Analytical vectorial structure of non-paraxial four-petal Gaussian beams in the far field

The analytical vectorial structure of non-paraxial four-petal Gaussian beams(FPGBs) in the far field has been studied based on vector angular spectrum method and stationary phase method. In terms of analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam are derived in the far field, respectively. According to our investigation, the FPGBs can evolve into a number of small petals in the far field. The number of the petals is determined by the order of input beam. The physical pictures of the FPGBs are well illustrated from the vectorial structure, which is beneficial to strengthen the understanding of vectorial properties of the FPGBs

Vectorial structure of a hard-edged-diffracted four-petal Gaussian beam in the far field

Based on the vector angular spectrum method and the stationary phase method and the fact that a circular aperture function can be expanded into a finite sum of complex Gaussian functions, the analytical vectorial structure of a four-petal Gaussian beam (FPGB) diffracted by a circular aperture is derived in the far field. The energy flux distributions and the diffraction effect introduced by the aperture are studied and illustrated graphically. Moreover, the influence of the f-parameter and the truncation parameter on the nonparaxiality is demonstrated in detail. In addition, the analytical formulas obtained in this paper can degenerate into un-apertured case when the truncation parameter tends to infinity. This work is beneficial to strengthen the understanding of vectorial properties of the FPGB diffracted by a circular aperture

The Influence of Oxygen Vacancies on Luminescence Properties of Na₃LuSi₃O₉:Ce³⁺

Oxygen vacancies play an important role in the luminescence processes of inorganic scintillator materials. In order to study the effects of oxygen vacancies on the luminescence properties of Na₃LuSi₃O₉:Ce³⁺, these phosphors were prepared using a high temperature solid-state reaction method under different atmosphere and raw materials. It was found that oxygen vacancy had great influence on the absorption, photoluminescence and decay curves of Na₃LuSi₃O₉:Ce³⁺. The luminescence intensity and peak position showed a regular change when synthesizing atmosphere changed. Na₃LuSi₃O₉:Ce³⁺ with more oxygen vacancies showed much stronger luminescence intensity at high temperature than that without vacancies. And it was also found that the decreasing of oxygen vacancies can quicken the photoluminescence decay of Ce³⁺ in Na₃LuSi₃O₉. The existence of oxygen vacancies in Na₃LuSi₃O₉:Ce³⁺ was confirmed by Zr⁴⁺ doping and thermoluminescence emission spectra. At last, emission bands of Ce³⁺ and oxygen vacancies were well distinguished under X-ray excitation and probable cause of the formation of oxygen vacancies was discussed