Analytic solution to field distribution in two-dimensional inhomogeneous waveguides

We present a novel theoretical approach for analytically solving wave propagation through two-dimensional (2D) inhomogeneous slab waveguides. The validity and reliability of our analytical approach is verified by its application to electrical field distribution in 2D waveguides, when compared with numerically exact solution. The main advantage of this theoretical treatment is that the obtained solution is global and can be presented in an analytical form. The effects of the refractive index profile on the guided modes are analyzed by introducing the field distributions of the guided modes. Our analytical calculations show significant potential for use in various applications.