Method for manipulating propagation of ultrasonic second harmonic based on bilinear nonlinear phononic crystal material

Abstract

The application discloses a method for realizing quadratic harmonic focusing and curve propagation based on a bilinear nonlinear phononic crystal. Based on the bilinear nonlinear phononic crystal, quadratic harmonic enhancement is realized through certain parameter design, and by changing the parameters of the bilinear nonlinear material, the corresponding relationship between the parameters and the quadratic harmonic phase is obtained, so that the quadratic harmonic phase can be controlled. On this basis, the parameters of the bilinear nonlinear material are designed to meet the corresponding quadratic harmonic phase profile requirement, thereby realizing quadratic harmonic focusing and curve propagation.

Description

Technical Field

[0001] This invention relates to the use of nonlinear phonon crystal materials to enhance and phase-modulate second harmonics, thereby achieving the goal of focusing and curvilinear propagation of ultrasonic second harmonics. Background Technology

[0002] Currently, ultrasound is widely used in medical diagnosis and treatment due to its safety and harmlessness to the human body. On the one hand, ultrasound can be used for imaging; on the other hand, given its ability to penetrate blood-tissue barriers and its high-frequency energy and relatively high control precision, high-intensity focused ultrasound (HIFU) can also be used directly for tumor treatment and to deliver antibodies to specific sites for targeted therapy. With technological advancements and increasing human needs, the traditional method of ultrasound imaging using only the fundamental wave is gradually failing to meet the precision and accuracy requirements of medical diagnosis and treatment. It has been found that it is necessary to use harmonics to assist in achieving high-resolution imaging, thereby obtaining more detailed information about the observed object. However, generally speaking, even if harmonics can be generated using nonlinear effects, the harmonic components are usually few, which can lead to them being masked by the higher-concentration fundamental wave, causing inconvenience to high-resolution imaging.

[0003] Furthermore, when using ultrasound for medical treatment, it is unavoidable to bypass organs such as ribs. Curved propagation of sound waves can avoid energy loss at these organs, ensuring precise treatment and maximizing drug efficacy. Currently, research on curved propagation of sound waves mainly focuses on the fundamental frequency. However, because ultrasound wavelengths are relatively short, higher frequencies of emitted sound waves place higher demands on the precision of ultrasound devices. This is often limited by existing manufacturing processes; therefore, current research mostly involves relatively low frequencies. If the second harmonic generated by the emitted wave could be used for curved propagation, the precision of controlling sound waves or drugs along curved paths could be greatly improved under the same conditions of ultrasound devices. However, generally speaking, the amplitude of the second harmonic generated after passing through nonlinear materials is much lower than that of the fundamental frequency. Summary of the Invention

[0004] Purpose of the invention: To enhance the second harmonic of ultrasound using bilinear nonlinear phonon crystal materials, so as to allow the second harmonic to fully exert its function; to achieve phase modulation of the second harmonic to achieve focusing of the second harmonic and thus improve imaging accuracy; and to achieve curved propagation of the second harmonic to facilitate medical treatment and targeted drug delivery.

[0005] Technical Solution: A method for manipulating the propagation of ultrasonic second harmonics based on bilinear nonlinear phonon crystal materials. This involves periodically arranging bilinear nonlinear materials to form a one-dimensional longitudinal nonlinear phonon crystal. To manipulate the second harmonic in practice, these one-dimensional longitudinal bilinear nonlinear phonon crystals are then arranged laterally to form a two-dimensional phonon crystal. Specifically, the one-dimensional longitudinal bilinear nonlinear phonon crystal consists of isotropic materials spaced between bilinear nonlinear material phonon crystals. The distance between adjacent bilinear nonlinear material units is L (period), the density of the isotropic material is ρ, the longitudinal wave velocity is c, and the total number of isotropic materials between bilinear nonlinear material units is N, i.e., the number of bilinear nonlinear material units is N+1. The length of each bilinear nonlinear phonon crystal unit is much smaller than the length of the isotropic material units (the ratio of the length of the bilinear nonlinear material unit to the length of the isotropic material unit is 0.5%-10%).

[0006] Based on this, according to the requirements of ultrasonic second harmonic enhancement, we derived the conditions that the parameters of the corresponding bilinear nonlinear materials need to meet.

[0007] Furthermore, we varied the parameters of the bilinear nonlinear material within a certain range, and based on the second harmonic enhancement, we obtained the relationship between the second harmonic phase and the parameters of the bilinear nonlinear material.

