Design of waveguides, bends and splitters in photonic crystal slabs with hexagonal holes in a triangular lattice

Waveguides in photonic crystal slabs (PCS) can be obtained by omitting a row of holes (W1-waveguides). In general the propagation properties in such waveguides suffer from the unavoidable periodic sidewall corrugation caused by the remaining parts of the crystal. The corrugation acts as a Bragg reflector, causing the occurrence of so-called mini stopbands in the transmission of the waveguide. The effect is quite strong in PCS with circular holes, but it can be significantly reduced if correctly oriented hexagonal holes are used. This so-called hexagon-type PCS allows the design of waveguides, bends and splitters having a relatively high group velocity and a wide transmission window in the PCS stopband for modes having their magnetic field oriented mainly perpendicular to the slab

Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity

We show that the n-fold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the "Ising class", or n-fold integrals from enumerative combinatorics, like lattice Green functions, are actually diagonals of rational functions. As a consequence, the power series expansions of these solutions of linear differential equations "Derived From Geometry" are globally bounded, which means that, after just one rescaling of the expansion variable, they can be cast into series expansions with integer coefficients. Besides, in a more enumerative combinatorics context, we show that generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions. We give a large set of results illustrating the fact that the unique analytical solution of Calabi-Yau ODEs, and more generally of MUM ODEs, is, almost always, diagonal of rational functions. We revisit Christol's conjecture that globally bounded series of G-operators are necessarily diagonals of rational functions. We provide a large set of examples of globally bounded series, or series with integer coefficients, associated with modular forms, or Hadamard product of modular forms, or associated with Calabi-Yau ODEs, underlying the concept of modularity. We finally address the question of the relations between the notion of integrality (series with integer coefficients, or, more generally, globally bounded series) and the modularity (in particular integrality of the Taylor coefficients of mirror map), introducing new representations of Yukawa couplings.Comment: 100 page

Waveguides, bends and Y-junctions with improved transmission and bandwidth in hexagon-type SOI photonic crystal slabs

This paper presents novel ways of implementing waveguide components in photonic crystal slabs based on silicon-on-insulator (SOI). The integration platform we consider consists of hexa¬gonal holes arranged in a triangular lattice (‘hexagon-type’ photonic crystal). The waveguides are made of one missing row of holes (W1) with triangular air inclusions symmetrically added on each side of the waveguide. \ud Size and position of these inclusions are tuning parameters for the band diagram and can be used for minimizing the distributed Bragg reflection (DBR) effect. The waveguides show single-mode behavior with reasonably high group velocity and large transmission window, inside the gap between H-like modes**. These waveguides, closely resembling conventional ridge waveguides, can be combined to form efficient bends and Y-junctions. The bends and Y-junctions include intermediate short waveguide sections at half the bend angle playing the role of corner ‘mirrors’. Qualitative design rules were obtained from 2D calculations based on effective index approximation.\u

Ising n-fold integrals as diagonals of rational functions and integrality of series expansions

We show that the n-fold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the "Ising class", or n-fold integrals from enumerative combinatorics, like lattice Green functions, correspond to a distinguished class of function generalising algebraic functions: they are actually diagonals of rational functions. As a consequence, the power series expansions of the, analytic at x=0, solutions of these linear differential equations "Derived From Geometry" are globally bounded, which means that, after just one rescaling of the expansion variable, they can be cast into series expansions with integer coefficients. We also give several results showing that the unique analytical solution of Calabi-Yau ODEs, and, more generally, Picard-Fuchs linear ODEs, with solutions of maximal weights, are always diagonal of rational functions. Besides, in a more enumerative combinatorics context, generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions. We finally address the question of the relations between the notion of integrality (series with integer coefficients, or, more generally, globally bounded series) and the modularity of ODEs.Comment: This paper is the short version of the larger (100 pages) version, available as arXiv:1211.6031 , where all the detailed proofs are given and where a much larger set of examples is displaye

Inventor CEOs and Firm Innovation

Using a novel, manually-collected dataset, we find that firms whose chief executive officer (CEO) is an inventor experience significantly better innovation outcomes, as measured by patents and future citations. We obtain these results in models with firm fixed effects, in difference-in-difference analysis of transitioning CEOs that controls for the CEO fixed effects, and among firms with founder CEOs. Firms led by an inventor CEO also exhibit greater tolerance for failure as indicated by a greater number of both highly cited and uncited patents, and engage more in explorative search strategies that exploit new technological trajectories. Stock market, however, seems unable to fully capture the positive impact of inventor CEOs on future innovation: firms whose CEO transitions to be an inventor experience positive abnormal stock returns, especially during the early years following the transition

Do Insiders Trade on Innovation?

We find that pure insider share purchases—which we define as insider purchases over two successive years without any corresponding sales—are a strong predictor of a firm’s patent applications. The predictability increases with the quality of the patent: Applications for the highest-quality, breakthrough patents increase by 21% in the year following pure insider purchases in our sample. These purchases are associated with large abnormal stock returns of 1.1% per month (14% annualized) over the subsequent three-year period. We also document that stock price responds less to the subsequent announcement of the grant of patent if the application for the patent has been preceded by pure insider purchases, consistent with the idea that insider purchases reveal information about future firm innovation. Our evidence has implications for understanding insider trading within technology companies that have become a dominant feature of US stock markets in recent decades

Alignment issues in photonic crystal device fabrication

An important requirement in the fabrication of photonic crystal structures is the correct relative alignment of structural elements. Accuracy should be in the order of some tens of nanometres. Some of the options for providing such accuracy are discussed. Examples are given of aligning defects with respect to a predefined 2D lattice, aligning access waveguides with respect to a small local photonic crystal structure, and the alignment of successive periodically structured layers in a 3D "woodpile" structure

