  In transformation optics, the space transformation is viewed as the
deformation of a material. The permittivity and permeability tensors in the
transformed space are found to correlate with the deformation field of the
material. By solving the Laplace's equation, which describes how the material
will deform during a transformation, we can design electromagnetic cloaks with
arbitrary shapes if the boundary conditions of the cloak are considered. As
examples, the material parameters of the spherical and elliptical cylindrical
cloaks are derived based on the analytical solutions of the Laplace's equation.
For cloaks with irregular shapes, the material parameters of the transformation
medium are determined numerically by solving the Laplace's equation. Full-wave
simulations based on the Maxwell's equations validate the designed cloaks. The
proposed method can be easily extended to design other transformation materials
for electromagnetic and acoustic wave phenomena.
