Search results for "Toe"

showing 10 items of 3824 documents

Properties of a Class of Toeplitz Words

2021

We study the properties of the uncountable set of Stewart words. These are Toeplitz words specified by infinite sequences of Toeplitz patterns of the form $\alpha\beta\gamma$, where $\alpha,\beta,\gamma$ is any permutation of the symbols 0,1,?. We determine the critical exponent of the Stewart words, prove that they avoid the pattern $xxyyxx$, find all factors that are palindromes, and determine their subword complexity. An interesting aspect of our work is that we use automata-theoretic methods and a decision procedure for automata to carry out the proofs.

FOS: Computer and information sciencesDecision procedureSubword complexityDiscrete Mathematics (cs.DM)Combinatorics on wordsSettore INF/01 - InformaticaGeneral Computer ScienceFormal Languages and Automata Theory (cs.FL)Computer Science - Formal Languages and Automata TheoryToeplitz wordTheoretical Computer ScienceComputer Science::Discrete MathematicsPattern avoidanceFOS: MathematicsAutomatic sequenceMathematics - CombinatoricsCombinatorics (math.CO)Computer Science::Formal Languages and Automata TheoryComputer Science - Discrete Mathematics
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Cyclic Complexity of Words

2014

We introduce and study a complexity function on words $c_x(n),$ called \emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity distinguishes between Sturmian words of different slopes. We prove that if $x$ is a Sturmian word and $y$ is a word having the same cyclic complexity of $x,$ then up to renaming letters, $x$ and $y$ have the same set of factors. In particular, $y$ is also Sturmian of slope equ…

FOS: Computer and information sciencesDiscrete Mathematics (cs.DM)Formal Languages and Automata Theory (cs.FL)Computer Science - Formal Languages and Automata Theory0102 computer and information sciences68R15Characterization (mathematics)[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]01 natural sciencesTheoretical Computer ScienceCombinatoricsConjugacy class[INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL][MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]FOS: MathematicsDiscrete Mathematics and CombinatoricsMathematics - Combinatorics0101 mathematics[MATH]Mathematics [math]Discrete Mathematics and CombinatoricMathematicsDiscrete mathematicsFactor complexity010102 general mathematicsSturmian wordSturmian wordComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Sturmian wordsCyclic complexity factor complexity Sturmian words minimal forbidden factorInfimum and supremumToeplitz matrixComputational Theory and Mathematics010201 computation theory & mathematicsCyclic complexityBounded functionComplexity functionCombinatorics (math.CO)Word (group theory)Computer Science::Formal Languages and Automata TheoryComputer Science - Discrete Mathematics
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Compact 20-pass thin-disk amplifier insensitive to thermal lensing

2019

We present a multi-pass amplifier which passively compensates for distortions of the spherical phase front occurring in the active medium. The design is based on the Fourier transform propagation which makes the output beam parameters insensitive to variation of thermal lens effects in the active medium. The realized system allows for 20 reflections on the active medium and delivers a small signal gain of 30 with M$^2$ = 1.16. Its novel geometry combining Fourier transform propagations with 4f-imaging stages as well as a compact array of adjustable mirrors allows for a layout with a footprint of 400 mm x 1000 mm.

FOS: Physical sciences02 engineering and technology7. Clean energy01 natural scienceslaw.invention010309 opticsFootprint (electronics)symbols.namesake020210 optoelectronics & photonicsOpticslaw0103 physical sciencesThermal0202 electrical engineering electronic engineering information engineeringThin-disk lasers; Multi-pass amplifier; Optical Fourier transform; High power; Relay imaging; Thermal lens; Mirror arrayPhysicsbusiness.industryAmplifierLens (optics)Fourier transformThin disksymbolsThermal lensingbusinessBeam (structure)Optics (physics.optics)Physics - Optics
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Spontaneous emission of a sodium Rydberg atom close to an optical nanofibre

2019

International audience; We report on numerical calculations of the spontaneous emission rate of a Rydberg-excited sodium atom in the vicinity of an optical nanobre. In particular, we study how this rate varies with the distance of the atom to the bre, the bre's radius, the symmetry s or p of the Rydberg state as well as its principal quantum number. We nd that a fraction of the spontaneously emitted light can be captured and guided along the bre. This suggests that such a setup could be used for networking atomic ensembles, manipulated in a collective way due to the Rydberg blockade phenomenon.

