Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {Ch. Sch\"{u}tte and M. Dinand and G. W. Zumbusch and R.
  title = {Dynamics of {E}rbium-doped Waveguide Lasers: Modelling,
		  Reliable Simulation, and Comparison with Experiments},
  institution = {Konrad-Zuse-Zentrum},
  address = {Berlin, Germany},
  year = {1995},
  number = {SC-95-19},
  ps = { 1},
  pdf = { 1},
  annote = {unrefereed},
  abstract = { A theoretical investigation of the dynamic properties of
		  integrated optical Erbium doped waveguide lasers is
		  presented. It includes the construction of a physical model
		  and of numerical techniques which allow reliable
		  simulations of the dynamical behaviour of the laser signal
		  depending on essential parameters of the laser device and
		  on its external, time-dependent pump radiation. Therefore,
		  a physical theory is developed which describes the
		  propagation of light and its interaction with the active
		  substrate in the laser cavity. This is realized in two
		  steps. First, a fundamental model based on Maxwell's
		  equations and on rate equations for the transitions in the
		  active medium is constructed. Since this turns out to
		  prohibit reliable simulations, it is, in a second step,
		  reformulated via averaging in time and space which
		  suppresses the fluctuations on the fastest time scales but
		  represents them correctly. For this reduced model reliable
		  and efficient simulation techniques using adaptive control
		  schemes are designed and implemented. We apply the linear
		  implicit Euler discretization with extrapolation in time
		  and a multilevel quadrature scheme in space. Finally the
		  model is justified in comparison with experimental
		  observations in four cases of technological relevance. }