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.
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…
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.
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.
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.
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.
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…
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.
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.
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.