupling tube;

[0037] Additional losses are introduced into at least one coupling tube.

[0038] In a specific embodiment, the acoustic resonance cavity is a rectangular parallelepiped acoustic resonance cavity.

[0039] In a specific embodiment, the coupling tube is a cylindrical coupling tube.

[0040] In a specific embodiment, the introduction of additional loss into at least one coupling tube is achieved by adding sound absorbing material at the corresponding coupling tube opening to introduce additional loss.

[0041] In a specific embodiment, specifically, the one-dimensional phononic crystal includes 4 acoustic resonant cavities.

[0042] In a specific embodiment, specifically, the coupling tube between the first acoustic resonant cavity and the second acoustic resonant cavity, and the coupling tube between the second acoustic resonant cavity and the third acoustic resonant cavity both introduce additional losses.

[0043] In a specific embodiment, the resonant cavity wall and the coupling tube wall are both considered as hard boundaries.

[0044] like Figure 2 As shown in the figure, the cylindrical coupling tube located at the outermost layer of the phononic crystal structure and all the acoustic resonant cavities have only background losses, and the distribution order of the phononic crystal structure is: the first cylindrical coupling tube, the first acoustic resonant cavity, the second cylindrical coupling tube, the second acoustic resonant cavity, the third cylindrical coupling tube, the third acoustic resonant cavity, the fourth cylindrical coupling tube, the fourth acoustic resonant cavity, and the fifth cylindrical coupling tube. In the figure, the gray domain represents the acoustic resonant cavity and the coupling tube without introducing loss, and only considers the inherent background loss; the blue domain represents the cylindrical coupling tube that introduces additional loss.

[0045] The radius of the cylindrical coupling tube is 4 mm, the length is 18 mm, and the size of the acoustic resonance cavity is 40*10*80 mm.

[0046] Compared with the previous method of obtaining a topological insulator by changing the intracellular and extracellular coupling, the present invention has not been studied in the way of adding loss in the coupling tube, which can make the one-dimensional topological insulator in the non-Hermitian system easier to realize without calculating its intracellular and extracellular strength. In addition, the current topological insulator based on non-Hermitian realization is realized by the loss introduced in the resonant cavity. This method of introducing loss in the coupling tube enriches the method of realizing topological insulators in non-Hermitian systems. Under normal circumstances, the loss of acoustic energy by the capillary is significantly stronger than that of the resonant cavity, so this method of introducing loss in the coupling tube is expected to have important guiding significance for future research on non-Hermitian systems.

[0047] Example 2

[0048] like Figure 3 As shown, a one-dimensional coupled resonant cavity chain includes five of the above-mentioned phononic crystals; additional loss is introduced at the same position in each phononic crystal; and every two phononic crystals are connected by a coupling tube.

[0049] In the figure, the blue area represents the cylindrical coupling tube that introduces additional loss.

[0050] Example 3

[0051] In this embodiment, in order to observe whether there will be topological boundary states when additional losses are introduced into the cylindrical coupling tube, a one-dimensional coupled resonant cavity chain is tested: the energy state change and the acoustic field intensity distribution of the one-dimensional coupled resonant cavity chain are obtained by simulation, and its band gap is confirmed based on the energy state change and the acoustic field intensity distribution, and its topological properties are confirmed.

[0052] In this embodiment, before the test, Floquet periodic boundary conditions were applied to the left and right sides of the phononic crystal without introducing additional loss, and the sound speed was set to 341.8*(1+0.0066i)m / s, and the following was obtained: Figure 4 The dispersion relation of the structure shown in the figure shows that the band gap is continuous and there is no band gap. After introducing additional losses in the coupling tube between the first acoustic resonant cavity and the second acoustic resonant cavity, and the coupling tube between the second acoustic resonant cavity and the third acoustic resonant cavity, the sound velocity of the coupling rod is set to 341.8*(1+0.2393i)m / s, and the following is obtained: Figure 5 The dispersion relation of the structure shown in Figure 1 shows that the degeneracy of the first and second energy bands is opened, a gap is formed, and a topological phase appears in the gap.

[0053] The energy state change and acoustic field intensity distribution of the one-dimensional coupled resonant cavity chain obtained by simulation are shown in Figure 6 As shown in the figure, the multi-color illustration shows the distribution of its sound field intensity; Figure 6 It can be seen that the band gap below is opened, and Figure 5 The dispersion relation of the original cell is consistent with that of the original cell. The yellow area in the figure is the band gap frequency of the original cell. Since the opened band gap is topologically nontrivial, there is an edge state at the frequency of f = 2100.3 Hz.

[0054] In this embodiment, the volume of the ninth resonant cavity of the one-dimensional coupled resonant cavity chain is also reduced to 3 / 8 of the original volume, and the simulation is continued to obtain the following Figure 7 The energy state change and acoustic field intensity distribution of the one-dimensional single chain finite structure are shown in Figure 7 It can be seen that the boundary state still exists and is related to Figure 6 The results are basically consistent with those of , so the structure shows extremely strong robustness and will be helpful in the design of acoustic transmission devices.

[0055] Obviously, the above embodiments of the present invention are only examples for clearly explaining the present invention, and are not intended to limit the implementation methods of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A method for constructing a phononic crystal based on a non-Hermitian induced topological insulator, characterized in that: The following steps are involved: Constructing several acoustic resonant cavities; Connect every two acoustic resonant cavities via a coupling tube; Additional losses are introduced into at least one coupling tube.

2. The method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to claim 1, characterized in that: The acoustic resonance cavity is specifically a rectangular parallelepiped acoustic resonance cavity.

3. The method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to claim 1, characterized in that: The coupling tube is specifically a cylindrical coupling tube.

4. The method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to claim 1, characterized in that: The introduction of additional loss into at least one coupling tube is specifically achieved by adding sound absorbing material at the corresponding coupling tube opening to introduce additional loss.

5. The method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to claim 1, characterized in that: Specifically, the one-dimensional phononic crystal includes four acoustic resonant cavities.

6. The method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to claim 5, characterized in that: Specifically, the coupling tube between the first acoustic resonant cavity and the second acoustic resonant cavity, and the coupling tube between the second acoustic resonant cavity and the third acoustic resonant cavity both introduce additional losses.

7. The method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to claim 5, characterized in that: Specifically, the coupling tube between the second acoustic resonant cavity and the third acoustic resonant cavity, and the coupling tube between the third acoustic resonant cavity and the fourth acoustic resonant cavity both introduce additional losses.

8. The method for constructing a phononic crystal based on a non-Hermitian induced topological insulator according to claim 1, characterized in that: The resonant cavity wall and the coupling tube wall are considered as hard boundaries.

9. A one-dimensional coupled resonant cavity chain, characterized in that: The invention comprises a plurality of phononic crystals as claimed in any one of claims 1 to 8; additional loss is introduced at the same position in each phononic crystal; and every two phononic crystals are connected by a coupling tube.

10. The one-dimensional coupled resonant cavity chain according to claim 9, characterized in that: Specifically, it includes 5 of the phononic crystals.

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