• Korean Journal of Optics and Photonics
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• v.16 no.3
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• pp.182-190
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• 2005

The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).

• Journal of Korean Society of Environmental Engineers
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• v.30 no.11
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• pp.1146-1153
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• 2008

Numerical simulation was carried out to study the trichloroethylene (TCE) degradation by permeable reactive barrier (PRB), and revealed the effect of concentration of TCE, iron medium mass, and concentration of iron-reducing bacteria (IRB). Newly developed model was based on axial dispersion reactor model with chemical and biological reaction terms and was implemented using MATLAB ver R2006A for the numerical solutions of dispersion, convection, and reactions over column length and elapsed time. The reaction terms include reactions of TCE degradation by zero-valent iron (ZVI, Fe$^0$) and ferrous iron (Fe$^{2+}$). TCE concentration in the column inlet was maintained as 10 mg/L. Equation for Fe$^0$ degradation includes only TCE reaction term, while one for Fe$^{2+}$ has chemical and biological reaction terms with TCE and IRB, respectively. Two coupled equations eventually modeled the change of TCE concentration in a column. At Fe$^0$ column, TCE degradation rate was found to be more than 99% from 60 hours to 235 hours, and declined to less than 1% in 1,365 hours. At the Fe$^{2+}$ and IRB mixed column, TCE degradation rate was equilibrated at 85.3% after 210 hours and kept it constant. These results imply that the ferrous iron produced by IRB has lowered the TCE degradation efficiency than ZVI but it can have higher longevity.http://kci.go.kr/kciportal/ci/contents/ciConnReprerSearchPopup.kci#