[0008] To manipulate the second harmonic in practice, one-dimensional bilinear nonlinear phononic crystals are arranged longitudinally to form a two-dimensional phononic crystal.

[0009] To achieve second harmonic focusing, we designed the parameters of the bilinear nonlinear units within the one-dimensional nonlinear phonon crystal at different longitudinal positions, guided by the relationship between the second harmonic phase and the parameters of the bilinear nonlinear material, based on the second harmonic phase requirements of the one-dimensional nonlinear phonon crystal at different longitudinal positions.

[0010] Similar to the above method, we calculated the second harmonic phase requirements of the one-dimensional nonlinear phonon crystal at different longitudinal positions to achieve second harmonic curve propagation. Based on the relationship between the second harmonic phase and the parameters of the bilinear nonlinear material, we designed the parameters of the bilinear nonlinear unit at the corresponding positions to achieve the curve propagation of the second harmonic.

[0011] The specific parameters can be adjusted according to actual needs. That is, the range of parameters is not limited to the parameter values ​​specified in this invention. The corresponding parameters can also be adjusted to achieve ultrasonic second harmonic enhancement in other frequency bands, and further achieve second harmonic focusing and curve propagation.

[0012] Beneficial effects:

[0013] The method used in this invention can be extended to harmonic imaging in medical ultrasound. Compared with existing technologies, the beneficial effects of this invention are as follows: It utilizes a bilinear nonlinear phonon crystal material to achieve ultrasound second harmonic enhancement, avoiding the second harmonic being submerged by the fundamental wave and thus unable to exert its due effect; it achieves second harmonic focusing based on second harmonic enhancement, providing a solution for improving imaging resolution; furthermore, it achieves curved propagation of the second harmonic based on second harmonic enhancement, which is beneficial for medical treatment and targeted drug delivery. Attached Figure Description

[0014] Figure 1 (a) Schematic diagram of the periodic arrangement of bilinear nonlinear material elements and isotropic material elements; (b) Discretized model of the periodic arrangement of bilinear nonlinear material elements and isotropic material elements.

[0015] Figure 2 Schematic diagram of the principle of ultrasonic second harmonic enhancement: (a) transmission coefficient of the fundamental wave as a function of the excitation frequency; (b) transmission coefficient of the second harmonic as a function of the second harmonic frequency.

[0016] Figure 3 Schematic diagram of the effect of ultrasonic second harmonic enhancement: (a) transmission coefficient of the fundamental wave as a function of the excitation frequency; (b) transmission coefficient of the second harmonic as a function of the excitation frequency.

[0017] Figure 4 When k1 = 0.2k0 and k2 = 0.14k0, the transmission rates of the fundamental and second harmonics as excitation frequency functions (second harmonic enhancement).

[0018] Figure 5 The variation of k1 within the range (k1∈[0.15k0, 0.35k0]) enables full coverage of the second harmonic phase in [0, 2π] while enhancing the second harmonic. Specifically, as follows: Figure 5 As shown.

[0019] from Figure 5 (a) It can be seen that second harmonic enhancement can indeed be achieved consistently when k1∈[0.15k0, 0.35k0]. To achieve phase control of the second harmonic, we choose k1∈[0.162k0, 0.293k0] (e.g. Figure 5 (b) The shaded area is shown to meet the requirements of second harmonic phase change.

[0020] To achieve second harmonic focusing, we arranged a one-dimensional phonon crystal composed of bilinear nonlinear materials vertically, such as... Figure 6 As shown, the required second harmonic phase is then determined based on the path difference between different longitudinal positions and the focal position. The specific calculation formula is as follows:

[0021]

[0022] Here, we set up 99 one-dimensional phonon crystals arranged vertically, with a center-to-center distance of 3 mm between adjacent phonon crystals, and set the focal point as (0.174m, 0m). Therefore, the total second harmonic phase profile calculated according to the above formula is as follows: Figure 7 As shown by the gray line in (a). Figure 7 The black dots in (a) represent the phase of the second harmonic that these one-dimensional phonon crystals, spaced 3 mm apart, should acquire. Next, we will... Figure 5 (b) shows the relationship between the second harmonic phase and k1. For one-dimensional phonon crystals at different longitudinal positions, appropriate bilinear nonlinear parameters are selected, and the results are as follows: Figure 7 As shown in (b), the black dots in the figure represent the values ​​of k1 that the bilinear nonlinear units in a one-dimensional phononic crystal at different longitudinal positions should achieve (for ease of representation, the vertical axis is expressed in the form of k1 / k0). That is, in order to achieve the purpose of second harmonic focusing, for a two-dimensional phononic crystal, the k2 of the bilinear nonlinear units in the one-dimensional phononic crystal at different longitudinal positions is 0.14k0, while k1 is determined according to... Figure 7 (b) Take the value.

