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The axicon-based-Bessel-Gauss resonator (ABGR) has been proposed for the production of Bessel-Gauss beams. To analyze eigenfields of the ABGR with a plane or spherical output coupler, we present and demonstrate the transfer-matrix method. Since the method is slow to converge to eigenmodes of the ABGR by use of the Fox and Li iterative algorithm, in this paper the Huygens-Fresnel diffraction integral equations associated with ray matrices are converted into finite-sum matrix equations, and mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of the laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. Moreover, eigenfields across arbitrary interfaces between the axicon and the output coupler, and the propagation of output beams, are simulated by using the fast-Fourier transform (FFT). The calculation results reveal that because of the ABGR's poor transverse mode discrimination the ABGR should be improved to produce good-quality Bessel-Gauss beams.

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One of the many design and control issues of Automated Guided Vehicles System (AGVS) is the AGV fleet size. This paper presents a new solution method to determining the number of vehicles in the AGVS based on FlexibleManufacturing System (FMS). The approach relies on two procedures-estimate and simulation. With estimate procedure, the mathematic method will be used to estimate the AGV fleet size. In the next procedure, the estimate value will be used in the simulation model of AGVS for further study. The reliable number of vehicles can be reached after two procedures. The objective of this paper is to increase the efficiency and accuracy of the process in determining the AGV fleet size.