Abstract:
Objective Diffraction gratings are widely used in ultra-high precision displacement measurement systems, instrument calibration and other fields. The self-traceable grating prepared by atomic lithography is different from ordinary diffraction gratings in that its characteristic parameters can be directly traced to "meters" through natural constants, so the grating has the natural advantage of being used as a ruler without measuring a fixed value. Diffraction efficiency is an important indicator to measure the performance of gratings, and the diffraction efficiency of self-traceable gratings will affect the accuracy and precision of measurement results. Therefore, by analyzing the diffraction efficiency of self-traceable gratings, an important basis is provided for the preparation and application of self-traceable gratings.
Methods Based on the vector diffraction theory and rigorous coupled-wave method, a theoretical model of self-traceable grating with a sinusoidal structure and its diffraction efficiency under different incident conditions are established (Fig.2). The influence of structural parameters and laser incident conditions on the diffraction efficiency of self-traceable gratings are analyzed using the method of controlling variables. The results of model calculation are compared with the Gsolver simulation results to verify the feasibility of model calculation. A measurement system for grating diffraction efficiency is constructed (Fig.10). Combined with the grating equation, the diffraction efficiency corresponding to different Littrow angles is calculated (Tab.1).
Results and Discussions The simulation results show that the diffraction efficiency of the self-traceable grating −1-order is at its peak state, reaching 4.3%, when the incident wave is TM polarized, the incident wavelength is 420 nm, and the incident angle is 80° (Fig.6). In the Littrow structure, the diffraction efficiency of the self-traceable grating −1-order is at its maximum, and is close to the peak diffraction efficiency of the self-traceable grating corresponding to non-Littrow angles, when the incident wave is TM polarized, the incident wavelength is 415.51 nm, and the Littrow angle is 77.5° (Tab.1). The experimental results show that the variation trend of diffraction efficiency is consistent with the theoretical calculation results (Tab.2, Fig.4).
Conclusions The diffraction efficiency of the self-traceable grating is analyzed by establishing a strict coupled wave model of the self-traceable grating and solving the accurate solution of Maxwell's equation system that satisfies the boundary conditions of the electromagnetic field in each region after the laser incident self-traceable grating structure. Through the measurement and research of the diffraction efficiency of self-traceable gratings, this paper provides an important basis for the preparation and application of self-traceable gratings. In the practical application of self-tracing gratings, it is necessary to combine the influence of various parameters on the diffraction efficiency and select the best incident conditions to maximize the diffraction efficiency. For the diffraction efficiency analysis of self-traceable gratings, the factors affecting the structural parameters of self-traceable gratings during the preparation process will be studied from the preparation principle of self-traceable gratings, and combined with the grating diffraction efficiency analysis in this paper, so as to prepare a self-traceable grating that maximizes diffraction efficiency.
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