Tunable Localization and Oscillation of Optical Signals in Planar Graded Optical Waveguide Arrays

The optical Bloch oscillation has been studied theoretically in planar graded optical waveguide arrays with nearest-neighbor couplings. The gradient in the propagation constants can be achieved conveniently by the eletro-optic effects. We identified a variety of normal modes (called gradons) in the waveguide arrays with the aid of a phase diagram. Moreover, the localization properties of the normal modes are characterized and the transitions among these modes are obtained from the analysis of a picture of overlapping bands. The existence of the Bloch oscillation and other oscillations are confirmed by using the field evolution analysis with various initial Gaussian beams. From the results, we obtain a correspondence between gradon localization and Bloch oscillation. The results offer great potential applications in controlling wave propagation by means of graded materials and graded systems, which can be used to explore the tunability of light manipulation and applied to design suitable optical devices.