Dark Solitons in Discrete Lattices: Saturable versus Cubic Nonlinearities

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them with those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both on-site and inter-site modes, are examined analytically and corroborated by numerical results. Furthermore, their dynamical evolution when they are found to be unstable is obtained through appropriately crafted numerical experiments.Comment: 15 pages, 5 figure

Plasmonic communications : light on a wire

The emerging field of plasmonics promises the generation, processing, transmission, sensing and detection of signals at optical frequencies along metallic surfaces much smaller than the wavelengths they carry. Plasmonic technology has applications in a wide range of fields, including biophotonics, sensing, chemistry and medicine. But perhaps the area where it will have the most profound impact is in optical communications, since plasmonic waves oscillate at optical frequencies and thus can carry information at optical bandwidths

Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schroedinger Lattices

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately crafted Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss.Comment: 12 pages, 17 figure

Das Rückwirkungsverbot im Strafprozessrecht

Prohibition of retroactivity, which is established in the Constitution as well as in the Penal Code, is of paramount importance for the safety of criminal law. Every human action is judged, in criminal terms, according to the statute in force at the time of commission of the act. Prohibition of retroactivity of penal statutes aims for the protection of the individual from state power arbitrariness (legislative, judiciary and executive state power) and is activated in case of adverse legislative amendment. It namely prohibits the ex post characterisation of an act as punishable as well as the more severe characterisation of a previously punishable behaviour. This prohibition refers to every element constituting the substance of an offence or the envisaged penalty despite the functional incorporation of the relevant provisions in the general or the special part of the Penal Code. Furthermore, the meaning of punishment, as far as prohibition of retroactivity is concerned, involves main penalties (e.g. imprisonment, pecuniary penalty), supplementary penalties (e.g. deprivation of civil rights, prohibition to exercise a profession) and the penal consequences of punishment (e.g. registration of criminal record).An exception from the prohibition of retroactivity is found in the Greek penal law:The penal procedural laws are applied when put into effect even during pending criminal trials. This opinion calls for the equivalent ‘general principle of conflicts of laws’, for the better servicing of public interest, for the fact that no vested rights are founded on certain procedure and that procedural rules don’t refer to guilt but to the verification of an offence etc. On the other hand, a large body of legal literature has voiced serious objections during recent years with regards to the constitutionality of this choice by bringing in the danger of state power arbitrariness, the positive legality of substantive and procedural penal law and the need for protection of the individual. On this basis, the principle nullum crimen, nulla poena sine lege must be applied altogether in the criminal procedure, in order to avoid a worsening of the defendant’s position (e.g. for temporary imprisonment, when defining the competent court, for the provision of remedies etc).Η διατριβή καλύπτει την προβληματική των χρονικών ορίων εφαρμογής των ποινικών δικονομικών. Αρχικά εκτίθεται το πλαίσιο ρύθμισης και λειτουργίας της ισχύος των νόμων προκειμένου αυτή να διακριθεί ακολούθως από την έννοια της εφαρμογής των νόμων. Ακολούθως τίθεται το ερώτημα: Ισχύει η συνταγματική απαγόρευση της αναδρομικότητας πλην του ουσιαστικού και στο δικονομικό ποινικό δίκαιο; Κατ’ αρχήν η αποτίμηση του συναφούς ιστορικοφιλοσοφικού υλικού αποδεικνύει τη στενή σύνδεση της απαγόρευσης της αναδρομικότητας με το γενικότερο κοινωνικό και πολιτικό ζητούμενο. Η μορφή που σε κάθε εποχή προσλαμβάνει η σχέση εξουσίας - ατόμου αποβαίνει καθοριστική για τη θέση χρονικών ορίων κατά τη νομοθέτηση και την εφαρμογή των ποινικών νόμων. Καταγράφεται το πλαίσιο θεσμικής ρύθμισης της αρχής της νομιμότητας της ποινικής καταστολής και της απαγόρευσης της αναδρομικότητας ενώ παράλληλα αναλύονται οι περιπτώσεις υποχώρησής τους (π.χ. μεταβολές νομολογία, προσωρινοί νόμοι). Ακολουθεί επισκόπηση των θεωρητικών απόψεων και των νομολογιακών παραδοχών που αφορούν την αναδρομικότητα των ποινικών δικονομικών νόμων, στις περισσότερες ευρωπαϊκές χώρες καθώς και στις Η.Π.Α. Στο τέλος αυτής της επισκόπησης προσεγγίζονται κριτικά τα επιμέρους επιχειρήματα της κρατούσας γνώμης. Η βασική θέση της διατριβής συνίσταται στη θεώρηση του ποινικού φαινομένου ως ενότητας με επιμέρους στοιχεία το έννομο αγαθό, το έγκλημα και την ποινή. Η διαδικασία επιβολής της ποινής πρέπει να συντελείται σύμφωνα με σταθερούς κανόνες που να εγγυώνται τη νομιμοποίηση της: nullum crimen, nulla poena sine processu. Παράλληλα ερευνάται η σχέση των κανόνων επιβολής της ποινής (ποινική δικονομία) με τους κανόνες του ουσιαστικού δικαίου και προτείνεται η αναφορά σε κατασταλτικούς κανόνες και η υιοθέτηση μιας νέας ορολογίας με βάση την ποινή: δίκαιο απειλής της ποινής (ουσιαστικό π. δ.), δίκαιο επιβολής της ποινής (δικονομικό π. δ.) και δίκαιο έκτισης της ποινής. Παραπέρα ερευνάται η φύση της ποινικής δίκης η οποία λειτουργεί ως μηχανισμός επιβολής της οργανωμένης απαντήσεως της κοινωνίας στο έγκλημα. Έτσι και η ποινική δικονομία, ως μέρος του όλου δικαιικού συστήματος, αποτελεί εργαλείο διαχείρισης κοινωνικών συγκρούσεων και εκφράζει τον γενικά ταξικό χαρακτήρα της κοινωνικής οργάνωσης και συνιστά παράλληλα ένα εγγυητικό μηχανισμό και μια βάση προστασίας των ανθρωπίνων δικαιωμάτων.Τέλος διατυπώνονται τα επιχειρήματα για την ισχύ της απαγόρευσης της αναδρομικότητας στο ποινικό δικονομικό δίκαιο: Αποτροπή της αυθαιρεσίας της εξουσίας ως κεντρικού σημείου της ιστορικής έρευνας, Αρχή του κράτους δικαίου ως γενική εγγύηση της νομιμότητας, δημοσιότητας και ελεγξιμότητας της κρατικής δραστηριότητας, Αρχή της δικαιικής ασφάλειας, Σύνδεση της γενικότητας του νόμου με την αναδρομικότητα, Αρχή της ίσης μεταχείρισης των ατόμων, Επέκταση του πεδίου προστασίας του άρθρου 7 § 1 του Συντάγματος και στο χώρο της ποινικής δικονομίας. Ο κανόνας συνεπώς δεν είναι η επιλογή του νόμου πράξης ή εκδίκασης αλλά η αποτροπή εφαρμογής εκείνου που είναι δυσμενέστερος. Η ποινική δίκη λοιπόν θα διεξαχθεί με βάση τον ομόχρονό της νόμο (σε αναδρομική εφαρμογή) τότε μόνο όταν κριθεί ότι αυτός δεν είναι δυσμενέστερος από κείνον που ίσχυε κατά την τέλεση της αξιόποινης πράξης. Στο επίμετρο της εργασίας δοκιμάζονται οι θέσεις που έχουν προηγηθεί μέσα από την εξέταση της αναδρομικότητας, στο χώρο των ενδίκων μέσων

