A novel multi-focusing metalens in the longitudinal direction has been proposed and investigated based on the equal optical path principle, which is independent on the incident polarizations and can be suitable for both of the linear and circular polarization incidences simultaneously. Here, three novel designing principles: partitioned mode, radial alternating mode and angular alternating mode, have been proposed firstly for constructing different types of the longitudinal multi-focusing metalenses. The performances of the designed metalenses based on the different designed methods have also been analyzed and investigated in detail, and the intensity ratio of the focusing spots can be tuned easily by modulating the numbers of the relative type of nanoantennas, which is significant for the micro-manipulating optics and the multi-imaging technology in the integrated optics.

The vortex beam carrying orbital angular momentum (OAM) has attracted great attentions in optical communication field, which can extend the channel capacity of communication system due to the orthogonality between different OAM modes. Generally, atmospheric turbulence can distort the helical phase fronts of OAM beams, which presents a critical challenge to the effective recognition of OAM modes. Recently, convolutional neural network (CNN), as a model of deep learning, has been widely applied to machine vision. In this paper, based on the CNN theory, we make a tradeoff between the computational complexity of the system and the efficiency of recognition by establishing a specially designed six-layer CNN structure in CPU station to efficiently achieve the recognition of OAM mode in turbulent environment through the feature extraction of the received Laguerre-Gaussian beam's intensity distributions. Furthermore, we examine the performances of our designed CNN with respect to various turbulence levels, transmission distances, mode spacings, and we have also compared the performances of recognizing single OAM mode with multiplexed OAM modes. The numerical simulation shows that basing on CNN method, the coaxial multiplexed OAM modes can obtain higher recognizing accuracy about 96.25% even under long transmission distance with strong turbulence. It is anticipated that the results might be helpful for future implementation of high-capacity OAM-based optical communication technology.

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A novel Monte Carlo model is proposed to acquire the reflective polarization information from a rough surface with arbitrary layers and profiles. Based on the micro-facets theory, the local normal vectors can be randomly sampled from the normal vector distribution of each layer. The incident light that propagates inside of the multi-layer media will be traced until being collected after leaving the surface or be ignored due to lacking enough energy. The simulated results (by our proposed theoretical model) agree well with the reported measured data and the analytical models from SCATMECH, which demonstrates the correctness and effectiveness of our model. Based on our model, the effects of the surface layer number, the surface geometry, the incident wavelength and polarization states of incidence on the reflective polarization from multi-layer surfaces have been analyzed in detail, which can be a guide in tasks such as target detection and so on.

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