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

Abstract

The invention discloses a method for realizing second harmonic focusing and curve propagation based on a bilinear nonlinear photonic crystal. On the basis of the bilinear nonlinear photonic crystal, second harmonic enhancement is achieved through certain parameter design, the corresponding relation between the bilinear nonlinear material and the second harmonic phase is obtained by changing parameters of the bilinear nonlinear material, and therefore regulation and control over the second harmonic phase can be achieved. On the basis, parameters of the bilinear nonlinear material are designed to meet corresponding second harmonic phase profile requirements, and second harmonic focusing and curve propagation are achieved.

Description

Technical Field

[0001] The present invention relates to utilizing nonlinear phononic crystal materials to realize the enhancement and phase regulation of the second harmonic, and to achieve the purpose of realizing the focusing and curved propagation of the ultrasonic second harmonic. Background Art

[0002] At present, ultrasound has been widely used in medical diagnosis and treatment due to its safety and harmlessness to the human body. On the one hand, people can use ultrasound for imaging. On the other hand, given the characteristics of ultrasound penetrating the blood-tissue barrier, high-frequency energy, and relatively high control accuracy, high-intensity focused ultrasound (HIFU) can also be used directly for tumor treatment and delivery of antibodies to designated sites to achieve the purpose of targeted treatment. With the advancement of science and technology and the improvement of human needs, the traditional method of using only fundamental waves for ultrasound imaging has gradually failed to meet the requirements of precision and accuracy in medical diagnosis and treatment. People have found that it is necessary to use harmonics to assist in high-resolution imaging, so as to obtain more and more detailed information about the observed object. However, in general, even if harmonics can be generated by nonlinear effects, the harmonic components are usually small, which will cause them to be masked by the higher-component fundamental waves and bring inconvenience to high-resolution imaging.

[0003] In addition, when using ultrasound for medical treatment, it is inevitable to bypass organs such as ribs. The curved propagation of sound waves can avoid energy loss at organs such as ribs, and can also ensure precise treatment and maximize the effectiveness of drugs. At present, research on the curved propagation of sound waves mainly focuses on the fundamental wave. However, because the wavelength of ultrasound is short, if the frequency of the emitted sound waves is too high, higher requirements will be placed on the accuracy of ultrasonic devices, but this is often restricted by existing manufacturing processes. Therefore, the sound wave frequencies involved in current research are mostly not high. If the second harmonic generated by the emitted wave can be used for curved propagation, the accuracy of manipulating sound waves or drug propagation along a curved path can be greatly improved under the same conditions of the ultrasonic device. However, in general, after passing through nonlinear materials, the amplitude of the second harmonic generated is much lower than the fundamental wave. Summary of the invention

[0004] Purpose of the invention: To enhance the second harmonic of ultrasound by using bilinear nonlinear phononic crystal materials, so as to enable the second harmonic to fully exert its effect; to achieve phase control of the second harmonic to achieve second harmonic focusing to improve imaging accuracy, as well as curved propagation of the second harmonic, so as to facilitate medical treatment and directional delivery of targeted drugs.

[0005] Technical solution: Based on the method of manipulating the propagation of ultrasonic second harmonics using bilinear nonlinear phononic crystal materials, the bilinear nonlinear materials are periodically arranged to form a one-dimensional longitudinal nonlinear phononic crystal. In order to manipulate the second harmonic in practice, the one-dimensional longitudinal bilinear nonlinear phononic crystals are arranged laterally in sequence to form a two-dimensional phononic crystal. The specific structure is: the one-dimensional longitudinal bilinear nonlinear phononic crystal is a bilinear nonlinear material phononic crystal with isotropic materials between the bilinear nonlinear material units, 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, the total number of isotropic materials between the bilinear nonlinear material units is N, that is, the number of bilinear nonlinear material units is N+1; the length of the bilinear nonlinear material phononic crystal unit is much smaller than the length of the isotropic material unit (the ratio of the length of the bilinear nonlinear material unit to the length of the isotropic material unit is 0.5%-10%);

[0006] On this basis, we derived the conditions that the parameters of the corresponding bilinear nonlinear materials need to satisfy according to the needs of ultrasonic second harmonic enhancement;

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

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

[0009] In order to achieve the purpose of second harmonic focusing, we design the parameters of the bilinear nonlinear unit in the one-dimensional nonlinear phononic crystal at different longitudinal positions according to the second harmonic phase requirements of the one-dimensional nonlinear phononic crystal at different longitudinal positions, under the guidance of the parameter relationship between the second harmonic phase and the bilinear nonlinear material, to achieve second harmonic focusing.

