ution of RLoG wave, the closed-form expressions, including integral and differ-Рential representations, are derived for this kind of RLoG wave, which yields the paraxialРapproximation for the RLoG beams in the appropriate regime. From the spectral repre-Рsentation of this beam, the first three orders corrections of nonparaxial approximationsР - V -Р哈尔滨工业大学理学博士学位论文Рare determined for corresponding paraxial RLoG beams. Using the numerical simulation,Рthe first three orders corrections of nonparaxial approximations RLoG beams, the paraxialРapproximations RLoG beams and the exact solution of RLoG wave have beem researchedРand analyzed, and their differences with each other have been paratively.РKeywords: Axicon; Spiral phase plate; Spiraling Bessel beams; Dark-hollow beams;Р Virtual sourceР - VI -