Measuring Topological Charges of Optical Vortices with Multi-Singularity Using a Cylindrical Lens

We present a simple method to measure the topological charges of optical vortices with multiple singularities. Using a cylindrical lens, a vortex beam can decay into a light field distribution with multiple separated dark holes, whose number just equals the topological charge of the input beam. This conclusion is then verified via experiments and numerical simulations of the propagation of vortex beams with multiple singulaxities. This method is also reliable to measure the topological charges of broadband vortex beams with different distributions of singularities, which does not resort to multiple beam interferometrie experiments.

Techniques for Determining the Geographic Location of IP Addresses in ISP Topology Measurement

A brief survey on the state-of-the-art research of determining geographic location of IP addresses is presented. The problem of determining the geographic location of routers in Internet Service Provider （ISP） topology measurement is discussed when there is inadequate information such as domain names that could be used. Nine empirical inference rules are provided, and they are respectively （1） rule of mutual inference, （2） rule of locality, （3） rule of ping-pong assignment, （4） rule of bounding from both sides, （5） rule of preferential exit deny, （6） rule of uureachable/timeout, （7） rule of relay hop assignment, （8） rule of following majority, and （9） rule of validity checking based on interface-finding. In totally 2,563 discovered router interfaces of a national ISP topology, only 6.4% of them can be located by their corresponding domain names. In contrast, after exercising these nine empirical inference rules, 38% of them have been located. Two methods have mainly been employed to evaluate the effectiveness of these inference rules. One is to compare the measured topology graph with the graph published by the corresponding ISP. The other is to contact the administrator of the corresponding ISP for the verification of IP address locations of some key routers. The conformity between the locations inferred by the rules and those determined by domain names as well as those determined by whois information is also examined. Experimental results show that these empirical inference rules play an important role in determining the geographic location of routers in ISP topology measurement.

Measuring the topological charge of optical vortices with a single plate

Measuring the topological charge(TC) of optical vortex beams by the edge-diffraction pattern of a single plate is proposed and demonstrated. The diffraction fringes can keep well discernible in a wide three-dimensional range in this method. The redundant fringes of the diffracted fork-shaped pattern in the near-field can determine the TC value, and the orientation of the fork tells the handedness of the vortex. The plate can be opaque or translucent, and the requirement of the translucent plate for TC measurement is analyzed. Measurement of TCs up to ±40 is experimentally demonstrated by subtracting the upper and lower fringe numbers with respect to the center of the light. The plate is easy to get, and this feasible measurement can bring great convenience and efficiency for researchers.

Trivial and Simple Spectrum for SL(d,R) Cocycles with Free Base and Fiber Dynamics

Let ACD（M, SL（d,R）） denote the pairs （f, A） so that f∈ A C Diff^1（M） is a C^1-Anosov transitive diffeomorphisms and A is an SL（d,R） cocycle dominated with respect to f. We prove that open and densely in ACD（M, SL（d,R））, in appropriate topologies, the pair （f,A） has simple spectrum with respect to the unique maximal entropy measure μf. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AUtLeb（M） × LP（M, SL（d, R））.