High-directivity and high-power emission of a line source through conducting gratings backed with a slab of left-handed material

We propose a theoretical foundation for the high-directivity and high-power emission of a line source through small holes on a perfectly conducting screen backed with a slab of left-handed material (LHM). When a line source is placed in the left region of a conducting screen, electromagnetic or optical waves will be transmitted to the right region through small holes on the screen. If the screen and line source are surrounded by air, the transmitted beam is broad and the transmitted power is small. If the screen is backed with the LHM slab appropriately, however, a very narrow beam with much higher power can be transmitted through the grating to the far-field zone. The reason to cause such a magic phenomenon is due to the proper usage of surface waves on the boundaries of the LHM slab. Exact analysis is given to set up the theoretical foundation of such a problem based on the equivalence principle, and numerical results are provided by solving an integral equation using the method of moments.