Controllable optical Bloch oscillation in planar graded optical waveguide arrays

Optical Bloch oscillation is studied theoretically in planar graded optical waveguide arrays with nearest-neighbor couplings. The gradient in the propagation constants can be achieved with the eletro-optical effect. We identify 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 a picture of overlapping bands. The existence of Bloch oscillation and other oscillations are confirmed by using the field-evolution analysis with various input Gaussian beams. From the results, we obtain a correspondence between gradon localization and Bloch oscillation. This study can be extended to more general waveguide arrays in higher dimensions and with further neighbor couplings. 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.