Dirac Point and Edge States in a Microwave Realization of Tight-Binding Graphene-like Structures

We present a microwave realization of finite tight-binding graphene-like structures. The structures are realized using discs with a high index of refraction. The discs are placed on a metallic surface while a second surface is adjusted atop the discs, such that the waves coupling the discs in the air are evanescent, leading to the tight-binding behavior. In reflection measurements the Dirac point and a linear increase close to the Dirac point is observed, if the measurement is performed inside the sample. Resonances due to edge states are found close to the Dirac point if the measurements are performed at the zigzag-edge or at the corner in case of a broken benzene ring.Comment: 4 pages, 6 figure

Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method

According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87, 061107 (2005)], the triangular lattice of triangular air holes may allow to achieve a complete photonic band gap in two-dimensional photonic crystal slabs. In this work we present a systematic theoretical study of this photonic lattice in a high-index membrane, and a comparison with the conventional triangular lattice of circular holes, by means of the guided-mode expansion method whose detailed formulation is described here. Photonic mode dispersion below and above the light line, gap maps, and intrinsic diffraction losses of quasi-guided modes are calculated for the periodic lattice as well as for line- and point-defects defined therein. The main results are summarized as follows: (i) the triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode, but the useful region is generally limited by the presence of second-order waveguide modes; (ii) the lattice may support the usual photonic band gap for even modes (quasi-TE polarization) and several band gaps for odd modes (quasi-TM polarization), which could be tuned in order to achieve doubly-resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second-harmonic frequency; (iii) diffraction losses of quasi-guided modes in the triangular lattices with circular and triangular holes, and in line-defect waveguides or point-defect cavities based on these geometries, are comparable. The results point to the interest of the triangular lattice of triangular holes for nonlinear optics, and show the usefulness of the guided-mode expansion method for calculating photonic band dispersion and diffraction losses, especially for higher-lying photonic modes.Comment: 16 pages, 11 figure

Playing relativistic billiards beyond graphene

The possibility of using hexagonal structures in general and graphene in particular to emulate the Dirac equation is the basis of our considerations. We show that Dirac oscillators with or without restmass can be emulated by distorting a tight binding model on a hexagonal structure. In a quest to make a toy model for such relativistic equations we first show that a hexagonal lattice of attractive potential wells would be a good candidate. First we consider the corresponding one-dimensional model giving rise to a one-dimensional Dirac oscillator, and then construct explicitly the deformations needed in the two-dimensional case. Finally we discuss, how such a model can be implemented as an electromagnetic billiard using arrays of dielectric resonators between two conducting plates that ensure evanescent modes outside the resonators for transversal electric modes, and describe an appropriate experimental setup.Comment: 23 pages, 8 figures. Submitted to NJ

Mimicking graphene physics with a plane hexagonal wire mesh

This is the final version of the article. Available from AIP Publishing via the DOI in this record.A hexagonal metallic-wire mesh is fabricated and experimentally characterized to demonstrate graphene-physics in an electromagnetic analogue. In contrast to previous studies, our structure has a smaller ratio of out-of-plane to in-plane dimensions, more akin to real graphene. This allows for the development of a simple analytical treatment using equivalent electric circuit theory, and we demonstrate that the predicted dispersion curves of the supported eigenmodes agree well with those obtained from experimental measurements.The authors wish to acknowledge the financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom, via the EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1) and from the Higher Education Funding Council for England (HEFCE)

Comportement dynamique des lasers semiconducteurs en régime de modulation directe

A detailed study of the dynamic response of directly modulated semiconductor lasers is presented. The non-linearity of the gain is included in the laser equations. A performing numerical simulation method allows us to present the results in the form of bifurcation diagrams in the 3d space of modulation parameters. It is shown that the occurrence of unstable behaviours is directly related to the laser damping coefficient. Concerning InGaAsP lasers which generally exhibit strong damping, a simple periodic response is mostly predicted. Nevertheless, oscillation relaxations may occur within a single periode at low modulation frequencies. For AsGa lasers which exhibit a weakest damping period doubling may occur either at low or high modulation frequencies. In contrast, a chaotic behaviour seems to be excluded for realistic values of the laser parameters.Une étude détaillée des comportements dynamiques des lasers à semiconducteurs modulés en courant est présentée. La non-linéarité du gain est prise en compte dans les équations laser. Une méthode de résolution numérique performante permet de donner les résultats sous forme de diagrammes de bifurcation dans l'espace 3d des paramètres de modulation. Il est montré que la possibilité de comportements instables est directement liée au facteur d'amortissement du laser. En ce qui concerne les lasers InGaAsP dont l'amortissement est généralement élevé, il est essentiellement prédit un comportement périodique simple. Des oscillations de relaxation peuvent néanmoins se manifester à basse fréquence de modulation. En ce qui concerne les lasers AsGa à plus faible amortissement, des doublements de période sont possibles, soit à basse ou à haute fréquence de modulation. En revanche, un comportement chaotique semble exclu pour des valeurs réalistes de paramètres-laser

Design of a stable CW HCN laser for far infrared frequency synthesis

An HCN laser for infrared frequency synthesis has been designed to satisfy both conditions of high frequency stability and ouptut power. The influence of all the descriptive parameters of the laser on its frequency stability and power are analyzed. The optimization of the two above criteria is discussed with emphasis on frequency stability. On the 891 GHz line the laser shows a natural frequency stability (Δ f/f) = 5 x 10-9 with an output power of 20 mW-30 mW, and its maximum power is 100 mW.Nous décrivons la réalisation d'un laser HCN à la fois puissant et stable en fréquence, qui constitue ainsi un bon générateur pour la synthèse de fréquences infrarouges. L'influence des divers paramètres descriptifs du laser sur sa stabilité de fréquence et sa puissance de sortie a été analysée. Nous avons optimisé chacun des deux critères précédents en donnant la priorité à la stabilité de fréquence. Sur la raie d'émission à 891 GHz (λ = 337 μm), il est possible d'obtenir une stabilité de fréquence (Δf/f ) = 5 x 10-9 avec une puissance de sortie de 20 mW-30 mW lorsque le laser fonctionne en oscillateur libre. Sa puissance maximale est de 100 mW

Diodes lasers en régime de forte modulation sinuso\"ıdale de courant : modélisation et expériences à 1.3~μm

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