Inverse symmetric Dammann grating is a special grating, whose transition points are reflection symmetric about the midpoint with inverse phase offset in one period. It can produce even-numbered or oddnumbered array illumination when the phase modulations are p or a specific value. Numerical solutions optimized by the steepest-descent algorithm for binary phase and multilevel phases with splitting ratio from 1 × 4 to 1 × 14 are given. Fabrication of 1 × 6 array without the zero-order intensity and 1 × 7 array with the zero-order intensity are made from the same amplitude mask. A 6 × 6 output without the crossed zero-orders was achieved by crossing two one-dimensional 1 × 6 inverse symmetric Dammann gratings. This grating may have potential value for practical applications.

A deep binary silicon grating as high-extinction-ratio reflective polarizing beam splitter (PBS) at the wavelength of 1550 nm is presented. The design is based on the phenomenon of total internal reflection (TIR) by using the rigorous coupled wave analysis (RCWA). The extinction ratio of the rectangular PBS grating can reach 2.5\times10^5 with the optimum grating period of 397 nm and groove depth of 1.092 \mum. The efficiencies of TM-polarized wave in the 0th order and TE-polarized wave in the -1st order can both reach unity at the Littrow angle. Holographic recording technology and inductively coupled plasma (ICP) etching could be used to fabricate the silicon PBS grating.