Theoretical study on on-chip gain characteristics of Er³⁺ in LiNbO₃-on-insulator photonic wire pumped at 980 nm wavelength

On-chip 1.53 μm amplification in 980-nm-pumped Er³⁺-doped lithium niobate on insulator (Er:LNOI) photonic wire (PW) has been studied theoretically in comparison with that in Ti:Er:LiNbO₃ waveguide on the basis of three- and six-level models of Er³⁺. We show that the six-level model gives more accurate analysis and its validity is confirmed by comparing the simulated results with the previously reported experiment data. The study shows that the Er:LNOI PW has a larger Er³⁺ population inversion extent than the Ti:Er:LiNbO₃ because of larger overlapping factor of mode field and Er³⁺ population profiles, and ultra-compact mode field. As a result, the Er:LNOI PW displays better gain performance than the Ti:Er:LiNbO₃ as described below. (1) Maximum/saturation gain of Er:LNOI PW can be as much as two/three times higher than that of the Ti:Er:LiNbO₃. (2) Gain of the Er:LNOI PW increases with propagation length more strongly in the initial stage and decreases more slowly beyond optimal length. It also shows stronger dependences on both pump power (in the initial stage) and signal power. (3) Gain in the Er:LNOI PW saturates more easily, and the Er:LNOI PW has a threshold pump power one order of magnitude lower than the Ti:Er:LiNbO₃.