Due to their very high integration density, echelle grating spectrometers based on silicon nanophotonic platforms have received great attention for their applications in many areas, such as optical sensors, optical communications, and optical interconnections. The design of echelle gratings requires an effective modeling and simulation technique. Though we have used a boundary integral method to accurately analyze the polarization-dependent performance of the echelle grating, it is complicated and time-consuming for the simulation due to its large size and aperiodic structure. In the present paper, we will present a faster simulation method for the grating with twice total internal reflection facets based on a modified Kirchhoff-Huygens principle with the influence of the Goos-Hachen shift considered. On the one hand, the presented simulation results agree well with our previous results obtained by the boundary integral method when the shift can accurately be calculated using a FDTD method. On the other hand, the biggest advantage of the new method over the existing methods is that it can also provide an insightful physical explanation for many numerical results. Finally, we will effectively apply the present method to design an on-chip spectrometer with very low noise floor.
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