I. Introduction
For the applications of terahertz (THz) waves, compact and easy-to-use emitter with sufficient output power is strongly required. Quantum cascade lasers (QCLs) including a type based on difference-frequency-generation (DFG)[1] and THz parametric oscillators (TPOs)[2] or generators (TPGs)[3] are the good candidates. In these devices, the extraction of THz waves not via the side facets but via the top or bottom surface would be beneficial to avoid the reabsorption of the THz waves inside the device. For such purpose, grating or prism is necessary [4]. Here we consider the gratings which can be fabricated by a standard lithographic method.