Optical waveguides have been a subject of an intensive theoretical research, resulting in applications in several fields, and stimulated research in integrated optics. Homogeneous dielectric waveguides and their properties are covered in detail in many articles and textbooks. However, in waveguides loaded with arbitrary inhomogeneous dielectrics, analytical solutions are possible only for a limited number of permittivity profiles in simple geometries. The analysis of longitudinally inhomogeneous waveguides has been already proposed, but the main drawback of this approach is that it requires cumbersome and time-consuming integration. We therefore suggest to take this a step further by applying our new original analytical approach that does not require integration. The aim of this work is to establish a different method that is generally applicable to any vectorial time-dependent, anisotropic, non-linear, inhomogeneous, dissipative and dispersive media to analyze the field distribution of inhomogeneous 1-D and 2-D waveguides with symmetric and asymmetric permittivity profiles. Our initial consideration of slab problems with arbitrary profiles by means of analytical method shows a great deal of potential for use in applications in fields such as physics, and engineering.