FOS: Physical sciences02 engineering and technologyoptical nanofibres01 natural sciencessymbols.namesake020210 optoelectronics & photonics[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]0103 physical sciencesAtomPrincipal quantum number0202 electrical engineering electronic engineering information engineeringSpontaneous emissionPhysics::Atomic Physics010306 general physicsPhysicsQuantum Physics[PHYS.PHYS.PHYS-ATOM-PH]Physics [physics]/Physics [physics]/Atomic Physics [physics.atom-ph]Spontaneous emission ratesRadiusCondensed Matter Physicsspontaneous emission ratesAtomic and Molecular Physics and OpticsSymmetry (physics)Optical nanobresRydberg atomRydberg formulasymbols[PHYS.PHYS.PHYS-CHEM-PH]Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph]Atomic physicsRydberg stateQuantum Physics (quant-ph)Rydberg atoms
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The temporal analogue of diffractive couplers

2020

International audience; Based on the space-time duality of light, we numerically demonstrate that temporal dispersion grating couplers can generate from a single pulse an array of replicas of equal amplitude. The phase-only profile of the temporal grating is optimized by a genetic algorithm that takes into account the optoelectronic bandwidth limitations of the setup.

FOS: Physical sciencesDuality (optimization)Physics::Optics02 engineering and technologyGrating01 natural sciences010309 optics020210 optoelectronics & photonicsOptics0103 physical sciencesDispersion (optics)Genetic algorithm0202 electrical engineering electronic engineering information engineeringUltrafast processingPhysics[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics]business.industryBandwidth (signal processing)Single pulseGeneral MedicineQC350-467Optics. LightAmplitudePhase modulationSpace-time analogybusinessOptics (physics.optics)Physics - Optics
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Hyperspectral optical near-field imaging: Looking graded photonic crystals and photonic metamaterials in color

2012

International audience; Using a scanning near-field optical microscope operating with a hyperspectral detection scheme, we report the direct observation of the mirage effect within an on-chip integrated artificial material made of a two dimensional graded photonic crystal. The light rainbow due to the material dispersion is quantified experimentally and quantitatively compared to three dimensional plane wave assisted Hamiltonian optics predictions of light propagation.

FREQUENCIESMaterials sciencePhysics and Astronomy (miscellaneous)business.industryNear-field opticsPlane waveMetamaterialHyperspectral imaging02 engineering and technologyHamiltonian optics021001 nanoscience & nanotechnology01 natural sciencesPhotonic metamaterial[SPI.AUTO]Engineering Sciences [physics]/AutomaticOpticsLIGHT0103 physical sciencesDispersion (optics)OptoelectronicsSPACE010306 general physics0210 nano-technologybusinessSILICONPhotonic crystal
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Optimized substrates and measurement approaches for Raman spectroscopy of graphene nanoribbons

2019

The on-surface synthesis of graphene nanoribbons (GNRs) allows for the fabrication of atomically precise narrow GNRs. Despite their exceptional properties which can be tuned by ribbon width and edge structure, significant challenges remain for GNR processing and characterization. In this contribution, we use Raman spectroscopy to characterize different types of GNRs on their growth substrate and to track their quality upon substrate transfer. We present a Raman-optimized (RO) device substrate and an optimized mapping approach that allows for acquisition of high-resolution Raman spectra, achieving enhancement factors as high as 120 with respect to signals measured on standard SiO2/Si substra…

