Alexandre Fafin

Theoretical investigation of the more suitable rare earth to achieve high gain in waveguide based on silica containing silicon nanograins doped with either Nd3+ or Er3+ ions

We present a comparative study of the gain achievement in a waveguide whose active layer is constituted by a silica matrix containing silicon nanograins acting as sensitizer of either neodymium ions (Nd3+) or erbium ions (Er3+). By means of an auxiliary differential equation and finite difference time domain (ADE-FDTD) approach that we developed, we investigate the steady states regime of both rare earths ions and silicon nanograins levels populations as well as the electromagnetic field for different pumping powers ranging from 1 to 104 mW/mm2. Moreover, the achievable gain has been estimated in this pumping range. The Nd3+ doped waveguide shows a higher gross gain per unit length at 1064 nm (up to 30 dB/cm) than the one with Er3+ doped active layer at 1532 nm (up to 2 dB/cm). Taking into account the experimental background losses we demonstrate that a significant positive net gain can only be achieved with the Nd3+ doped waveguide.

Modeling of the electromagnetic field and level populations in a waveguide amplifier: a multi-scale time problem

A new algorithm based on auxiliary differential equation and finite difference time domain method (ADE-FDTD method) is presented to model a waveguide whose active layer is constituted of a silica matrix doped with rare-earth and silicon nanograins. The typical lifetime of rare-earth can be as large as some ms, whereas the electromagnetic field in a visible range and near-infrared is characterized by a period of the order of fs. Due to the large difference between these two characteristic times, the conventional ADE-FDTD method is not suited to treat such systems. A new algorithm is presented so that the steady state of rare earth and silicon nanograins electronic levels populations along with the electromagnetic field can be fully described. This algorithm is stable and applicable to a wide range of optical gain materials in which large differences of characteristic lifetimes are present.

Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method.

By means of ADE-FDTD method, this paper investigates the electromagnetic modelling of a rib-loaded waveguide composed of a Nd3+ doped Silicon Rich Silicon Oxide active layer sandwiched between a SiO2 bottom cladding and a SiO2 rib. The Auxilliary Differential Equations are the rate equations which govern the levels populations. The Finite Difference Time Domain (FDTD) scheme is used to solve the space and time dependent Maxwell equations which describe the electromagnetic field in a copropagating scheme of both pumping (λ pump = 488 nm) and signal (λ signal = 1064 nm) waves. Such systems are characterized by extremely different specific times such as the period of electromagnetic field ~ 10-15 s and the lifetimes of the electronic levels between ~ 10-10s and ~ 10-4 s. The time scaling method is used in addition to specific initial conditions in order to decrease the computational time. We show maps of the Poynting vector along the propagation direction as a function of the silicon nanograin (Si-ng) concentrations. A threshold value of 1024 Si-ng m-3 is extracted below which the pump wave can propagate so that a signal amplication is possible.

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

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 (Nd3+) or erbium ions (Er3+). Due to the large difference between population levels characteristic times (ms) and finite-difference time step (10−17s), 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 104 mW/mm2 . Furthermore, the three dimensional distribution of achievable gain per unit length has been estimated in this pumping range. The Nd3+ doped waveguide shows a higher gross gain per unit length at 1064 nm (up to 30 dB/cm-1) than the one with Er3+ 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 Nd3+ doped waveguide. The developed algorithm is stable and applicable to optical gain materials with emitters having a wide range of characteristic lifetimes.