1.76 μm on-chip gain characteristics of Tm3+ in a rib waveguide based on Tm3+-doped LiNbO3 thin-film on insulator

A theoretical study has been performed on 1.76 mu m on-chip amplification characteristics of Tm3+ in a rib waveguide of LiNbO3 on insulator (Tm:LNOI) under 795 nm wavelength pumping. Steady-state rate equations and propagation equations of signal and pump waves are established on the basis of a three-level model of Tm3+ system with the cross relaxation process H-3(4)-> F-3(4): H-3(6)-> F-3(4) included. The validity of the three-level model is demonstrated by referencing previously reported experiment result of Er3+-doped LNOI waveguide amplifier and by examining the effect of Tm3+ blue upconversion emissions on the 1.76 mu m amplification. Besides the relations of signal gain to propagation length, launched pump power and input signal power, the effects of waveguide cross-section geometry and Tm3+ concentration on the gain characteristics are also studied. The results show that the waveguide cross-section geometry affects definitely the gain performance via its effect on mode field. The Tm3+ concentration affects the signal gain also via its effect on the H-3(4)-> F-3(4): H-3(6)-> F-3(4) cross relaxation coefficient, besides the conventional effect that higher active ion concentration yields larger signal gain. A comparison with conventional Ti4+(Zn2+)-diffused Tm3+-doped LN [Ti(Zn):Tm:LN] waveguide shows that the Tm:LNOI waveguide has much better gain performance than the Ti(Zn):Tm:LN waveguide, including much stronger pump power and propagation distance dependences of signal gain, much higher signal gain and much lower threshold pump power. These features are associated with significantly increased Tm3+ population inversion extent due to ultra-compact mode field and larger overlapping factor of mode field and Tm3+ population profiles in the Tm:LNOI waveguide.