51 resultados para quadratic polynomial


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Up-conversion luminescence characteristics under 975 nm excitation have been investigated with Tb3+/Tm3+/Yb3+ triply doped tellurite glasses. Here, green (547 nm: D-5(4) --> F-7(4)) and red (660 nm: D-5(4) --> F-7(2)) up-conversion (UC) luminescence originating from Tb3+ is observed strongly, because of the quadratic dependences of emission intensities on the excitation power. Especially, the UC luminescence was intensified violently with the energy transfer from the Tm3+ ions involves in the Tb3+ excitation. To the Tb3+/Tm3+/Yb3+ triply doped glass system, a novel up-conversion mechanism is proposed as follows: the energy of (3)G(4) level (Tm3+) was transferred to D-5(4) (Tb3+) and the 477-nm UC luminescence of Tm3+ was nearly quenched. (C) 2006 Elsevier B.V. All rights reserved.

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Topography of a granite surface has an effect on the vertical positioning of a wafer stage in a lithographic tool, when the wafer stage moves on the granite. The inaccurate measurement of the topography results in a bad leveling and focusing performance. In this paper, an in situ method to measure the topography of a granite surface with high accuracy is present. In this method, a high-order polynomial is set up to express the topography of the granite surface. Two double-frequency laser interferometers are used to measure the tilts of the wafer stage in the X- and Y-directions. From the sampling tilts information, the coefficients of the high-order polynomial can be obtained by a special algorithm. Experiment results shows that the measurement reproducibility of the method is better than 10 nm. (c) 2006 Elsevier GmbH. All rights reserved.

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The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

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Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian (HG) and cosh Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.

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Infrared-to-visible upconversion fluorescence of Er(3+)/Yb(3+) co-doped lithium-strontium-lead-bismuth (LSPB) glasses for developing potential upconversion lasers has been studied under 975-nm excitation. Based on the results of energy transfer efficiency and upconversion spectra, the optimal Yb(3+)-Er(3+) concentration ratio is found to be 5:1. Intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions 2H_(11/2)-->4I_(15/2), 4S_(3/2)-->4I_(15/2), and 4F_(9/2)-->4I_(15/2), respectively, were observed. The quadratic dependence of the 525-, 546-, and 657-nm emissions on excitation power indicates that a two-photon absorption process occurs under 975-nm excitation. The high-populated 4I_(11/2) level is supposed to serve as the intermediate state responsible for the upconversion processes. The intense upconversion luminescence of Er(3+)/Yb(3+) co-doped LSPB glasses may be a potentially useful material for developing upconversion optical devices.

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We report on the energy transfer and frequency upconversion spectroscopic properties of Er3+-doped and Er3+/Yb3+-codoped TeO2-ZnO-Na2O-PbCl2 halide modified tellurite glasses upon excitation with 808 and 978 nm laser diode. Three intense emissions centered at around 529, 546 and 657 nm, alongwith a very weak blue emission at 4 10 nm have clearly been observed for the Er3+/Yb3+-codoped halide modified tellurite glasses upon excitation at 978 nm and the involved mechanisms are explained. The quadratic dependence of fluorescence on excitation laser power confirms the fact that the two-photon contribute to the infrared to green-red upconversion emissions. And the blue upconversion at 410 nm involved a sequential three-photon absorption process. (c) 2005 Elsevier Ltd. All rights reserved.

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This paper reports on the successful preparation and a detailed study on the up-conversion properties of Er3+ -doped TeO2-ZnO-PbCl2 oxylialide tellurite glasses. Three intense emissions centered at around 527, 549 and 666 nm have been clearly observed under 977 nm excitation and the involved mechanisms have been explained. The green emissions centered at 527 and 549 nin are due to the H-2(11/2 ->) I-4(15/2) and S-4(3/2) -> I-4(15/2) transitions, and the red up-conversion emission centered at 666 nm is associated with the F-4(9/2) -> I-4(15/2) transitions of Er3+ ions, respectively. The quadratic dependence of fluorescence on excitation laser power confirm that two-photons contribute to up-conversion of the green-red emissions. (c) 2005 Elsevier B.V. All rights reserved.

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Er3+ -doped strontium lead bismuth glass for developing upconversion lasers has been fabricated and characterized. The Judd-Ofelt intensity parameters Omega(1) (t = 2,4,6), calculated based on the experimental absorption spectrum and Judd-Ofelt theory, were found to be Omega(2) = 2.95 x 10(-20), Omega(4) = 0-91 X 10(-20), and Omega(6) = 0.36 x 10(-20) cm(2). Under 975 nm excitation, intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions H-2(11/2) --> I-4(15/2), S-4(3/2) I-4(15/2), and F-4(9/2) --> I-4(15/2) respectively were observed. The upconversion mechanisms are discussed based oil the energy matching and quadratic dependence on excitation power, and the dominant mechanisms are excited state absorption and energy transfer upconversion for the green and red emissions. The long-lived I-4(11/2) level is supposed to serve as the intermediate state responsible for the upconversion processes. (C) 2004 Published by Elsevier B.V.

