Acoustic Luneburg meta lens and design method thereof
Provided are an acoustic Luneburg meta lens including a lens structure on the substrate or a lens structure connected to each other by connecting rods, wherein the lens structure includes a plurality of unit structures, the volume of the unit structures decreases from the center of the lens structure toward an edge thereof, and positions of the unit structures are determined by direction components of a polar coordinate system or a spherical coordinate system, and a method for designing the acoustic Luneburg meta lens.
1. An acoustic Luneburg meta lens comprising:
a lens structure;
a substrate under the lens structure; and
a reflection plate on the substrate, wherein:
the lens structure includes a plurality of unit structures;
a volume of the unit structures decreases from a center of the lens structure toward an edge thereof;
positions of the unit structures are determined by a radial direction component and a tangential direction component of a polar coordinate system;
the lens structure has a semi-circular shape; and
one surface of the lens structure is in contact with the reflection plate.
2. The acoustic Luneburg meta lens of claim 1 , further comprising connecting rods connecting the unit structures to each other.
3. The acoustic Luneburg meta lens of claim 1 , wherein a refractive index of the lens structure varies according to a following [Equation 1]:
n =√{square root over (2−( r/R ) 2 )} [Equation 1]
wherein, n represents a refractive index, r represents a distance from the center of the lens structure, and R represents a radius of the lens structure.
4. The acoustic Luneburg meta lens of claim 1 , wherein an upper surface of each of the unit structures has a circular or polygonal shape.
5. The acoustic Luneburg meta lens of claim 4 , wherein areas of the upper surfaces of the unit structures decrease as a distance from the center of the lens structure increases.
6. The acoustic Luneburg meta lens of claim 1 , wherein an upper surface of each of the unit structures has a sector shape with a truncated central portion.
7. The acoustic Luneburg meta lens of claim 1 , wherein a diameter of the lens structure in a first direction is less than a diameter thereof in a second direction orthogonal to the first direction.
8. The acoustic Luneburg meta lens of claim 7 , wherein the diameter of the lens structure in the first direction is 1/n times, n is a natural number, the diameter thereof in the second direction.
9. The acoustic Luneburg meta lens of claim 7 , wherein the unit structures comprise a material having a greater impedance than a background material.
10. The acoustic Luneburg meta lens of claim 1 , wherein:
an upper limit of an operation frequency domain is inversely proportional to a pitch at which the unit structures are arranged in a radial direction; and
a lower limit of the operation frequency domain is inversely proportional to a diameter of the lens structure.
11. The acoustic Luneburg meta lens of claim 1 , wherein a thickness of the lens structure is smaller than a wavelength of an operation wave.
12. A method for designing an acoustic Luneburg meta lens, the method comprising:
designing unit cells; and
respectively disposing a unit structure in each of the unit cells, wherein:
a volume of the unit structures decreases from a center toward an edge; and
positions of the unit cells and the unit structures are determined by direction components of a polar coordinate system or a spherical coordinate system;
wherein the designing of unit cells comprises:
designing a plurality of unit cell rows; and
dividing each of the unit cell rows into unit cells of a same volume,
wherein each of the unit cell rows has a concentric ring shape, and
an upper surface of each of the unit cells has a sector shape with a truncated central portion; and
wherein:
radii of the unit cell rows increase at regular intervals as a distance from the center increases; and
a radius of each of the unit structures is less than or equal to the interval of the unit cell rows.
13. The method of claim 12 , wherein:
an upper surface of each of the unit structures has a shape in which an upper surface of each of the unit cells is reduced to a predetermined ratio; and
the upper surface of each of the unit structures is similar to the upper surface of each of the unit cells.
14. The method of claim 12 , wherein an upper surface of each of the unit structures has a shape of a circle, ellipse, polygon, or cross.