The dynamics of EDFA's and networks of EDFA's may have an important impact on the performance of multi channel optical communication systems and networks with wavelength routing'. A model of EDFA dynamics is needed to understand the transient behavior in large systems or networks. Most previous EDFA models are represented by sets of coupled partial differential equations, which can be solved only through iterative, computationally intensive numerical calculations, especially for multi-channel WDM systems with counter-propagating pump or signals. An exception is a steady state model2 which reduces the coupled partial differential equations to a single transcendental equation. In this letter we show that the coupled time dependent partial differential equations can be dramatically simplified, first to a set of coupled ordinary differential equations and then further to a single ordinary differential equation. The simulation results agree with experimental data. atoms in the first excited state Nz(z, t) and the photon equation for the kth channel are2, respectively, Under conditions that are commonly satisfied in WDM systems, the rate equation for the fraction of where p is the number density of the active erbium atoms in the fiber core of cross-section S, and T is the spontaneous lifetime of the upper level. There are N optical channels each of wavelength and optical power p k ( Z , t) at location z and time t, with confinement factor r k and emission and absorption cross sections ut and o: , respectively. The optical powers are expressed in units of number of photons per unit time. Beams traveling along the z direction are indicated by unit vector Uk = f l ; beams moving the opposite direction by U k = -1. The upper state population can be found from the photon equation, which is then substituted into the rate equation to obtain, -a k aPj(z, t ) az N 8 1 a P k ( z , t ) T u k -at (-p k az ) = -U k where f & = p r k a g is the absorption constant and P~S = s/rk ( o~ + 0 ; ) r is the intrinsic saturation power of the kth channel. After integration over z from 0 to L, we have, N pis [ T y f G k ( t ) f Ak] = -Pj'"(t) [exp (Gj(t)) -11, j=1 where G k ( t ) = In [ F t ( ( t ) / P p ( t ) ]is the overall gain parameter, Ak = a k h is the total absorption constant where L is the length of the erbium-doped fiber, and PF(t) and p t ( t ) are the input and output powers of the kth channel at time t. With given input power @ ( t ) and initial conditions G k ( 0 ) = for all the channels, the above set of coupled ordinary differential equations c m be numerically solved.These coupled ordinary differential equations can be further reduced to a single equation. Since the right side of the above equation is the same for all the channels, we can express the gain of channel j in terms of 365

To achieve wavelength-selectable and stable erbium-doped fiber (EDF) laser, a dual-Sagnacring configuration is designed to reach single-longitudinal-mode (SLM) oscillation and power-flattened output simultaneously. The presented and experimentally demonstrated EDF laser can also obtain the output power of 7.5 to 11.8 dBm in the continuous-wave (CW) tunability of 1523.0 to 1571.0 nm. Here, the power variation of lasing wavelength can be below than 1.0 dB over a wide working range of 1525.0-1565.0 nm for power-flattened output. Moreover, the 3-dB spectrum linewidth of presented EDF-based laser is measured in the range of 16.4-22.2 kHz via the Lorentzian fitting.

In this demonstration, an erbium-doped fiber (EDF) based laser with stable, wide and wavelength-selectable single-longitudinal-mode (SLM) performances is designed and demonstrated. Here, to achieve SLM oscillation, a compound-ring scheme is constructed in the EDF laser cavity serving as a mode-restriction-filter for densely side-mode suppression. Moreover, the continuous-wave tunability can be scaled from 1520.0 to 1582.0 nm by using the proposed compound-ring scheme and commercial C-band EDF amplifier. In the measurement, the output stability and 3 dB Lorentzian linewidth of each lasing wavelength in the proposed EDF compound-ring laser have also been discussed.

Restenosis remains a significant problem after angioplasty of hemodialysis vascular access. Both experimental and clinical studies have shown a protective effect of antioxidants against post-angioplasty restenosis. A prospective, randomized, feasibility study was conducted to investigate the effect of ascorbic acid to prevent restenosis. Ninety-three hemodialysis patients were randomized into three groups after angioplasty: placebo (n = 31), 300 mg ascorbic acid (n = 31), and 600 mg ascorbic acid (n = 31), treated intravenously 3 times per week for 3 months. Eighty-nine completed the clinical follow-up, and 81 had angiographic follow-up. In the angiographic follow-up, the mean (stand deviation) late loss of luminal diameter for the placebo, 300 mg, and 600 mg groups were 3.15 (1.68) mm, 2.52 (1.70) mm (P = 0.39 vs. placebo group), and 1.59 (1.67) mm (P = 0.006, vs. placebo group), with corresponding angiographic binary restenosis of 79%, 67% (P = 0.38 vs. placebo group), and 54% (P = 0.08 vs. placebo group). The post-interventional primary patency rates at 3 months were 47%, 55% (P = 0.59 vs. placebo group), and 70% (P = 0.18 vs. placebo group) for placebo, 300 mg, and 600 mg groups. Our results demonstrated that intravenous 600 mg ascorbic acid was a feasible therapy and might attenuate restenosis after angioplasty; however, its effect on post-interventional primary patency was modest.

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