[0023] The normalized effective sound pressure field obtained according to the above method is as follows: Figure 7 As shown in (c) Figure 7 (d) is Figure 7 (c) Magnified result near the focal point Figure 7 (e) and (f) are respectively Figure 7 (d) shows the effective transmitted sound pressure distribution along the white dashed lines A and B. The dashed lines indicate the maximum values ​​of the effective transmitted sound pressure distribution along the two directions A and B and their corresponding specific locations. It can be seen that the focusing position matches the preset focus position.

[0024] In addition, based on the second harmonic enhancement (i.e., still using k2 = 0.14k0, k1 ∈ [0.162k0, 0.293k0]), we preset the propagation path of the second harmonic curve to be a cubic Bézier curve (i.e. determined by 4 points P0, P1, P2 and P3), the specific expression of which is as follows:

[0025] P(t)=(1-t) 3 P0+3t(1-t) 2 P1+3(1-t)t 2 P2+t 3 P3(0≤t≤1)

[0026]

[0027]

[0028]

[0029]

[0030] The numerical solution can be obtained by solving the above equations. Among them, A represents the amplitude of the emitted wave.

[0031] Furthermore, we also obtained an approximate dispersion curve formula for the fundamental wave. Since ω should actually be greater than 0, we take the following value in practical applications:

[0032]

[0033] in, And k0=2ρc 2 / L,

[0034] Based on this, the design concept of the present invention is as follows: Figure 2 As shown, assuming the maximum frequency of the fundamental acoustic branch is f1, and the minimum frequency of the optical branch is f... 21 The maximum value is f 22 ,like Figure 2 As shown in (a), considering only the acoustic and optical branches of the fundamental wave, the corresponding second harmonic passbands are [0, 2f1] and [2f1], respectively. 21 ,2f 22 ],like Figure 2 As shown in (b). From Figure 2 (a) It can be seen that for the phonon crystal designed in this invention, [f] is allowed. 21 f 22 Sound waves in this frequency band pass through, therefore, if the frequency value of the second harmonic (the frequency of the second harmonic is twice the corresponding fundamental frequency) is in [f 21 f 22 Within the specified range, it is permissible, such as... Figure 2 As shown in the dashed box in (b), simply put, it is equivalent to adding a passband for the second harmonic.

[0035] The specific effects that the above design can achieve are as follows: Figure 3 As shown, when the frequency of the emitted wave is located at [f 21 / 2,f 22 At frequency band / 2], the corresponding fundamental frequency is in the stopband, while the corresponding second harmonic is in the passband, such as Figure 3 As shown in the dashed box in [f], therefore, in [f] 21 / 2,f 22The / 2] frequency band achieves the effect of second harmonic enhancement.

[0036] Based on the above approach, we designed L = 3mm, c = 6420m / s, and ρ = 2700kg / m. 3 With N = 20, and the parameters of the bilinear nonlinear material element being k1 = 0.2k0 and k2 = 0.14k0, the transmission curves of the fundamental and second harmonic waves are obtained, as follows: Figure 4 As shown in the figure, the dashed box indicates that when the transmission frequency is in this band, the second harmonic enhancement effect can be achieved, meaning that the amplitude of the second harmonic at the receiving end is higher than that of the fundamental frequency.

[0037] Based on this, we fix one of the parameters of the bilinear nonlinear material element, k2 = 0.14k0, and within a certain range... Figure 5 (a) The amplitude of the fundamental and second harmonics varies with k1 (for ease of representation, the horizontal axis is represented in the form of k1 / k0); (b) The phase of the second harmonic varies with k1 (for ease of representation, the horizontal axis is represented in the form of k1 / k0), where the gray shaded area represents k1∈[0.162k0, 0.293k0].

[0038] Figure 6 A two-dimensional phononic crystal is formed by longitudinally arranging one-dimensional phononic crystals made of bilinear nonlinear materials.

