Spectral noise analysis of single- and double-pass Er³⁺- doped LiNbO₃waveguide amplifiers

Modelling the output statistics of Er-doped LiNbO3 curved waveguide amplifiers

“…In order to analyse the interaction of the pump and signal photons with Er 3 ‡ ions in LiNbO 3 in the wavelength range 1440 nm < ¶ < 1640 nm, we consider a quasi-two-level system model, and we neglect the excited state absorption [5,9].…”

“…The absorption and emission rates of the ampli®ed spontaneous emission are W ASE 12 and W ASE 21 respectively. The interaction of the pump and signal photons with Er 3 ‡ ions can be represented using the rate equations [5,9] …”

“…The population densities N 2 of the upper atomic level and the intensities of the pump, signal and ASE ®elds are described in the linear regime by a system of coupled di erential equations [1,5,9]. For the steady-state regime ( d= dtˆ0), the system is given by three-level system is envisaged (pumpting at 980 nm), the opical pro®les would have to be calculated for each wavelength window [5,9].…”

“…For the steady-state regime ( d= dtˆ0), the system is given by three-level system is envisaged (pumpting at 980 nm), the opical pro®les would have to be calculated for each wavelength window [5,9]. ¬ km represents the optical losses.…”

“…represent the spectral gain and the ASE photon number respectively at the coordinate z [1,5]. The statistics variance is de®ned by ¼ 2 …z †ˆhn 2 …z †i ¡ ‰hn…z †iŠ 2 .…”