Line-distortion, Bandwidth and Path-length of a graph

We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour's path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: - if a graph $G$ can be embedded into the line with distortion $k$, then $G$ admits a Robertson-Seymour's path-decomposition with bags of diameter at most $k$ in $G$; - for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; - there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; - AT-free graphs and some intersection families of graphs have path-length at most 2; - for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem

On the 3-distortion of a path

We prove that, when a path of length n is embedded in R^2, the 3-distortion is an Omega(n^{1/2}), and that, when embedded in R^d, the 3-distortion is an O(n^{1/d-1})

Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber

We report the generation of slow light using Brillouin amplification in a short length of highly nonlinear bismuth-oxide fiber. By using just 2m of fiber, we demonstrate a five-fold reduction in group velocity for ~200ns pulses, which we believe to be a record for a slow-light propagation in an optical fiber. Moreover, by virtue of the high nonlinearity per unit length of this fiber, we achieve this at a very modest pump power level of just ~400mW and with a low inherent device latency of 14ns. These results highlight both the merits and practicality of using high nonlinearity nonsilica fibers for slow-light devices

Choosing a Better Delay Line Medium between Single-Mode and Multi-Mode Optical Fibers: the Effect of Bending

Optical fiber cables are materials whose core is made of silica and other materials such as chalcogenide glasses; they transmit a digital signal via light pulses through an extremely thin strand of glass. The light propagates and is being guided by the core which is surrounded by the cladding. Light travels in the optical fiber in the form of total internal reflection in the core of the fibers. The flexibility, low tensile strength, low signal loss, high bandwidth and other characteristics of optical fibers favors it for use as a delay medium in many applications. Another favorable characteristic of optical fiber delay lines is are their relative insensitivities to environmental effects and electromagnetic interferences. The immunity of optical fibers to interferences and their less weight added advantages to it for use as delay medium. Single-mode and multi-mode are the two most popular types of optical fibers. Single-mode fibers have good propagation and delay properties with a minimal loss that allows the signal to propagate in a large distance with insignificant distortion or attenuation. The percentage of power transmission of single-mode fibers is found to be higher than that of the multi-mode fibers. It is, therefore, a preferred type for use as a delay line. In this paper, relative studies of the two optical fibers modes, and the results of power input/output measurement of the two modes are presented with a view to coming up with a better type for use as a delay medium

Clock synchronization with dispersion cancellation

The dispersion cancellation feature of pulses which are entangled in frequency is employed to synchronize clocks of distant parties. The proposed protocol is insensitive to the pulse distortion caused by transit through a dispersive medium. Since there is cancellation to all orders, also the effects of slowly fluctuating dispersive media are compensated. The experimental setup can be realized with currently available technology, at least for a proof of principle.Comment: 4 pages, 3 figure