We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel-Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel-Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber.

Abstract-Sun et al.[1] succeeded in reducing the set of coupled first-order nonlinear partial differential equations determining the wavelength-dependent, time-varying amplifier gain into a single ordinary differential equation (ODE). In this paper, we further simplify the ODE bringing into greater evidence the physical meaning of the amplification process, and greatly enhancing the utility of the ODE as an analysis and design tool. We find that the gain dynamics of a doped-fiber amplifier are completely specified by its total number of excited ions r, whose time behavior is described by a simple first-order differential equation. We exploit this new understanding of amplifier gain dynamics: 1) to develop an equivalent circuit model for amplifier gain dynamics, 2) to identify that channel addition causes much faster transients than channel dropping in wavelength division multiplexing networks, and 3) to demonstrate that gain excursions can be significant in multichannel packet switching applications, which unlike timemultiplexed signals are characterized by bursts and lulls in communications. We are also able to revisit the most significant previously published results on both steady-state and dynamic analysis of doped-fiber amplifiers with a much more concise and more intuitive derivation.Index Terms-Doped-amplifier gain dynamics, EDFA, packet switching.

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