Using the rate equation, several optical methods of characterizing the threshold of a laser diode(LD) were analyzed. The thresholds determined by all methods are consistent if the spontaneous-emission-coefficient(β) is small. If β>0.05, the thresholds obtained by different methods are different. Especially, for micro-nano LDs with a large β, these methods are starting to become inaccurate. However, the d^2S/dI^2-I is a relatively accurate method to characterize threshold of these LDs compared to other methods. The effects of the spontaneous-emission-lifetime(τsp) and the photon-lifetime(τp) on thresholds were analyzed. The exact functions between the threshold and the β, τsp and τp were obtained.
Metalenses are expected to play an increasingly important role in miniaturized and integrated optical imaging components/systems.However,devising broadband achromatic metalenses with high focusing efficiencies is still quite challenging.In this work,we proposed an aperture-shared partition phase cooperative manipulation approach for designing a highefficiency broadband achromatic metalens composed of two concentric sub-metalenses.As a proof-of-concept,an achromatic polarization-independent metalens is successfully designed for the visible and near-infrared range from450 nm to 1400 nm with the focusing efficiency over 70% for the wavelength range of 600 nm to 1400 nm.The approach reported here provides a possibility for designing a high-performance metalens,which has great potential applications in integrated optics.