Research On The Application Of Space Transform In The Design Of New Functional Devices

Metamaterials consist of artificial units arranged in a regular manner with sizes much smaller than wavelength,covering a wide range of fields such as electromagnetics and acoustics.By designing the size and shape of the metamaterial unit,the field distribution in space can be adjusted accordingly.The theoretical basis of transformation optics and transformation acoustics is the invariance of the form of Maxwell equation and wave equation under coordinate transformation.The process of constructing new electromagnetic and acoustic devices is simplified by coordinate transformation at the cost of increasing the complexity of material parameters.With the development of metamaterials,devices designed with theory of coordinate transformation can be verified by experiments.The main contents of the thesis are as follows:1.Based on the covariance of Helmholtz equation and Snell’s law,a near-zero refractive index lens is designed.The transformation function of the lens is logarithmic mapping,and the lens is square.The point source placed at the center of the lens can produce four beams after passing through the lens.The original two-dimensional lens is extended to three-dimensional space.2.Acoustic lens is designed by using conformal power function as transformation function.The single point source placed at the center of the lens can present the interference sound field as double point source.A single point source has the same so und pressure field as two point sources.By the general refractive index formula of conformal power function transformation and approximating it in large quantities,it is concluded that the single point source and the ring have the same field distribution.Then,the zero point in the refractive index is removed by the principle of coordinate transformation.The shape and refractive index formula of the lens are rotated simultaneously,so that the original lens can be extended to three-dimensional space.3.In conformal transformation,if the device is designed according to the shape of the contour line,the wave generated from the device’s boundary excitation source will propagate along the trajectory of the contour line.Based on this principle,the electromagnetic multifunctional lens and a quarter circular waveguide are designed.If the contour line and shape of the intercepting device do not coincide,the designed device should be explained by the principle of ray geometry,and the wave will be bent in the direction of high refractive index.Based on this principle,we designed deflection and focusing lens,and verified the performance of the lenses through experiments.