The variations of lower-order TM mode size and corresponding eå ective refractive index, eå ective pump area and coupling eae ciency between pump and laser modes with the controllable fabrication parameters, i.e. initial Ti-strip width W, diå usion temperature T and initial Ti-strip thickness H in ccut Ti-diå used Nd:LiNbO 3 waveguide lasers have been calculated by using a variational method, taking into account both laser wavelength, 1085 nm, and pump wavelength, 815 nm. The main features of these curves were summarized and discussed in detail; consequently, the single-mode, fundamental mode cutoå and multimode conditions were presented and compared with the published experimental data. The eå ective pump area, directly proportional to threshold pump power, reveals a weak dependence on W in the considered range 4± 16 mm and strong dependences on T and H in, respectively, the ranges studied 950± 1100 8 C and 40± 160 nm, while the coupling eae ciency, directly proportional to slope eae ciency, is hardly changed (with the values 0.82± 0.85) with these parameters. Finally, appropriate diå usion parameters were proposed for the fabrication of a more eae cient laser.
IntroductionNd:LiNbO 3 has been extensively studied as a promising solid laser material which combines the excellent laser properties of Nd 3 ‡ with the electro-optic, acousto-optic and nonlinear optical properties of LiNbO 3 . The doping of MgO and pumping at the near-infrared wavelength (815 nm) have practically eliminated photorefractive damage even in the case of high pumping intensity. In a waveguide con® guration this combination could lead to highly eae cient laser diode pumped lasers and ampli® ers, self-frequency-doubled, self Q-switched lasers, etc. Recently, continuous-wave (CW) operation annealed proton exchange (APE) Nd:MgO:LiNbO 3 [1± 5], Ti-diå used Nd:MgO:LiNbO 3 [6] and Nd:LiNbO 3 [7] channel waveguide lasers and integrated devices, including FM mode-locked [8], Q-switched [9] and pulsed [10] waveguide lasers, have been successfully demonstrated. The optimization of the laser eae ciency of Ti-diå used Nd:LiNbO 3 waveguide lasers requires knowledge of the dependence of mode size and the corresponding eå ective refractive index, optical loss, threshold pump power and slope eae ciency on controllable waveguide fabrication parameters. From these dependences the waveguide fabrication parameters can be optimized. The variation of the optical loss with diå usion temperature at 1.15 mm has been investigated