The diffraction properties of optical signals by multi-layered periodic structures is formulated in two-dimensional space by using Fourier expansions associated with basic grating profile. The fields in each layer are then expressed in terms of characteristic modes, and the complete solution is found rigorously by using a modal transmission-line theory(MTLT) to address the pertinent boundary-value problems. Such an approach can treat periodic arbitrary gratings containing arbitrarily shaped dielectric components, which may generally have optical properties along directions that are parallel or perpendicular to the multi-layers. This paper illustrates the present approach by comparing our numerical results with data reported in the past for simple periodic circular 2D structures. In addition, this proposed theory can apply easily for more complex configurations, which include multiple periodic regions with several possible canonic shapes and high dielectric constants.