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

[0011] The specific parameters can be adjusted accordingly according to actual needs, that is, the parameter range is not limited to the parameter values ​​clearly described in the present 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 curved propagation.

[0012] Beneficial effects:

[0013] The method used in the present invention can be extended and applied to harmonic imaging of medical ultrasound. The beneficial effects of the present invention, compared with the prior art, have the following characteristics: using bilinear nonlinear phononic crystal materials, the effect of ultrasonic second harmonic enhancement is achieved, avoiding the second harmonic being submerged by the fundamental wave so that it cannot play its due role; on the basis of second harmonic enhancement, second harmonic focusing is achieved, providing a solution for improving the resolution of imaging; in addition, on the basis of second harmonic enhancement, the curve propagation of the second harmonic is achieved, which is beneficial to medical treatment and targeted drug directional delivery. BRIEF DESCRIPTION OF THE DRAWINGS

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

[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) second harmonic transmission coefficient 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 Transmission ratio of the fundamental and second harmonic as a function of the excitation frequency when k1=0.2k0 and k2=0.14k0 (second harmonic enhancement).

[0018] Figure 5 The k1 is changed within the range (k1∈[0.15k0, 0.35k0]) so that the second harmonic phase can be fully covered in the range [0, 2π] under the premise of second harmonic enhancement. Figure 5 shown.

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

[0020] In order to achieve second harmonic focusing, we arranged the one-dimensional phononic crystals made of bilinear nonlinear materials longitudinally, such as Figure 6 As shown, the required second harmonic phase is determined according to the sound path difference between different longitudinal positions and the focal position. The specific calculation formula is as follows:

[0021]

[0022] Here, we set 99 one-dimensional phononic crystals to be arranged vertically, and the center distance between adjacent phononic crystals is 3mm, and the focusing point is set to (0.174m, 0m). Therefore, the total second harmonic phase profile calculated according to the above formula is as follows: Figure 7 Indicated by the grey line in (a). Figure 7 The black dots in (a) are the phases of the second harmonics that should be obtained by these one-dimensional phononic crystals that are 3 mm apart from each other. Figure 5 (b) The relationship between the second harmonic phase and k1. For one-dimensional phononic crystals at different longitudinal positions, the corresponding bilinear nonlinear parameters are selected. The results are shown in Figure 7 As shown in (b), the black dots in the figure are the values ​​of k1 that the bilinear nonlinear units in the one-dimensional phononic crystal at different longitudinal positions should obtain (for the convenience of representation, the ordinate is expressed in the form of k1 / k0). That is, in order to achieve the purpose of second harmonic focusing, for the two-dimensional phononic crystal, the k2 of the bilinear nonlinear units in the one-dimensional phononic crystal at different longitudinal positions is 0.14k0, and k1 is calculated according to Figure 7 (b) Obtaining values.

[0023] The normalized effective sound pressure field obtained according to the above method is as follows: Figure 7 (c) Figure 7 (d) Figure 7 (c) The enlarged result near the focus. Figure 7 (e) and (f) are Figure 7 In (d), the effective transmitted sound pressure distribution along the white dotted lines A and B is shown. The dotted lines indicate the maximum values ​​of the effective transmitted sound pressure distribution along the A and B directions and their corresponding specific positions. It can be seen that the focus position is consistent with the preset focus position.

[0024] In addition, on the basis of the second harmonic enhancement (i.e., k2=0.14k0, k1∈[0.162k0, 0.293k0] is still used), the propagation path of the second harmonic curve is preset to be a cubic Bezier curve (i.e., determined by four points P0, P1, P2 and P3). The specific expression 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] Solving the above equations gives us the numerical solution. A is the amplitude of the transmitted wave.

[0031] In addition, we also get the approximate dispersion curve formula of the fundamental wave. Since ω should be greater than 0 in practice, we take:

[0032]

[0033] in, And k0=2ρc 2 / L,

[0034] On this basis, the design idea of ​​the present invention is as follows Figure 2 As shown, it is assumed that 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), for the acoustic and optical branches of the fundamental wave alone, the corresponding two passbands of the second harmonic are [0, 2f1] and [2f 21 , 2f 22 ],like Figure 2 (b). Figure 2 (a) It can be seen that for the phononic crystal designed by the present invention, it is allowed to [f 21 , f 22 ] This frequency band of sound waves passes through, so if the frequency value of the second harmonic (the frequency of the second harmonic is twice the corresponding fundamental frequency) is between [f 21 , f 22 ] range is passable, such as Figure 2 As shown in the dotted box in (b), in simple terms, it is equivalent to adding a passband for the second harmonic.

