We realize the directional ultrasound emission by designing the metasurface consisting of six identical cascaded elements. The schematic of an individual element is shown in Figure 1A, which is the combination of a rectangular cavity located in the center of the element and two symmetric inclined channels on both sides of the rectangular cavity. The structure is made of stainless steel, whose mass density, sound speed, Young’s modules, and Poisson’s ratio are ρ s = 7800   kg / m 3 , c s =   6100   m / s , E =   215   GPa , and σ = 0.3 , respectively, and the background medium is water ( ρ w = 1000   kg / m 3 , c w =   1500   m / s ). The acoustic impedance of stainless steel is approximately 31 times higher than that of water. The lengths (heights) of the element and cavity are t (h) and t ₁ (h ₁), respectively, and the height and inclined angle of the two channels are h ₂ and θ. All these parameters contribute to the phase control of the transmitted wave. By analyzing the ultrasound response dependence on these parameters, we choose the parameter t ₁ as a knob to manipulate the phase delay since the phase of the transmitted ultrasound is found to be relatively sensitive to t ₁. As a result, this single-parameter-based control makes it much easier in designing the ultrasound metasurface. The metasurface is designed for the underwater ultrasound at 300 kHz, with the wavelength λ = 5   mm and other parameters fixed to be t = 1.4   mm , h = 1.25   mm , h 1 = 1.1   mm , h 2 = 0.1   mm , and θ = 45 ° . The transmission performance of the metasurface is simulated by employing the acoustic–structure interface, frequency domain with the finite element method based on COMSOL Multiphysics software. Figure 1B shows the phase delay (red solid line) and the transmittance (blue solid line) of an element as functions of parameter m ( m = t 1 / t ), where t ₁ is varied in the range from 0.7   mm to 1.3   mm . It can be observed that the phase delay covers a 0.4 π range in this parameter region where the transmittance remains higher than 82%, which guarantees the high efficiency in the following nondestructive evaluation applications.

For achieving the full-2π-phase control, we connect six identical elements in series in the x-direction to construct a single unit, with the periodicity of the elements being a = 2.3   mm . The schematic of a unit which is constructed by six elements is illustrated in Figure 1C. The ultrasound incident from the left accumulates the phase delay after passing through the structure, while keeping the transmittance higher than 80%, as shown in Figure 1D.

The units consisting of six cascaded elements are arranged in the y-direction according to the generalized Snell’s law to design the ultrasound metasurface for directional emission. Considering the ultrasound wave normally incident from the x-direction, the transmitted ultrasound with the refraction angle θ t ( y ) can be realized by the metasurface with the phase distribution: θ t ( y ) = arcsin ( 1 k d φ ( y ) d y ) (1) where φ ( y ) represents the phase distribution on the metasurface, k = 2 π f / c is the wave vector in water, and f = 300   kHz is the frequency of the incident ultrasound. The continuous distribution of the phase profile is discretized to facilitate the implementation with the metasurface, and the discretization resolution is determined by the unit height ( h = 1.25   mm ) on the metasurface. Two sets of directional ultrasound emission with the refraction angles of 30° and 45° are realized by constructing two different planar metasurfaces, both of which has 80 units.

We numerically simulate the directional ultrasound emission based on COMSOL Multiphysics software. The distributions of the directional ultrasound fields with the refraction angles of 30° and 45° are illustrated in Figures 2A,B. The normally incident plane wave propagates along the x-direction and impinges on the metasurface, whose phase distribution is tuned by the metasurface. As a result, the transmitted ultrasound wave is endowed with the additional transverse momentum along the y-direction and passes through the metasurface with the targeted refraction angle. In Figures 2A,B, it can be observed that the incident ultrasound wave is deflected by 30° and 45° after passing through the metasurfaces, respectively, agreeing well with the targeted directions. In addition, the amplitude of the transmitted wave remains relatively high compared with the incident wave, which proves the high transmission of the metasurface and contributes to its application in nondestructive evaluation.

We first demonstrate the thickness evaluation of a plexiglass block underwater with the directional ultrasound emission of the refraction angle θ t = 45 ° . The density and sound speed of plexiglass block are ρ s = 1180   kg / m 3 and c s =   2730   m / s , respectively. A planar metasurface consisting of 100 elements are constructed according to the phase profile, with the total height of H = 125   mm .

