The numerical analysis of low diffraction efficiency phenomenon at the blaze wavelength for echelle gratings

In this paper, we explain and unify the low diffraction efficiency behavior of echelle gratings at blaze wavelengths under Littrow mount in terms of the metal refractive index (RI). The similarity in the diffraction efficiency (DE) behavior (e.g., efficiency decline and valley-like diffraction curves for low-efficiency orders) of echelle gratings with different metals at TM polarization points the research line of sight to the RIs. Further, the numerical calculations based on the rigorous vector diffraction theory show that the efficiency behavior of the echelle grating at TM polarization is extremely sensitive to the imaginary part of the RI. This is because there is a series of low light-collecting ability (LCA) regions as the imaginary part of the RI changes in the echelle grating, resulting in several disturbed DE zones. In addition, the increase in groove depth improves the LCA at both polarizations, which moves away from the low LCA region at the TM polarization. This leads to low polarization sensitivity and higher DE for echelle gratings, further revealing the essence of the efficiency improvement by increasing the groove depth. From the RI to the LCA, these results will give new concepts to designing and fabricating broadband high-efficiency echelle gratings. •It is the first to explain and unify the low diffraction efficiency behavior of echelle gratings at blaze wavelengths under Littrow mount from the view of the metal's refractive index.•The calculations point out that with the change of the imaginary part of the metal's refractive index, a series of low light-collecting ability regions of the echelle grating are formed, thus forming multiple disturbed diffraction efficiency regions.