Most commonly used are binary gratings, also known as Dammann gratings [4], i.e. gratings that impose phase shifts varying between two discrete values. Multilevel stepped phase gratings offer more flexibility and, therefore, are used quite often [5] [6], although they are more difficult to manufacture. Gratings with a sinusoidal phase variation have also gained some importance in the optical part of the spectrum.
While elaborate structures for optical gratings can be manufactured with today's photolithography techniques, the structures used so far in the submillimeter spectral region are less complex. The standard manufacturing technique here is direct milling of the gratings. In the case of stepped phase gratings this introduces a serious constraint: due to the relatively large diameter of the endmill it is difficult to produce good structures for two-dimensional dispersion. For instance, a two-dimensional rectangular Dammann-grating resembles a chess board with the white fields elevated with respect to the black fields. Direct milling of this structure with sharp corners is impossible with a finite size endmill. Therefore, two-dimensional gratings are usually manufactured as transmission gratings, where the two surfaces act as one-dimensional gratings in orthogonal directions. Transmission gratings, however, suffer from reflection and absorption losses and -- since they are usually made of plastic materials -- from lower machining accuracy than metallic reflection gratings.
We introduce the Fourier grating, which overcomes these limitations by replacing the discrete phase modulation of binary or multi-level phase gratings by a continuous phase modulation. The grating structure of these gratings can be optimized to produce a very high diffraction efficiency and the structure can be manufactured easily with very high accuracy. We have produced a variety of two-dimensional, reflective beam splitters for a 500 GHz beam to illustrate the feasibility of the concept.