Search results for "GRADE"
showing 10 items of 695 documents
Group graded algebras and almost polynomial growth
2011
Let F be a field of characteristic 0, G a finite abelian group and A a G-graded algebra. We prove that A generates a variety of G-graded algebras of almost polynomial growth if and only if A has the same graded identities as one of the following algebras: (1) FCp, the group algebra of a cyclic group of order p, where p is a prime number and p||G|; (2) UT2G(F), the algebra of 2×2 upper triangular matrices over F endowed with an elementary G-grading; (3) E, the infinite dimensional Grassmann algebra with trivial G-grading; (4) in case 2||G|, EZ2, the Grassmann algebra with canonical Z2-grading.
A note on cocharacter sequence of Jordan upper triangular matrix algebra
2016
Let UJn(F) be the Jordan algebra of n × n upper triangular matrices over a field F of characteristic zero. This paper is devoted to the study of polynomial identities satisfied by UJ2(F) and UJ3(F). In particular, the goal is twofold. On one hand, we complete the description of G-graded polynomial identities of UJ2(F), where G is a finite abelian group. On the other hand, we compute the Gelfand–Kirillov dimension of the relatively free algebra of UJ2(F) and we give a bound for the Gelfand–Kirillov dimension of the relatively free algebra of UJ3(F).
The enveloping algebra of the Lie superalgebra osp(1,2)
1990
International audience
Star-products and phase space realizations of quantum groups
1992
It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
Waveguiding properties of a photonic crystal fiber with a solid core surrounded by four large air holes
2009
The polarization-dependent guiding properties of a hexagonal-lattice photonic crystal fiber with a solid-core surrounded by four large air holes are investigated. The appearance of a polarization dependent cutoff frequency, together with several parameters as the birefringence, the modal effective area, the group velocity dispersion and the polarization dependent loss are analyzed. A collection of fibers with different structural parameters were fabricated and characterized. An effective anti-guide structure from at least 450 nm to 1750 nm, a polarizing fiber with a polarization dependent loss of 16 dB/m at 1550 nm, and an endlessly singlemode polarization-maintaining fiber with group biref…
A Refractive Index Sensor Based on the Resonant Coupling to Cladding Modes in a Fiber Loop
2013
We report an easy-to-build, compact, and low-cost optical fiber refractive index sensor. It consists of a single fiber loop whose transmission spectra exhibit a series of notches produced by the resonant coupling between the fundamental mode and the cladding modes in a uniformly bent fiber. The wavelength of the notches, distributed in a wavelength span from 1,400 to 1,700 nm, can be tuned by adjusting the diameter of the fiber loop and are sensitive to refractive index changes of the external medium. Sensitivities of 170 and 800 nm per refractive index unit for water solutions and for the refractive index interval 1.40-1.442, respectively, are demonstrated. We estimate a long range resolut…
Sensitivity optimization with cladding-etched long period fiber gratings at the dispersion turning point
2016
This work presents a refractive index sensor based on a long period fiber grating (LPFG) made in a reduced cladding fiber whose low order cladding modes have the turning point at large wavelengths. The combination of these parameters results in an improved sensitivity of 8734 nm/refractive index unit (RIU) for the LP0,3 mode in the 1400-1650 wavelength range. This value is similar to that obtained with thin-film coated LPFGs, which permits to avoid the coating deposition step. The numerical simulations are in agreement with the experimental results. This work was supported in part by the Spanish Ministry of Education and Science-FEDER TEC2013-43679-R. J.L. Cruz also acknowledges financial s…
Visible Light Generation and its Influence on Supercontinuum in Chalcogenide As2S3 Microstructured Optical Fiber
2011
We demonstrate visible light generation in chalcogenide As2S3 microstructured optical fiber. The generated visible light causes irreversible damage to the fiber core because of the high absorption coefficient of chalcogenide glasses in the visible band. The SCs (supercontinua) are measured in both untapered and tapered As2S3 fibers, no wider SC is obtained in the tapered one. The SC growth is prevented by the visible light generation since the damage to the fiber core decreases the fiber transmission substantially. This effect can be avoided by designing the fiber to enable the pump source to work in single-mode operation.
Resonant and thermal changes of refractive index in a heavily doped erbium fiber pumped at wavelength 980 nm
2004
We report a theoretical and experimental study of the refractive index variation in a heavily doped erbium silica fiber within the spectral range 1500-1580 nm under the pumping at the wavelength 980 nm. The two main contributions in the refractive index change are addressed the resonant part determined by the saturation effect in the fiber and the thermal part stemming from the fiber heating due to the excited-state absorption and Stokes losses. We demonstrate that the thermal contribution in the resultant refractive index change is a notable value, which is the feature of erbium fibers with a high concentration of erbium ions.
Two-core transversally chirped microstructured optical fiber refractive index sensor
2014
We present a sensing architecture consisting of a two-core chirped microstructured optical fiber (MOF) for refractive index sensing of fluids. We show that by introducing a chirp in the hole size, the MOF can be a structure with decoupled cores, forming a Mach-Zehnder interferometer in which the analyte directly modulates the device transmittance by its differential influence on the effective refractive index of each core mode. We show that by filling all fiber holes with analyte, the sensing structure achieves high sensitivity (transmittance changes of 300 per RIU at 1.42) and has the potential for use over a wide range of analyte refractive index.