Mingjie Zheng

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.

Anomalous Size Dependence of Inverse Participation Ratio of Eigenfunctions in Graded Elastic Lattices

We have studied the inverse participation ratio (IPR) denoted by P -1 of vibrational modes in one-dimensional graded elastic chains. The size dependence of IPR can be shown to derive from a quantum interpretation of vibrational modes. The quantum analogue of peculiar vibrational modes (gradons) to graded systems is established for the hump structure of the gradon front via the fact that the probability of a quantum particle is inversely proportional to its velocity. In this way, the envelope function can be determined analytically, and matches the mode pattern quite well. We find that the IPR exhibits an anomalous size ( N ) dependence and can be captured accurately by the relation: N P -1 = C 1 log N + C 2 , where C 1 and C 2 are constants. This interpretation is important in understanding a wide variety of properties of graded systems.

Tunable hybridization in metal nanoshell chains.

We have studied the coupled surface plasmon (SP) modes in periodic metal nanoshell chains by including long range electromagnetic interactions. The eigen-decomposition method is used to analyze the dispersion and dissipation of the SP modes. The resulting band structure can be understood as a hybridization between a hole band and a particle band with a structurally tunable band gap in the middle of the first Brillouin zone. The mode quality, which is defined as the imaginary part of the generalized polarizability, increases as the shell thickness decreases. This indicates a larger energy loss and an increasing coupling between the bands. Through the manipulation of the band structures, the propagation of the coupled SP modes in the nanoshell chain can be controlled.

Energy Relaxation in Damped Two-Dimensional Graded Elastic Lattices

We have studied the relaxation rate of vibrational modes in damped two-dimensional graded mass lattices. The relaxation rate spectrum in the weak damping limit can be obtained analytically through a perturbation theory based on the semiclassical quantum analogue envelope function. We found dip or peak structures on the relaxation rate spectrum. The dip or peak structures can be described quantitatively by the asymptotic behavior of relaxation rate at the transition frequencies. The frequency dependence of the relaxation rate is qualitatively explained by the mode patterns of gradon modes. The validity of the analytic results is confirmed by numerical solution with weak damping. In the strong damping case, we need to retain higher-order perturbations. These results can be applied to the energy relaxation in analogous systems.