Approximate analytical description for fundamental-mode fields of graded-index fibers: Beyond the Gaussian approximation

An approximate analytical description for fundamental-mode fields of graded-index fibers is explicitly presented by use of the power-series expansion method, the maximum-value condition at the fiber axis, the decay properties of fundamental-mode fields at large distance from the fiber axis, and the approximate modal parameters U obtained from the Gaussian approximation. This analytical description is much more accurate than the Gaussian approximation and at the same time keep the simplicity of the latter. As two special examples, we present the approximate analytical formulas for the fundamental-mode fields of a step profile fiber and a Gaussian profile fiber, and we find that they are both highly accurate in the single-mode range by comparing them with the corresponding exact solutions.

The analytical description and experiments of the optical bottle generated by an axicon and a lens

Based on the interferential theory, we deduce a new type of analytic expression suitable for describing the evolutions of the optical bottle beam generated from the axicon-lens optical system illuminated by the Gaussian beam for the first time. The theory does not use much approximation in the process of mathematical analysis and can better illustrate the optical bottle beam evolutions at any positions. With the derived expression, the three-dimensional (3D) longitudinal and transverse intensity profiles of the optical bottle beam are simulated numerically. The numerical calculations have been confirmed by the experimental results.

Effects of annealing on the color, absorption spectra, and light yield of Ce : YAlO3 single crystal grown by the temperature gradient technique

YAlO3 single crystal doped with Ce3+ at concentration 1% was grown by the temperature gradient technique. The as-grown crystal was pink. After H-2 annealing or air annealing at 1400degreesC for 20 h, the crystal was turned into colorless. We concluded there were two kinds of color centers in the as-grown crystal. One is F+ center attributed to absorption band peaking at about 530 nm, the other is O- center attributed to absorption band peaking at about 390 nm. This color centers model can be applied in explaining the experiment phenomena including the color changes, the absorption spectra changes, and the light yield changes of Ce:YAP crystals before and after annealing. (C) 2004 American Institute of Physics.

Phi 140 mm sapphire crystal growth by temperature gradient techniques and its color centers

Sapphire crystals, 140 mm in diameter and 90 turn in height, have been grown by temperature gradient techniques (TGT). The growth direction of the boule was fixed by means of Lane X-ray diffraction. A prominent 204 nm absorption band in TGT-Al2O3. which does not appear in single crystals grown by Czochralski method has been studied. Analysis further substantiates the F-center model of this band. Two relatively weaker bands absorbing at 232 nm and 254 nm were ascribed to F+ centers. F-type centers concentration was determined using Smakula's equation. (c) 2005 Elsevier B.V. All rights reserved.

Color centers and charge state change in Ce : YAG crystals grown by temperature gradient techniques

Color centers and impurity defects of Ce:YAG crystals grown in reduction atmosphere by temperature gradient techniques have been investigated by means of gamma irradiation and thermal treatments. Four absorption bands associated with color centers or impurity defects at 235, 255, 294 and 370 nm were observed in as-grown crystals. Changes in optical intensity of the 235 and 370 nm bands after gamma irradiation indicate that they are associated with F+-type color center. Charge state change processes of Fe3+ impurity and Ce3+ ions take place in the irradiation process. The variations of Ce3+ ions concentration clearly indicate that Ce4+ ions exist in Ce:YAG crystals and gamma irradiations could increase the concentration of Ce3+ ions. Annealing treatments and the changes in optical density suggest that a heterovalent impurity ion associated with the 294 nm band seems to be present in the crystals. (c) 2005 Elsevier B.V. All rights reserved.

Color centers and charge state recharge in gamma-irradiated Yb : YAP

Gamma-ray irradiation induced color centers and charge state recharge of impurity and doped ion in 10 at.% Yb:YAP have been studied. The change in the additional absorption (AA) spectra is mainly related to the charge exchange of the impurity Fe2+, Fe3+ and Yb3+ ions. Two impurity color center bands at 255 and 313 nm were attributed to Fe3+ and Fe2+ ions, respectively. The broad AA band centered at 385 nm may be associated with the cation vacancies and F-type center. The transition Yb3+ -> Yb2+ takes place in the process of gamma-irradiation. Oxygen annealing and gamma-ray irradiation lead to an opposite effect on the absorption properties of the Yb:YAP crystal. In the air annealing process, the transition Fe2+ -> Fe3+ and Yb2+ -> Yb3+ take place and the color centers responsible for the 385 nm band was destroyed. (c) 2005 Elsevier B.V. All rights reserved.

Color centers in Yb : YAG crystals grown by temperature-gradient techniques

Yb: YAG (Yb: Y3Al5O12) crystals have been grown by temperature-gradient techniques (TGT) and their color centers and impurity defects were investigated by means of gamma irradiations and thermal treatment. Two color centers located at 255 and 290 nm were observed in the as-grown TGT-Yb: YAG. Analysis shows that the 255 nm band may be associated with Fe3+ ions. Absorption intensity changes of the 290 nm band after gamma irradiation and thermal treatment indicate that this band may be associated with oxygen-vacancy defects. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.