Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the functional devices. Since inverse Laplace's equation with sliding boundary condition will determine a quasi-conformal mapping, and a quasi-conformal mapping will minimize the transformation material anisotropy, so in this work, the inverse Laplace's equation with sliding boundary condition is proposed for quasi-isotropic transformation material design. Examples of quasi-isotropic arbitrary carpet cloak and waveguide with arbitrary cross sections are provided to validate the proposed method. The proposed method is very simple compared with other quasi-conformal methods based on grid generation tools.

By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are symmetric, and can be used with Navier's equation to manipulate elastic waves. It is shown numerically that the method can provide a powerful tool to control elastic waves in solids in case of high frequency or small material gradient. Potential applications can be anticipated in nondestructive testing, structure impact protection, petroleum exploration and seismology.

There are great demands to design functional devices with isotropic materials, however the transformation method usually leads to anisotropic material parameters difficult to be realized in practice. In this letter, we derive the isotropic transformed material parameters in case of elastodynamic under local conformal transformation, they are subsequently used to design a beam bender, a four-beam antenna and an approximate carpet cloak for elastic wave with isotropic materials, the simulation results validate the derived transformed material parameters. The obtained materials are isotropic and greatly simplify subsequent experimental implementation. a Corresponding authors,

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A general conformal mapping is proposed to design omnidirectional broadband wave absorbers by transformation method. When applied to electromagnetic (EM) and acoustic waves, the existing material parameters of the EM and acoustic omnidirectional absorbers, which are previously obtained by Hamiltonian optics and geometry acoustics, can be recovered. In addition, magnetic and mass-density-controlled omnidirectional absorbers for EM and acoustic waves can also be designed, respectively. We then apply the conformal mapping to design an omnidirectional elastic wave absorber, the corresponding material realization of such elastic absorber is also proposed and validated by numerical simulation.