Guided mode resonance (GMR) gratings are used as filters due to the narrow bandwidth and high efficiency at the resonance wavelength. In this paper, a two-dimensional gradient-period GMR grating with rectangular array structure is proposed. Ta<sub>2</sub>O<sub>5</sub>, HfO<sub>2</sub> and SiO<sub>2</sub> are selected as grating materials. Double reflection peaks are obtained by matching the guide modes in two orthogonal planes of diffraction to different wavelengths. The rigorous coupled wave analysis (RCWA) are used to analyze the resonance characteristics of two-dimensional GMR grating. By comparing the resonance behavior, the resonance wavelengths of two-dimensional GMR grating can be approximated as the superposition of two one-dimensional GMR gratings, the periods of the two one-dimensional gratings are respectively equal to those of the two-dimensional GMR grating along x and y direction (Λ<sub>x</sub> and Λ<sub>y</sub>). Thus, we can control the two resonance wavelengths by changing the periods of Λ<sub>x</sub>, Λ<sub>y</sub>. According to the result of design, when the two resonance peaks are both in the spectrum range of 850nm-1050nm, the efficiencies of the two peaks are greater than 90%, and full width at half-maximum (FWHM) less than 1.5nm. This two-wavelength tunable filter will be a good two-dimensional displacement sensor. The effects of duty cycle, groove depth and other parameters on the resonance wavelength are also studied.
Crossed-grating is widely used as the standard element for metrology in two-dimensional precision positioning system. It has many advantages such as high resolution, compact structure, good environmental adaptability and less Abbe error. In this paper, the design of crossed planar reflecting phase grating used under the Littrow condition with circularly polarized light at 780nm wavelength has been carried out. The aim of the design is to find out the range of structure parameters of crossed-grating that has higher -1st order diffraction efficiency and good efficiency equilibrium for both of TE- and TM-polarized incident lights. By adoption of the Fourier modal method (FMM), the microstructure parameters of the 1200lines/mm crossed grating with the duty cycle range of 10% to 50% and the profile depth of 150nm to 350nm have been searched exactly. The calculation results show that: When the duty cycle range of the grating is 42% to 44% and profile depth is 210nm to 220nm, the -1<sup>st</sup> diffraction efficiencies of TE- and TM-polarized lights are both above 60% and the efficiency equilibrium is better than 80%.
The high diffraction efficiency and high dispersion ability of diffraction grating plays a very important role in laser systems. Fused-silica transmission gratings not only have board band, high diffraction efficiency and high damage threshold, but also have the advantage of light path without shelter comparing to reflective gratings. In this paper, the study of polarization-independent transmission fused-silica grating is carried out, and the influence of rectangular and trapezoidal grating microstructures on the -1st diffraction efficiency of grating is analyzed. For trapezoidal groove structure, in the range of 80 to 90 degrees, the distributions of diffraction efficiency at different bottom angle are calculated and analyzed. The structure parameters of the grating are optimized by rigorous coupled wave theory. The designed grating groove density is 1440 lines/mm. The -1st diffraction efficiency of the grating is over 96% for both of TE and TM polarized waves at the Littrow angle (49.7 degrees) with the center wavelength of 1060nm. Within the bandwidth of 42nm (from 1039 to 1081nm), the -1st diffraction efficiency of the designed grating is theoretically greater than 90% for both of TE and TM polarized waves.