Modeling of optical amplifier waveguide based on silicon nanostructures and rare earth ions doped silica matrix gain media by a finite-difference time-domain method: comparison of achievable gain with Er³⁺or Nd³⁺ions dopants

Abstract

A comparative study of the gain achievement is performed in a waveguide optical amplifier whose active layer is constituted by a silica matrix containing silicon nanograins acting as sensitizer of either neodymium ions (Nd 3+ ) or erbium ions (Er 3+ ). Due to the large difference between population levels characteristic times (ms) and finite-difference time step (10 −17 s), the conventional auxiliary differential equation and finite-difference time-domain (ADE-FDTD) method is not appropriate to treat such systems. Consequently, a new two loops algorithm based on ADE-FDTD method is presented in order to model this waveguide optical amplifier. We investigate the steady states regime of both rare earth ions and silicon nanograins levels populations as well as the electromagnetic field for different pumping powers ranging from 1 to 10 4 mW.mm -2 . Furthermore, the three dimensional distribution of achievable gain per unit length has been estimated in this pumping range. The Nd 3+ doped waveguide shows a higher gross gain per unit length at 1064 nm (up to 30 dB.cm -1 ) than the one with Er 3+ doped active layer at 1532 nm (up to 2 dB.cm -1 ). Considering the experimental background losses found on those waveguides we demonstrate that a significant positive net gain can only be achieved with the Nd 3+ doped waveguide. The developed algorithm is stable and applicable to optical gain materials with emitters having a wide range of characteristic lifetimes.The FDTD method is based on time and space discretization scheme of Maxwell equations proposed by Yee 12 which allows to calculate the propagation of electromagnetic field (E,H) in time domain. 13 The ADE method consists in the use of extra terms such as current density J or polarization density P which are solutions