Owing to the planar configuration, the designed metasurface can be directly attached to the surface of the detected workpiece which helps to reduce the mismatch caused by the wedge in conventional methods and improve the efficiency of the evaluation. A plane ultrasound at 300 kHz is normally incident from the left and transmits through the metasurface. As shown in the ultrasound intensity field in Figure 3A, ultrasound wave can almost completely penetrate the plexiglass block (indicated by the red solid box), and the transmitted beam is deflected to the direction of 45° by the metasurface (an enlarged view of it is shown in the green dashed box). The ultrasound beam transmitted from the metasurface is directionally emitted to the plexiglass block from the left surface and then further reflected by the right surface of the plexiglass block and detected on the left surface. The position of maximum ultrasound intensity on the left surface of the plexiglass block reveals the geometrical relationship between the emitted and reflected ultrasound trajectories and can be used to evaluate the thickness of the target.

The trajectories of the directional ultrasound beam emitted from the metasurface and reflected from the right surface of the plexiglass block are illustrated in Figure 3B. The distance from the bottom of the metasurface on the left surface of the plexiglass block is denoted as l ₁. According to the geometric relationship (Figure 3B), the thickness of the block can be calculated by: d 1 = ( H / 2 + l 1 _ max ) cos ( θ t ) sin ( θ t ) (2)

where l _{1_max} is the position of the maximum ultrasound intensity.

An ultrasound intensity profile as a function of l ₁ is plotted in Figure 3C, which shows that the intensity reaches the maximum value at position l 1 _ max =   343   mm . The evaluated thickness of the block is then calculated to be d 1 = 202.75  mm by Eq. 2, which has a good agreement with the actual value d a 1 = 200  mm , with the relative error ε 1 = ( d 1 − d a 1 ) / d a 1 = 1.375 % smaller than 2%.

To compare the thickness evaluation performance based on ultrasound metasurface for the workpiece with different thicknesses, we conduct the evaluation of the plexiglass blocks with the thickness d _a1 ranging from 100 to 250 mm. The evaluation accuracy as a function of the thickness d _a1 is plotted in Figure 3D, where it is consistently higher than 98% over this thickness range. The consistency between the evaluated and actual thicknesses strongly proves the high accuracy and effectiveness of the implementation of the directional ultrasound emission based on metasurface in thickness evaluation, which provides broad interests on the applications in industrial engineering.

We further consider the defect detection inside the object with the metasurface-based directional emission. As an example, we demonstrate the testing of the defect inside a V-shaped workpiece, which is widely used in industry while quite challenging to detect for a conventional wedge-based method due to the special shape. Figure 4A shows the schematic of a V-shaped workpiece made of plexiglass with a strip of air defect inside it. We use the constructed metasurface which can emit the directional ultrasound beam to detect the strip defects inside the workpiece. Figure 4B shows the two-dimensional cross section of defect detection inside the V-shaped workpiece. The metasurface (indicated by the green dashed box) and the V-shaped workpiece (indicated by the red solid box) are immersed in water, and the planar metasurface is closely adherent to the surface of the workpiece. A plane ultrasound wave impinges on the upper surface of the metasurface and is transmitted through the metasurface with the refraction angle of 45°. The transmitted ultrasound beam is then emitted into the V-shaped workpiece and interacts with the defect inside, which leads to the reflection by the defect due to the acoustic impedance mismatch between the plexiglass and air stripe, and the reflected signal is detected on the top-right surface of the workpiece. Similarly, the position of the defect can be found by analyzing the trajectories of the emitted and reflected beams, and the geometric relationship of the V-shaped workpiece and the strip defect (Figure 4C).

Specifically, the position of the maximum ultrasound intensity on the top-right surface l _{2_max} indicates the position of the defect inside the workpiece. The V-shaped workpiece tested here has the included angle of α = 140 ° , and the distance between the workpiece concave corner and center of the metasurface is r = 73.14   mm . The distance from the concave corner of the V-shaped workpiece along the top-right surface is denoted as l ₂. The ultrasound intensity profile along the top-right surface as a function of l ₂ is plotted in Figure 4D, where the maximum ultrasound intensity is obtained at the position l 2 _ max =   75   mm . Therefore, the height of the strip defect from the concave corner of the V-shaped workpiece can be calculated as d 2 = [ r ⁡ sin 45 ° sin ( α − 45 ° ) + l 2 _ max ] sin ( 225 ° − α ) sin ( α − 90 ° ) sin 270 ° − α 2 − l 2 _ max ⁡ sin 180 ° − α 2 (3) which is calculated to be d 2 =   123 . 93   mm by substituting the l _{2_max} value. The actual position of strip defects is d a 2 =   120   mm , and the relative error of the detection is ε 2 = ( d 2 − d a 2 ) / d a 2 =   3.3 % , which remains smaller than 4%. These results reveal that the directional ultrasound emission based on the metasurface can be expediently employed to the special defect detection with high precision. The defect with the sub-wavelength size could also be detected by integrating the directional emission with other technologies, such as the ultrasound focusing, beam forming, and artificial intelligent algorithm.