The simplified mode method explains the physical processes inside the grating in terms of the Mach- Zehnder interferometer model. There are three modes include mode 0, 1, 2 in grating under second Bragg angle incidence. We report a special case of fused silica grating when its period is close to 1.3 times of wavelength, where the effective refractive index of mode 1 might be equal to mode 2. In this special case, we found that the joint effect of mode 1 and 2 on the diffraction efficiency for -2 order is not accurate entirely, and the diffraction of the 0th order is approaching to the maximum, both with a slight oscillation of efficiency when the depth of grating is increased. This phenomenon by using simplified mode method could help to understand the physics of grating theory.
This paper proposed a transmission two-dimensional (2D) slanted grating based on a double-layer cylindrical structure. We used rigorous coupled-wave analysis (RCWA) and simulated annealing algorithm (SA) to optimize the grating parameters. Results show that the diffraction efficiency of the (-1,0) and (0,-1) order exceed 35% under normal incidence in the range of 429–468 nm wavelength for TE and TM polarization. Meanwhile, the total diffraction efficiency can reach up to 78%. We also discuss the tolerances for the grating parameters to ensure high quality manufacturing processes. The relatively large tolerances ensure fabrication of the two-dimensional slanted grating and provides the possibility for practical applications. The proposed 2D slanted grating can be applied to 2D exit pupil expansion, which is of great importance in AR/VR applications.
In the displacement measurement of the wafer stage of the lithography machine, the two-dimensional grating measurement system has attracted much attention because of its short optical path and less impact from the environmental disturbances. Meanwhile, the high-efficiency polarization-independent two-dimensional grating can not only reduce the Abbe error but also improve the signal accuracy. In this paper, we propose a reflective two-dimensional metal-dielectric grating with excellent polarization-independent and high diffraction efficiency. Calculated by rigorous coupled wave analysis (RCWA) , when the incident azimuth angle is 45°, the (-1, -1) order diffraction efficiencies of transverse electric polarization (TE) and transverse magnetic polarization (TM) are 95.6% and 94.9% at 632 nm incident wavelength under Littrow mounting, respectively. The diffraction efficiency equilibrium is 98.9%. The high efficiency of TE and TM polarization makes them have great application potential in 2D grating measurement system (GMS). Furthermore, the structure based on the frustum of a cone performs well in manufacturing tolerance, which provides possibility for practical applications.
In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. When the measurement orientation is tangential to the center of the chuck, the influence of the homogeneous expansion of the chuck on the measurement can be reduced. In this research, we propose a reflective two-dimensional metal dielectric grating based on frustum array. With an incident azimuth angle of 45°, the (-1, -1) order diffraction efficiencies of transverse electric polarization (TE) and transverse magnetic polarization (TM) are 81.4% and 84.8% at 1550 nm incident wavelength under Littrow mounting, respectively. the diffraction efficiency balance is 95.99%. The high efficiency of TE and TM polarization makes them have great application potential in grating displacement measurement. Furthermore, the structure based on the frustum of a cone performs well in manufacturing tolerance, which provides possibility for practical applications.
This paper introduces a new device for one-dimensional grating period measurement with high accuracy. The scheme includes two subsystems: a grating interferometer and a laser interferometer. As the grating moves, the grating interferometer obtains periodic signal related to the grating period, while the laser interferometer measures the displacement simultaneously. The grating period is then obtained through data processing and least-square-fitting. Most of the grating period measurement devices have scattered structures, poor stability, which could be affected by the environment easily. In order to overcome this shortcoming, we adopt the structure of glued prisms, which is compact, and will significantly improve the stability of the system. Thus, the scheme has advantages in measurement accuracy as well as resolution. The system benefits from simple structure and cheap components, which can be widely used in grating period measurement technology.
In view of the fact that the current research of detection technology for large-size grating surface defect was very little, this paper builds a set of grating defect detection device based on the principle of darkfield imaging. The scheme includes three subsystems: displacement system, monochrome light illumination system and image acquisition system. When the displacement system drives the motion stage to move, the monochromatic light illumination system and the image acquisition system jointly complete the acquisition of the grating surface images. In this study, the surface of the diffraction grating with 170×170mm2 was detected for defects, and the statistical data of different defects is given. Experimental results show that, the device meets the needs of defect detection and evaluation on large-size grating surfaces and the mechanical structure is simple and compact, which has the great potential for large-scale detection.
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