Realization of 2-dimensional air-bridge silicon photonic crystals by focused ion beam milling and nanopolishing

We report the design and fabrication of small photonic crystal structures which are combined with conventional dielectric ridge waveguides. We describe in details the fabrication of both rough and smooth membranes, which are used as host for photonic crystals. Two Focused Ion Beam milling experiments are highlighted: the first one shows how photonic crystals can be fast and accurate milled into a Si membrane, whereas the second experiment demonstrates how focused ion beam milling can turn a rough surface into a well-patterned nano-smooth surface. The previously ultra rough surface showed no detectable roughness after milling due to the nanopolishing effect of the focused ion beam milling

On the functions counting walks with small steps in the quarter plane

Models of spatially homogeneous walks in the quarter plane ${\bf Z}_+^{2}$ with steps taken from a subset $\mathcal{S}$ of the set of jumps to the eight nearest neighbors are considered. The generating function $(x,y,z)\mapsto Q(x,y;z)$ of the numbers $q(i,j;n)$ of such walks starting at the origin and ending at $(i,j) \in {\bf Z}_+^{2}$ after $n$ steps is studied. For all non-singular models of walks, the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are continued as multi-valued functions on ${\bf C}$ having infinitely many meromorphic branches, of which the set of poles is identified. The nature of these functions is derived from this result: namely, for all the 51 walks which admit a certain infinite group of birational transformations of ${\bf C}^2$, the interval $]0,1/|\mathcal{S}|[$ of variation of $z$ splits into two dense subsets such that the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are shown to be holonomic for any $z$ from the one of them and non-holonomic for any $z$ from the other. This entails the non-holonomy of $(x,y,z)\mapsto Q(x,y;z)$, and therefore proves a conjecture of Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure

Penetrating heart injuries – our experience

Catedra Chirurgie nr.1 ”N.Anestiadi”, Laboratorul Chirurgie Hepato-pancreato-biliară, USMF ”Nicolae Testemițanu”, Secția Chirurgie nr.1 IMSP IMU, Chișinău, Republica Moldova, Al XII-lea Congres al Asociației Chirurgilor „Nicolae Anestiadi” din Republica Moldova cu participare internațională 23-25 septembrie 2015Introducere: Plăgile inimii care au reușit să fie transportate spre spital, fac parte din urgențele chirurgicale majore. Reprezintă 3,1% din toate traumatismele toracice conform EACTS. Cardiorafia care asigură hemostaza și vindecarea cordului poate avea rezultat bun și pentru o plagă cu dimensiuni importante. Scopul lucrării: Revizuirea conduitei intraspitalicești la pacienții cu plagă de cord cu evidențierea aspectelor intraoperatorii și a rezultatelor precoce ale tratamentului.Material și metode: Per total 36 de pacienți au fost internați cu plagă de cord (B:F – 35:1) în perioada: ianuarie 2005-mai 2015; dintre care 2 pacienți au avut plagă pericardică și unul – plagă cardiacă nepenetrantă. S-au analizat datele demografice, intervalul de timp de la traumatism până la operație, afectarea cavităților cardiace, examenele paraclinice efectuate preoperator în funcție de instabilitatea hemodinamicii. Pacienții au fost repartizați în două loturi: I – “răniții albi” (n=14), cu șoc hipovolemic și II – “răniții albaștri” (n=22) cu șoc cardiogen. Toți pacienții au fost operați de urgență prin toracotomie antero-laterală stângă (24) și dreaptă (12). Intraoperator s-a depistat plagă a VS (18), VD (8), AS (6), AD (3), VCS (1); în toate cazurile însoțite de hemopericard și hemopneumotorace. Rezultate: Durata medie de spitalizare – 17,6±3,6 zile, inclusiv în ATI – 2,4±1,2 zile. Au decedat 7 (19,4%) pacienți după stop cardiac pe masa de operație: lotul I – 4 (28,6%), iar lotul II – 3 (13,6%). Concluzii: Cardiorafia aplicată în timp reușit și gradul de agresivitate a plăgilor pe camerele cordului s-au soldat la pacienții cazuisticii prezentate cu o rată de supraviețuire de 80,6%, șocul hipovolemic fiind asociat cu pronostic mai rezervat, deşi fără diferenţă statistic semnificativă.Introduction: Cardiac injuries, in patients surviving until transportation to the hospital, represent major surgical emergencies. According to EACTS heart injuries account for 3.1% of all thoracic traumas. Cardiorrhaphy which provides heart wound closure and haemostasis may provide good results even for a large lesion. The purpose: Review of in hospital management of the patients with heart injury, highlighting intraoperative issues and early results of treatment. Material and methods: In the period January 2005-May 2015 there were 36 hospitalized patients (M:F – 35:1) with heart injury, out of which 2 patients have had pericardial injury and one – nonpenetrating cardiac injury. The following parameters were analyzed: demographic data, the time from injury to surgery, injured cardiac chambers, preoperative paraclinical examinations depending on the hemodynamic instability. Patients were distributed into two groups: I – “white injured” (n=14) with hypovolemic shock and II – “blue injured” (n=22) with cardiogenic shock. All patients were operated by emergency anterolateral thoracotomy: left (24) and right (12). Intraoperatively injury of LV (18), RV (8), LA (6), RA (3), SCV (1) were detected, in all cases accompanied by haemopericardium and haemopneumothorax. Results: The median hospital stay – 17.6±3.6 days, including in ICU – 2.4±1.2 days. Seven (19.4%) patients died after cardiac arrest on the operating table: in group I – 4 (28.6%), and in group II – 3 (13.6%). Conclusions: Cardiorrhaphy performed at proper time and degree of heart chambers injuries resulted in 80.6% survival in our case series; hypovolemic shock was associated with worse outcomes, though without statistically significant difference