Studies of the self-imaging effect in multimode waveguides

Optical waveguide structures have long been used for various applications, such as couplers or junctions. More recently complex waveguides are also applied to the design of filters or for signal processing. In this article, we would like to mention arrayed waveguide gratings (AWG) that are key-components for WDM - (Wavelength Division Multiplex) systems. Such AWGs are quasi-periodic structures. Other components are based on self-imaging, meaning that an input pattern repeats itself after a certain distance. Depending on the examined angles of the wave propagation we might distinguish between the Talbot or the Montgomery-effect, where the former is a special case of the latter. It was shown that the Talbot-effect can be used to design a time-domain filter. The behavior in time domain was examined recently with femtosecond pulses. The goal of this work is now to utilize the self-imaging effect in waveguides to design e.g. time filters or other circuits like couplers. For this purpose we did some theoretical examinations with the Method of Lines (MoL). In this contribution we begin with a description of the Talbot and Montgomery effect, followed by a short introduction of the applied numerical method. Finally, we show numerical results for the wave propagation in multimode-waveguides.