Directional and singular surface plasmon generation in chiral and achiral nanostructures demonstrated by Leakage Radiation Microscopy

In this paper, we describe the implementation of leakage radiation microscopy (LRM) to probe the chirality of plasmonic nanostructures. We demonstrate experimentally spin-driven directional coupling as well as vortex generation of surface plasmon polaritons (SPPs) by nanostructures built with T-shaped and $\Lambda$- shaped apertures. Using this far-field method, quantitative inspections, including directivity and extinction ratio measurements, are achieved via polarization analysis in both image and Fourier planes. To support our experimental findings, we develop an analytical model based on a multidipolar representation of $\Lambda$- and T-shaped aperture plasmonic coupler allowing a theoretical explanation of both directionality and singular SPP formation. Furthermore, the roles of symmetry breaking and phases are emphasized in this work. This quantitative characterization of spin-orbit interactions paves the way for developing new directional couplers for subwavelength routing

A Grammar Compression Algorithm based on Induced Suffix Sorting

We introduce GCIS, a grammar compression algorithm based on the induced suffix sorting algorithm SAIS, introduced by Nong et al. in 2009. Our solution builds on the factorization performed by SAIS during suffix sorting. We construct a context-free grammar on the input string which can be further reduced into a shorter string by substituting each substring by its correspondent factor. The resulting grammar is encoded by exploring some redundancies, such as common prefixes between suffix rules, which are sorted according to SAIS framework. When compared to well-known compression tools such as Re-Pair and 7-zip, our algorithm is competitive and very effective at handling repetitive string regarding compression ratio, compression and decompression running time

Linear-time Computation of Minimal Absent Words Using Suffix Array

An absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their computation provides a fast alternative for measuring approximation in sequence comparison. There exists an O(n)-time and O(n)-space algorithm for computing all minimal absent words on a fixed-sized alphabet based on the construction of suffix automata (Crochemore et al., 1998). No implementation of this algorithm is publicly available. There also exists an O(n^2)-time and O(n)-space algorithm for the same problem based on the construction of suffix arrays (Pinho et al., 2009). An implementation of this algorithm was also provided by the authors and is currently the fastest available. In this article, we bridge this unpleasant gap by presenting an O(n)-time and O(n)-space algorithm for computing all minimal absent words based on the construction of suffix arrays. Experimental results using real and synthetic data show that the respective implementation outperforms the one by Pinho et al

Highly efficient singular surface plasmon generation by achiral apertures

We report a highly efficient generation of singular surface plasmon (SP) field by an achiral plasmonic structure consisting of $\Lambda$-shaped apertures. Our quantitative analysis based on leakage radiation microscopy (LRM) demonstrates that the induced spin-orbit coupling can be tuned by adjusting the apex angle of the $\Lambda$-shaped aperture. Specifically, the array of $\Lambda$-shaped apertures with the apex angle $60^\circ$ is shown to give rise to the directional coupling efficiency. The ring of $\Lambda$-shaped apertures with the apex angle $60^\circ$ realized to generate the maximum extinction ratio (ER=11) for the SP singularities between two different polarization states. This result provides a more efficient way for developing SP focusing and SP vortex in the field of nanophotonics such as optical tweezers

Low Space External Memory Construction of the Succinct Permuted Longest Common Prefix Array

The longest common prefix (LCP) array is a versatile auxiliary data structure in indexed string matching. It can be used to speed up searching using the suffix array (SA) and provides an implicit representation of the topology of an underlying suffix tree. The LCP array of a string of length $n$ can be represented as an array of length $n$ words, or, in the presence of the SA, as a bit vector of $2n$ bits plus asymptotically negligible support data structures. External memory construction algorithms for the LCP array have been proposed, but those proposed so far have a space requirement of $O(n)$ words (i.e. $O(n \log n)$ bits) in external memory. This space requirement is in some practical cases prohibitively expensive. We present an external memory algorithm for constructing the $2n$ bit version of the LCP array which uses $O(n \log \sigma)$ bits of additional space in external memory when given a (compressed) BWT with alphabet size $\sigma$ and a sampled inverse suffix array at sampling rate $O(\log n)$. This is often a significant space gain in practice where $\sigma$ is usually much smaller than $n$ or even constant. We also consider the case of computing succinct LCP arrays for circular strings

Faster algorithms for 1-mappability of a sequence

In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y. We focus here on the version of the problem where k = 1. The fastest known algorithm for k = 1 requires time O(mn log n/ log log n) and space O(n). We present two algorithms that require worst-case time O(mn) and O(n log^2 n), respectively, and space O(n), thus greatly improving the state of the art. Moreover, we present an algorithm that requires average-case time and space O(n) for integer alphabets if m = {\Omega}(log n/ log {\sigma}), where {\sigma} is the alphabet size

Lightweight LCP Construction for Very Large Collections of Strings

The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several applications, especially in biological contexts. Nowadays, the input data for many problems are big collections of strings, for instance the data coming from "next-generation" DNA sequencing (NGS) technologies. In this paper we present the first lightweight algorithm (called extLCP) for the simultaneous computation of the longest common prefix array and the Burrows-Wheeler transform of a very large collection of strings having any length. The computation is realized by performing disk data accesses only via sequential scans, and the total disk space usage never needs more than twice the output size, excluding the disk space required for the input. Moreover, extLCP allows to compute also the suffix array of the strings of the collection, without any other further data structure is needed. Finally, we test our algorithm on real data and compare our results with another tool capable to work in external memory on large collections of strings.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The final version of this manuscript is in press in Journal of Discrete Algorithm