[0035] The above design can achieve the following specific effects: Figure 3 As shown, when the frequency of the transmitted wave is [f 21 / 2,f 22 / 2] frequency band, the corresponding fundamental wave is in the stop band, and the corresponding second harmonic is in the pass band, such as Figure 3 As shown in the dashed box in [f 21 / 2,f 22 / 2] frequency band achieves the effect of second harmonic enhancement.

[0036] According to the above ideas, we design L = 3mm, c = 6420m / s, ρ = 2700kg / m 3 , N = 20, the parameters of the bilinear nonlinear material unit are k1 = 0.2k0, k2 = 0.14k0, and the transmission curves of the fundamental wave and the second harmonic are obtained, such as Figure 4 As shown, it can be seen from the dotted box part in the figure that when the transmitting frequency is in this frequency band, the effect of second harmonic enhancement can be achieved, that is, the amplitude of the second harmonic at the receiving end is higher than the fundamental wave.

[0037] On this basis, we fix one of the parameters of the bilinear nonlinear material unit k2 = 0.14k0 and Figure 5 (a) The amplitude of the fundamental wave and the second harmonic changes with k1 (for the convenience of representation, the horizontal axis is expressed in the form of k1 / k0); (b) The phase of the second harmonic changes with k1 (for the convenience of representation, the horizontal axis is expressed in the form of k1 / k0), where the gray shaded part represents k1∈[0.162k0, 0.293k0].

[0038] Figure 6 A two-dimensional phononic crystal composed of one-dimensional phononic crystals made of bilinear nonlinear materials arranged longitudinally.

[0039] Figure 7 Focusing of the second harmonic: (a) Longitudinal second harmonic phase profile, the black dots are the second harmonic phases corresponding to the one-dimensional phononic crystal at different longitudinal positions; (b) The value of k1 that the bilinear nonlinear unit in the one-dimensional phononic crystal at different longitudinal positions should obtain (for the convenience of representation, the vertical axis shows the value of k1 / k0); (c) The normalized effective sound pressure field at the focusing point (0.174m, 0m); (d) Figure 7 (c) The result of zooming in 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 transmitted sound pressure distribution along the white dashed line B.

[0040] Figure 8 Curve propagation of the second harmonic: (a) Longitudinal phase profile, the black dots are the second harmonic phases corresponding to the one-dimensional phononic crystals at different longitudinal positions; (b) The value of k1 that the bilinear nonlinear unit in the one-dimensional phononic crystal at different longitudinal positions should obtain (for the convenience of representation, the vertical axis shows the value of k1 / k0); (c) Second harmonic curve propagation diagram (normalized effective sound pressure field); (d) Figure 8 (c) A preset Bezier curve is added based on Figure 1. DETAILED DESCRIPTION

[0041] The basic structure of the present invention is that bilinear nonlinear materials are periodically arranged to form a one-dimensional phononic crystal, such as Figure 1 As shown in (a), the black narrow band is the bilinear nonlinear material, and the remaining blank part is the 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 the bilinear nonlinear material units is N, that is, the number of bilinear nonlinear material units is N+1.

[0042] In the present invention, we set the length of the bilinear nonlinear material unit to be much smaller than that of the isotropic material, so that the corresponding structure can be discretized to facilitate subsequent processing and calculation. The model obtained after discretization is as follows: Figure 1 (b) is shown. The gray ball is the equivalent mass, the broken line is the linear spring equivalent to the isotropic material unit, and the broken line with an arrow is the nonlinear spring equivalent to the bilinear nonlinear material unit. Its characteristics are: the stiffness coefficient of the nonlinear spring equivalent to the bilinear nonlinear material unit per unit cross-sectional area is not a fixed value, which is specifically manifested as:

[0043]

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

[0045] Based on this theoretical deduction, the following four equations are obtained:

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

[0047] Based on the principle of making the emitted sound line tangent to the preset curved propagation path to achieve curved propagation, combined with Legendre transformation, the longitudinal second harmonic phase profile is calculated. The results are as follows: Figure 8 The gray line in (a) shows that the black dots are the phases of the second harmonic that should be obtained by a one-dimensional phononic crystal with a spacing of 2 mm. Figure 5 (b) The relationship between the second harmonic phase and k1. For one-dimensional phononic crystals at different longitudinal positions, the corresponding bilinear nonlinear parameters are selected. The results are shown in Figure 8As shown in (b), the black dots in the figure are the values ​​of k1 that the bilinear nonlinear units in the one-dimensional phononic crystal at different longitudinal positions should obtain (for the convenience of representation, the ordinate is expressed in the form of k1 / k0). That is, in order to achieve the purpose of propagation of the second harmonic along the curve, for the two-dimensional phononic crystal, the k2 of the bilinear nonlinear units in the one-dimensional phononic crystal at different longitudinal positions is 0.14k0, and k1 is according to Figure 8 (b) Obtaining values.

