The proposed necessary and sufficient condition for spectral switches with concave reflectance of aluminum metal

Abstract

Spectral switches have been widely studied, and many related applications and phenomena were proposed or verified. However, the conditions under which spectral switches can be found are not completely specified. In the past, the zero-intensity components or phase singularities are used as the sufficient conditions for spectral switches. Some kind of oscillatory behavior in the modifier function is also proposed to be the necessary condition for it. In this work, we suggest that the necessary and sufficient condition can be reduced to a simple condition: a strictly concave modifier with a minimum. An example with this condition is given using the reflectance of aluminum in the visible to near-infrared range. This result clarifies the conditions for spectral switches and helps identifying it under different circumstances in the future. The related spectral shift amplification and polarization–controlled spectral shift effect are also presented.