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Er3+/Yb3+-codoped bismuthate glasses for developing potential upconversion lasers have been fabricated and characterized. The optimal Yb3+ doping content was investigated in the glasses with different Yb3+-Er3+ concentration ratios and the optimal Yb3+-Er3+ concentration ratio is 5:1. Under 975 nm excitation, intense green and red emissions centered at 525, 546 and 657 nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2) and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The quadratic dependence of the 525, 546 and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs under 975 nm excitation. (c) 2004 Elsevier Ltd. All rights reserved.

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Er3+-doped lithium-barium-lead-bismuth glass for developing upconversion lasers has been fabricated and characterized. The Judd-Ofelt intensity parameters Omega(t) (t = 2, 4, 6), calculated based on the experimental absorption spectrum and Judd-Ofelt theory, were found to be Omega(2) = 3.05 x 10(-20) cm(2), Omega(4) = 0.95 x 10(-20) cm(2), and Omega(6) = 0.39 x 10(-20) cm(2). Under 975 nm excitation, intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The upconversion mechanisms are discussed based on the energy matching and quadratic dependence on excitation power, and the dominant mechanisms are excited state absorption and energy transfer upconversion for the green and red emissions. The long-lived I-4(11/2) level is supposed to serve as the intermediate state responsible for the intense upconversion processes. The intense upconversion luminescence of Er3+-doped lithium-barium-lead-bismuth glass may be a potentially useful material for developing upconversion optical devices. (c) 2004 Elsevier B.V. All rights reserved.

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Infrared-to-visible upconversion fluorescence property of Er3+/Yb3+ codoped novel bismuth-germanium glass under 975 nm LD excitation has been studied. Intense green and red emissions centered at 525, 546 and 657 nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The quadratic dependence of the 525, 546 and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs. The structure of the bismuth-germanium glass has been investigated by peak-deconvolution of FT-Raman spectrum, and the structural information was obtained from the peak wavenumbers. This novel bismuth-germanium glass with low maximum phonon energy (similar to 750 cm(-1)) can be used as potential host material for upconversion lasers. (c) 2005 Elsevier Ltd. All rights reserved.

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Er3+/Yb3+-codoped potassium-barium-strontium-lead-bismuth glasses for developing potential upconversion lasers have been fabricated and characterized. Based on the results of energy transfer efficiency, the optimal Yb3+/Er3+ concentration ratio is found to be 5:1. Intense green and red emissions centered at 525, 546, and 657 run, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed. The quadratic dependence of the 525, 546, and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs under 975 nm excitation. The long-lived I-4(11/2) level is supposed to serve as the intermediate state responsible for the upconversion processes. (c) 2004 Elsevier B.V. All rights reserved.

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Frequency upconversion fluorescence property of Er3+-doped oxychloride germanate glass is investigated. Intense green and red emissions centred at 525, 546, and 657nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> 4I(15/2), and F-4(9/2) -> I-4(15/2), respectively, were simultaneously observed at room temperature. The quadratic dependence of the 525, 546, and 657nm emissions on excitation power indicates that a two-photon absorption process occurs under 975nm laser diode (LD) excitation. The Raman spectrum investigation indicates that oxychloride germanate glass has the maximum phonon energy at similar to 805 cm(-1). The thermal stability of this oxychloride germanate glass is evaluated by differential scanning calorimetry, and thermal stability factor Delta T (Delta T = T-x-T-g) is 187 degrees C. Intense upconversion luminescence and good thermal stability indicate that Er3+-doped oxychloride germanate glass is a promising upconversion laser material.

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We study the structural and infrared-to-visible upconversion fluorescence properties of Er3(+)/Yb3+-codoped lead-free germanium-bismuth glass. The structure of lead-free germanium-bismuth-lanthanum glass is investigated by peak-deconvolution of Raman spectroscopy. Intense green and red emissions centred at 525, 546, and 657nm, corresponding to the transitions H-2(11/2) -> (IT15/2)-I-4 -> S-4(3/2) -> 4I(15/2), and F-4(9/2) -> I-4(15/2), respectively, are observed at room temperature. The quadratic dependence of the 525, 546, and 657nm emissions on excitation power indicates that a two-photon absorption process occurs under 975nm excitation.

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Structural and infrared-to-visible upconversion fluorescence properties of Er3+/Yb3+-codoped oxychloride lead-germanium-bismuth glass have been studied. The Raman spectrum investigation indicates that PbCl2 plays an important role in the formation of glass network, and has an important influence on the upconversion luminescence owing to lower phonon energy. Intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions H-2(11/2)-->I-4(15/2,) I-4(3/2)-->I-4(15/2), and F-4(9/2)-->I-4(15/2), respectively, were observed at room temperature. The quadratic dependence of the 525, 546, and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs under 975 nm excitation. (C) 2004 Elsevier Ltd. All rights reserved.