Fabrication530 PhysicsFOS: Physical sciences02 engineering and technologySubstrate (electronics)01 natural sciencessymbols.namesakeQuality (physics)540 Chemistry0103 physical sciencesRibbon010302 applied physicsCondensed Matter - Materials Sciencebusiness.industryMaterials Science (cond-mat.mtrl-sci)021001 nanoscience & nanotechnologyCondensed Matter PhysicsElectronic Optical and Magnetic MaterialsCharacterization (materials science)Molecular vibrationsymbols570 Life sciences; biologyOptoelectronics0210 nano-technologybusinessRaman spectroscopyGraphene nanoribbons
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Fabrication of polarizing photonic crystal fibres and photonic crystal fibre tapers: Applications

2007

We report the fabrication of an anisotropic photonic crystal fibre with polarization properties and photonic crystal fibre tapers for supercontinuum generation. The anisotropy of the fibre was created by enlarging four airholes next to the silica core. Different polarization regimes as a function of the geometric parameters, including polarizing behaviour at 1.55 mum, were obtained. In the second part of the paper, we report the fabrication of photonic crystal fibre tapers. We present experimental results on supercontinuum generation in photonic crystal fibre tapers using quasi-continuous pump pulses of 7 ns duration at 532 nm and at 1064 nm.

FabricationBirefringenceMaterials sciencebusiness.industryPhysics::OpticsNonlinear opticsYablonoviteSupercontinuumSubwavelength-diameter optical fibreOpticsOptoelectronicsbusinessPhotonic-crystal fiberPhotonic crystal
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Label swapper device for spectral amplitude coded optical packet networks monolithically integrated on InP

2011

In this paper the design, fabrication and experimental characterization of an spectral amplitude coded (SAC) optical label swapper monolithically integrated on Indium Phosphide (InP) is presented. The device has a footprint of 4.8x1.5 mm 2 and is able to perform label swapping operations required in SAC at a speed of 155 Mbps. The device was manufactured in InP using a multiple purpose generic integration scheme. Compared to previous SAC label swapper demonstrations, using discrete component assembly, this label swapper chip operates two order of magnitudes faster. © 2011 Optical Society of America.

FabricationComputer sciencePacket networksPhosphinesIntegrationIndium phosphideIndiumSemiconductor laser theoryFootprint (electronics)chemistry.chemical_compoundDiscrete componentsSpectral amplitudeComputer Communication NetworksTEORIA DE LA SEÑAL Y COMUNICACIONESMonolithically integratedOptical labelsOptical amplifierSignal processingbusiness.industryExperimental characterizationInPOptical DevicesSignal Processing Computer-AssistedEquipment DesignChipIntegration schemeAtomic and Molecular Physics and OpticsOptical packet networksEquipment Failure Analysischemistryvisual_artElectronic componentvisual_art.visual_art_mediumIndium phosphideOptoelectronicsMonolithic integrated circuitsbusinessLabel swapping
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Nonlinear Characterisation of an AsSe Chalcogenide Holey Fiber

2009

oral session TuA " Highly Nonlinear Fibers " [TuA1]; International audience; We report the nonlinear characterization of a chalcogenide holey fiber, based on the AsSe glass composition. A nonlinear coefficient as high as 15 000 W-1 km-1 has been measured.

FabricationKerr effectOptical fiberMaterials science[SPI.OPTI] Engineering Sciences [physics]/Optics / PhotonicChalcogenideChalcogenide glass02 engineering and technology01 natural scienceslaw.invention010309 opticschemistry.chemical_compound020210 optoelectronics & photonicsOpticslaw0103 physical sciences0202 electrical engineering electronic engineering information engineeringbusiness.industryNonlinear opticsNonlinear systemchemistry[SPI.OPTI]Engineering Sciences [physics]/Optics / PhotonicOptoelectronics[ SPI.OPTI ] Engineering Sciences [physics]/Optics / PhotonicbusinessRefractive index
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