[0039] Figure 7 Focusing of the second harmonic: (a) Longitudinal second harmonic phase profile, where black dots represent the second harmonic phases corresponding to the one-dimensional phonon crystal at different longitudinal positions; (b) The values ​​of k1 that the bilinear nonlinear units in the one-dimensional phonon crystal at different longitudinal positions should acquire (for ease of representation, the vertical axis shows the values ​​of k1 / k0); (c) The normalized effective sound pressure field at the focusing point (0.174m, 0m); (d) Figure 7 (c) The magnified result near the focal point in the figure; (e) Figure 7 (d) Normalized effective transmitted sound pressure distribution along the white dashed line A; (f) Figure 7 (d) Normalized effective transmission sound pressure distribution along the white dashed line B.

[0040] Figure 8 Second harmonic propagation curves: (a) Longitudinal phase profile, where black dots represent the second harmonic phases corresponding to the one-dimensional phonon crystal at different longitudinal positions; (b) The k1 values ​​that the bilinear nonlinear units in the one-dimensional phonon crystal at different longitudinal positions should acquire (for ease of representation, the vertical axis shows the k1 / k0 values); (c) Second harmonic propagation curve diagram (normalized effective sound pressure field); (d) In Figure 8 (c) A preset Bézier curve was added to the original figure. Detailed Implementation

[0041] The basic structure of this invention is a one-dimensional phononic crystal formed by the periodic arrangement of bilinear nonlinear materials, such as... Figure 1 As shown in (a), the black narrow band is a bilinear nonlinear material, and the remaining blank part is an isotropic material. We assume that the interval between adjacent bilinear nonlinear material units is L (period), the density of the isotropic material is ρ, the longitudinal wave velocity is c, and the total number of isotropic materials between bilinear nonlinear material units is N, that is, the number of bilinear nonlinear material units is N+1.

[0042] In this invention, we set the length of the bilinear nonlinear material element to be much smaller than that of the isotropic material, thereby enabling the corresponding structure to be discretized for subsequent processing and calculation. The model obtained after discretization is as follows: Figure 1 As shown in (b). The gray sphere represents the equivalent mass, the broken line represents the linear spring equivalent to an isotropic material element, and the broken line with the arrow represents the nonlinear spring equivalent to a bilinear nonlinear material element. Its characteristic is that the spring constant of the nonlinear spring equivalent to a bilinear nonlinear material element per unit cross-sectional area is not a fixed value, specifically manifested as follows:

[0043]

[0044] Where ξ represents displacement, and k2 < k1.

[0045] Based on this, theoretical derivation yields the following four equations:

[0046] Here, we select P0, P1, P2 and P3 as (-0.01555, 0), (0.10945, 0.05), (0.18445, 0.125), and (-0.06555, 0.49) respectively, and set 123 one-dimensional phonon crystals arranged vertically with a spacing of 2 mm between them.

[0047] Based on the principle of achieving curved propagation by tangenting the emitted sound ray to a predetermined curved propagation path, and combined with the Legendre transform, the longitudinal second harmonic phase profile was calculated, as shown in the figure. Figure 8 As shown by the gray line in (a), the black dots represent the phase of the second harmonic that a one-dimensional phononic crystal spaced 2 mm apart should achieve. According to Figure 5 (b) shows the relationship between the second harmonic phase and k1. For one-dimensional phonon crystals at different longitudinal positions, appropriate bilinear nonlinear parameters are selected, and the results are as follows: Figure 8As shown in (b), the black dots in the figure represent the values ​​of k1 that the bilinear nonlinear units in a one-dimensional phononic crystal at different longitudinal positions should acquire (for ease of representation, the vertical axis is expressed in the form of k1 / k0). That is, in order to achieve the purpose of second harmonic propagation along the curve, for a two-dimensional phononic crystal, the k2 of the bilinear nonlinear units in the one-dimensional phononic crystal at different longitudinal positions is 0.14k0, while k1 is determined according to... Figure 8 (b) Take the value.

[0048] The normalized effective sound pressure field obtained according to the above method is as follows: Figure 8 As shown in (c), a clear curved propagation path can be seen. To verify whether this path is the cubic Bézier curve path we preset, we... Figure 8 Based on (c), the preset cubic Bézier curve is drawn using black dashed lines, i.e. Figure 8 (d), from Figure 8 As can be seen in (d), the black dashed line matches the actual curve propagation path in the normalized effective sound pressure field quite well.

