Homogeneous and isotropic bends to tunnel waves through multiple different/equal waveguides along arbitrary directions

We propose a novel optical transformation to design homogeneous isotropic bends connecting multiple waveguides of different cross sections which can ideally tunnel the wave along any directions through multiple waveguides. First, the general expressions of homogeneous and anisotropic parameters in the bend region are derived. Second, the anisotropic material can be replaced by only two kinds of isotropic materials and they can be easily arranged in planarly stratified configuration. Finally, an arbitrary bender with homogeneous and isotropic materials is constructed, which can bend electromagnetic wave to any desired directions. To achieve the utmost aim, an advanced method is proposed to design nonmagnetic, isotropic and homogeneous bends that can bend waves along arbitrary directions. More importantly, all of the proposed bender has compact shape due to all flat boundaries, while the wave can still be perfectly tunneled without mode distortion. Numerical results validate these functionalities, which make the bend much easier in fabrication and application.