Discrete Optics in Femtosecond Laser Written Waveguide Arrays

The miniaturization of integrated optical devices can achieve geometric dimensions where crosstalk between adjacent waveguides is no longer negligible. In discrete optics, such interactions can be explained using the well-known coupled mode theory [1]. Based on this fundamental theory, systems of coupled waveguides are reduced to systems of discrete, i.e. countable, cells, and the spatial electromagnetic field is separated into the transverse mode profile of each waveguide and a longitudinal dependent amplitude. In the last years, femtosecond laser waveguide writing has been established as a versatile technique to fabricate three-dimensional optical waveguide systems. The following chapter begins with an overview of the basic principles of discrete light propagation. Linear propagation effects are envisaged in the second section. Here, straight and curved lattices are discussed. In the last section, third order nonlinearity is introduced to comprehend nonlinear propagation effects, which provide essential concepts for the development of ultrafast switching and routing devices.