Diode-pumped solid-state lasers (DPSSLs) with high power and good output beam quality are widely used in material processing, communication, remote sensing, and medical treatment. A preferable diode-pumped solid-state laser has the characteristics, such as high efficiency, long lifetime, high reliability, compact size and flexibility. Planar waveguide lasers can be formed by transition metal diffusion method, optical bonding technique, or ion-etching technique. Planar waveguides used for high-power lasers are usually the simplest one-dimensional waveguides, of which the width (the dimension along the ydirection) is much large than the laser wavelength. The laser beam is guided only in the xdirection as shown in Fig. 1.1. The behavior of beam along the y-direction is similar as the beam propagating in the free space. We consider a planar isotropic optical waveguide, where the active core x<d/2 is occupied by the homogeneous gain medium, and the claddings x>d/2 consist of the semi-infinite substrate. The z-axis is taken in the direction of beam propagation. The refractive index of core and cladding are n0 and n1, respectively.