Understanding and optimizing diffraction gratings by the blazing analysis of total internal reflection

The diffraction grating is a classic and important optical element, and its design usually traverses the whole parameter space to search for an optimal solution, which is time consuming and inefficient. In order to specify the optimization direction of the grating to obtain clearer physical images and to improve the design efficiency, a new blazing model based on the total internal reflection (TIR) is proposed to analyze the diffraction behavior of the grating from a geometry perspective. The optical tunnel along the ridge direction can be used to understand and quantify the blaze of the grating. This TIR blazing model is demonstrated via three types of surface-relief grating with simple formulas, resulting in the solution space decreasing significantly. By utilization of the estimated upper limit of the diffraction efficiency and the range of the depth and slanted angle generated by the TIR blazing model, how the grating delivers the majority of the light energy to a required diffraction order is revealed. Binary and slanted gratings with >0.93 efficiency of T₁ order have been obtained with high probability within the calculated parameter range, regardless of the duty cycle and polarization. The reason why a transmission sawtooth grating cannot blaze the most energy to a high order at normal incidence has been clarified, and the method of using the first or second TIR blaze has also been provided. Through this TIR blazing model, the grating design could be simplified, and accommodation to various application requirements could be optimized as well.