We demonstrate the efficient sorter of Bessel beams separating both the azimuthal and radial components. This is based upon the recently reported transformation of angular to transverse momentum states. We separately identify over forty azimuthal and radial components, with a radial spacing of 1588 m(-1), and outline how the device could be used to identify the two spatial dimensions simultaneously.

<abstract><p>The inverse Frobenius-Perron problem (IFPP) is a collective term for a family of problems that requires the construction of an ergodic dynamical system model with prescribed statistical characteristics. Solutions to this problem draw upon concepts from ergodic theory and are scattered throughout the literature across domains such as physics, engineering, biology and economics. This paper presents a survey of the original formulation of the IFPP, wherein the invariant probability density function of the system state is prescribed. The paper also reviews different strategies for solving this problem and demonstrates several of the techniques using examples. The purpose of this survey is to provide a unified source of information on the original formulation of the IFPP and its solutions, thereby improving accessibility to the associated modeling techniques and promoting their practical application. The paper is concluded by discussing possible avenues for future work.</p></abstract>

No abstract

Abstract-A novel solution of the inverse Frobenius-Perron problem for constructing semi-Markov chaotic maps with prescribed statistical properties is presented. The proposed solution uses recursive Markov state disaggregation to construct an ergodic map with a piecewise constant invariant density function that approximates an arbitrary probability distribution over a compact interval. The solution is novel in the sense that it provides greater freedom, as compared to existing analytic solutions, in specifying the autocorrelation function of the semiMarkov map during its construction. The proposed solution is demonstrated by constructing multiple chaotic maps with invariant densities that provide an increasingly accurate approximation of the asymmetric beta probability distribution over the unit interval. It is demonstrated that normalised autocorrelation functions with components having different rates of decay and which alternate in sign between consecutive delays may be specified. It is concluded that the flexibility of the proposed solution facilitates its application towards modelling of random signals in various contexts.

No abstract