The crescent nanostructure with gain medium inside is theoretically studied to analyze the characteristic of plasmonic emitting with wide bandwidth. An accurate analytical model is built based on the transformation optics. In this model, the poles of the electrostatic potential function are in the second and the fourth quadrant of the complex plane if the imaginary part of the relative permittivity of the gain medium is larger than the loss compensation threshold, and then the extinction cross section is to be negative by integrating the electrostatic potential over the half complex plane via an inverse Fourier transform. The positive extinction cross section corresponds to absorption, and the negative corresponds to emission. The proposed analytical model agrees well with the numerical simulation results based on the finite element method, to give a physical insight into the loss compensation property of the plasmonic nanostuctures. Results show that the negative extinction cross section is realizable by introducing the gain medium into a plasmonic crescent nanowire, which is equivalent to an emitting device with wide bandwidth.

Abstract-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-Hänchen 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.