Claims

1. A method for controlling the propagation of ultrasonic second harmonics based on bilinear nonlinear phonon crystal materials, characterized in that... A one-dimensional nonlinear phonon crystal is constructed by periodically arranging bilinear nonlinear materials. To manipulate second harmonics in practice, the one-dimensional longitudinal bilinear nonlinear phonon crystals are then arranged laterally to form a two-dimensional phonon crystal. Specifically, the one-dimensional longitudinal bilinear nonlinear phonon crystal consists of isotropic materials spaced between bilinear nonlinear material phonon crystals. The distance between adjacent bilinear nonlinear material units is L, the density of the isotropic material is ρ, the longitudinal wave velocity is c, and the total number of isotropic materials between bilinear nonlinear material units is N, i.e., the number of bilinear nonlinear material units is N+1. The length of each bilinear nonlinear material phonon crystal unit is much smaller than the length of the isotropic material unit, with the ratio of the length of the bilinear nonlinear material unit to the length of the isotropic material unit being 0.5%-10%. The parameters of the bilinear nonlinear material vary within a certain range. Based on the second harmonic enhancement, the relationship between the second harmonic phase and the parameters of the bilinear nonlinear material is obtained. To achieve second harmonic focusing, we arranged a one-dimensional phonon crystal made of bilinear nonlinear material longitudinally, and determined the required second harmonic phase based on the path difference between different longitudinal positions and the focal position. The specific calculation formula is as follows:

2. The method for controlling the propagation of ultrasonic second harmonics based on bilinear nonlinear phonon crystal materials according to claim 1, characterized in that, To achieve second harmonic focusing, based on the second harmonic phase requirements of the one-dimensional nonlinear phononic crystal at different longitudinal positions, and guided by the parameter relationship diagram between the second harmonic phase and the bilinear nonlinear material, the parameters of the bilinear nonlinear unit in the one-dimensional nonlinear phononic crystal at different longitudinal positions are designed to achieve second harmonic focusing. The second harmonic phase requirements of a one-dimensional nonlinear phonon crystal at different longitudinal positions are calculated to achieve second harmonic curve propagation. Based on the relationship between the second harmonic phase and the parameters of the bilinear nonlinear material, the parameters of the bilinear nonlinear unit at the corresponding position are designed to achieve the curve propagation of the second harmonic.

3. The method for controlling the propagation of ultrasonic second harmonics based on bilinear nonlinear phonon crystal materials according to claim 1, characterized in that, The model obtained after discretization: Using the approximate dispersion curve formula for the fundamental wave, ω is greater than 0, and in practical applications, we take: in, And k0=2ρc 2 / L, If the maximum frequency of the fundamental acoustic branch is f1, and the minimum frequency of the optical branch is f... 21 The maximum value is f 22 Therefore, considering only the acoustic and optical branches of the fundamental wave, the corresponding second harmonic passbands are [0, 2f1] and [2f1], respectively. 21 ,2f 22 For the designed phonon crystal, [f] is allowed. 21 f 22 Sound waves in this frequency band pass through, therefore, if the frequency value of the second harmonic is in [f 21 f 22 Within this range, it can pass through, which is equivalent to adding a passband for the second harmonic; When the frequency of the emitted wave is located at [f 21 / 2,f 22 At frequency band / 2], the corresponding fundamental frequency is in the stopband, while the corresponding second harmonic is in the passband. 21 / 2,f 22 The / 2] frequency band achieves the effect of second harmonic enhancement.

4. The method for controlling the propagation of ultrasonic second harmonics based on bilinear nonlinear phonon crystal materials according to claim 1, characterized in that, in When k1∈[0.15k0, 0.35k0], second harmonic enhancement can indeed be achieved consistently; in order to achieve the control of the second harmonic phase, k1∈[0.162k0, 0.293k0] is selected to meet the requirements of second harmonic phase change.

5. The method for controlling the propagation of ultrasonic second harmonics based on bilinear nonlinear phonon crystal materials according to claim 1, characterized in that, By adjusting the corresponding parameters, ultrasonic second harmonic enhancement can be achieved in other frequency bands, and second harmonic focusing and curved propagation can be further achieved.

6. The method for controlling the propagation of ultrasonic second harmonics based on bilinear nonlinear phonon crystal materials according to claim 1, characterized in that, The method used has been extended to acoustic diodes.

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