This thesis is an exploration of numerical modeling and design of intra-cavity frequency doubled green lasers, which is one of the three key light sources in laser display systems. In this thesis the time-domain traveling wave (TDTW) model, which is well developed to model integrated photonic devices, is derived for modeling and design of a new proposed device. The device is based on the intra-cavity frequency doubling of high power distributed Bragg reflector laser diodes (DBRLD) and MgO-doped periodically poled lithium niobate (MgO:PPLN) waveguides. The numerical modeling and design suggest the superiority of the proposed intra-cavity frequency doubled DBR-LD/MgO:PPLN green laser over traditional single-pass frequency doubled DBRLD-LD/MgO:PPLN green laser. A plane-wave based coupled-wave model is implemented to model miniature intra-cavity frequency doubled DPSS lasers. Good agreement between the planewave model and experiment has been obtained. By employing the plane-wave model, we have explained the phase problem in our optical contact Nd:YVO4/MgO:PPLN green laser. Design examples of wide temperature operation of Nd:YVO4/MgO:PPLN green lasers are also completed by this numerical method. Finally, to model high power bulk intra-cavity frequency doubled diodepumped solid-state (DPSS) green lasers, a three-dimensional coupled-wave model is developed and compared with experimental results. A two-dimensional thermal model is incorporated into the three-dimensional coupled-wave equations to model thermal lensing and thermal de-phasing effects in intra-cavity frequency doubled DPSS lasers. The numerical models we developed are validated by the experimental results. / Thesis / Doctor of Philosophy (PhD)