Dark solitons in discrete lattices: Saturable versus cubic nonlinearities

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them to those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both onsite and intersite modes, are examined analytically and corroborated by numerical results. Our findings indicate that for both models onsite solutions are stable for sufficiently small values of the coupling between adjacent nodes, while intersite solutions are always unstable. The nature of the instability (which is oscillatory for onsite solutions at large coupling and exponential for inter-site solutions) is probed via the dynamical evolution of unstable solitary waves through appropriately crafted numerical experiments; typically, these computations result in dynamic motion of the originally stationary solitary waves. Another key finding, consistent with recent experimental results, is that the instability growth rate for the saturable nonlinearity is found to be smaller than that of the cubic case

Slow-light dark solitons in insulator-insulator-metal plasmonic waveguides

The potential of slow-light propagation in an insulator-insulator-metal plasmonic waveguide is studied. Due to the high dispersion of the device in the frequency region where the signal group velocity is low, slow-light optical pulses broaden in time and intersymbol interference occurs, limiting the achievable data rates and transmission distance. In order to overcome this problem, we analytically and numerically investigate slow dark solitons in the normal dispersion regime of the waveguide. The storing capability of the waveguide is analyzed from an application point of view. © 2010 Optical Society of America

Dark solitons in discrete lattices: Saturable versus cubic nonlinearities

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them to those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both onsite and intersite modes, are examined analytically and corroborated by numerical results. Our findings indicate that for both models onsite solutions are stable for sufficiently small values of the coupling between adjacent nodes, while intersite solutions are always unstable. The nature of the instability (which is oscillatory for onsite solutions at large coupling and exponential for inter-site solutions) is probed via the dynamical evolution of unstable solitary waves through appropriately crafted numerical experiments; typically, these computations result in dynamic motion of the originally stationary solitary waves. Another key finding, consistent with recent experimental results, is that the instability growth rate for the saturable nonlinearity is found to be smaller than that of the cubic case. © 2007 The American Physical Society

Slow light in insulator-metal-insulator plasmonic waveguides

We study numerically the slow-light capability of insulator-metal-insulator (IMI) plasmonic waveguides. Metalinduced losses are included in the calculation of the dispersion relations, and their effect on the slow-light properties of the waveguide is investigated. In addition to reducing the propagation lengths of surface plasmon polaritons, losses are found to limit the achievable slowdown factors and the practical potential of the device. To alleviate the problem, we consider active materials. Using realistic parameters, we find that a spectral region is then formed where a slow-light pulsed signal can achieve infinite propagation lengths or be amplified. The optical buffering capabilities of the IMI waveguide with losses are analyzed, and we conclude that while losses limit the buffering capabilities of the passive device, the use of active materials may combat the problem effectively from an application point of view. © 2011 Optical Society of America

Discrete vector solitons in one-dimensional lattices in photorefractive media

We construct families of two-component spatial solitons in a one-dimensional lattice with saturable on-site nonlinearity (focusing or defocusing) in a photorefractive crystal. We identify 14 species of vector solitons, depending on their type (bright/dark), phase (in-phase/staggered), and location on the lattice (on/off-site). Two species of the bright/bright type form entirely stable soliton families, four species are partially stable (depending on the value of the propagation constant), while the remaining eight species are completely unstable. "Symbiotic" soliton pairs (of the bright/dark type), which contain components that cannot exist in isolation in the same model, are found as well. © 2006 The American Physical Society

Plasmonic communications : light on a wire

The emerging field of plasmonics promises the generation, processing, transmission, sensing and detection of signals at optical frequencies along metallic surfaces much smaller than the wavelengths they carry. Plasmonic technology has applications in a wide range of fields, including biophotonics, sensing, chemistry and medicine. But perhaps the area where it will have the most profound impact is in optical communications, since plasmonic waves oscillate at optical frequencies and thus can carry information at optical bandwidths