[0048] The normalized effective sound pressure field obtained according to the above method is as follows: Figure 8 As shown in (c), we can see that there is an obvious curve propagation path. In order to verify whether this path is the cubic Bezier curve path we preset, we Figure 8 Based on (c), a preset cubic Bezier curve is drawn with a black dotted line, namely Figure 8 (d) from Figure 8 As can be seen in (d), the black dashed line agrees well with the actual curve propagation path in the normalized effective sound pressure field.

Claims

1. A method for controlling ultrasonic second harmonic propagation based on bilinear nonlinear phononic crystal materials, characterized in that: The bilinear nonlinear material is periodically arranged to form a one-dimensional nonlinear phononic crystal. In order to manipulate the second harmonic in practice, the one-dimensional longitudinal bilinear nonlinear phononic crystals are arranged laterally in sequence to form a two-dimensional phononic crystal. The specific structure is: the one-dimensional longitudinal bilinear nonlinear phononic crystal is a bilinear nonlinear material phononic crystal with isotropic materials between the bilinear nonlinear material units, 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, the total number of isotropic materials between the bilinear nonlinear material units is N, that is, the number of bilinear nonlinear material units is N+1; the length of the bilinear nonlinear material phononic crystal unit is much smaller than the length of the isotropic material unit (the sum of the lengths of the bilinear nonlinear material unit: the ratio of the length of the isotropic material unit is 0.5%-10%); The parameters of the bilinear nonlinear material are changed within a certain range. On the basis of second harmonic enhancement, the relationship between the second harmonic phase and the parameters of the bilinear nonlinear material is obtained.

2. The method for controlling ultrasonic second harmonic propagation based on bilinear nonlinear phononic crystal materials according to claim 1 is characterized in that: In order to achieve the purpose of second harmonic focusing, according to the second harmonic phase requirements of the one-dimensional nonlinear phononic crystal at different longitudinal positions, under the guidance of the parameter relationship diagram of 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 requirement of the one-dimensional nonlinear phononic crystal at different longitudinal positions to achieve the second harmonic curve propagation is calculated, and according to the relationship diagram 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 ultrasonic second harmonic propagation based on bilinear nonlinear phononic crystal materials according to claim 1 is characterized in that: The specific parameters are adjusted accordingly according to actual needs, that is, the parameter range is not limited to the parameter values ​​clearly described in the present 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 curved propagation.

4. The method for controlling ultrasonic second harmonic propagation based on bilinear nonlinear phononic crystal materials according to claim 1 is characterized in that: The model obtained after discretization is: According to the approximate dispersion curve formula of the fundamental wave, ω is greater than 0, and in practical applications, it is taken as: in, And k0=2ρc 2 / L, If the maximum frequency of the fundamental acoustic branch is f1, the minimum frequency of the optical branch is f 21 , the maximum value is f 22 , then for the acoustic and optical branches of the fundamental wave alone, the corresponding two passbands of the second harmonic are [0, 2f1] and [2f 21 , 2f 22 ], for the designed phononic crystal, it is allowed that [f 21 , f 22 ] This frequency band of sound waves passes through, so if the frequency value of the second harmonic (the frequency of the second harmonic is twice the corresponding fundamental frequency) is between [f 21 , f 22 ] range, it can pass, which is equivalent to adding a passband for the second harmonic; When the frequency of the transmitted wave is [f 21 / 2,f 22 / 2] frequency band, the corresponding fundamental wave is in the stop band, and the corresponding second harmonic is in the pass band. 21 / 2,f 22 / 2] frequency band achieves the effect of second harmonic enhancement.

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

6. The method for controlling ultrasonic second harmonic propagation based on bilinear nonlinear phononic crystal materials according to claim 1 is 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.

7. The method for controlling ultrasonic second harmonic propagation based on bilinear nonlinear phononic crystal materials according to claim 1 is characterized in that: The method used is extended to acoustic diodes.

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