Experimental studies of nanoscale energy localization in periodic condensed matter systems

A. J. Sievers, LASSP, Cornell University, DMR-0301035

Bright and dark envelope solitons are a characteristic signature of continuous nonlinear systems. Both bright and dark traveling, locked, intrinsic localized modes (ILMs) have now been generated in a discrete system, i.e., in the acoustic spectrum of a small nonlinear micromechanical cantilever array.

Placing the uniform driver frequency above the plane wave spectrum of this array produces a stationary ILM while placing it in the finite gaps between the plane wave modes generates ILMs that have a well defined round trip time. These same dynamical properties may be expected to occur in other small nonlinear systems such as NEMS arrays or the vibrations of quantum dots.

Experimental observations of two kinds of nonlinear localized excitations for a MEMS array displayed as cantilever site vs time. Dark regions correspond to highly excited cantilevers. (a) Stationary ILM. White horizontal lines are images of stationary cantilevers. (b) A traveling ILM that is reflected at the boundaries.

Education:Two undergraduates (Michael Gerrity, Hovig Charchaflian), two graduate students (Bruce Hubbard, Jonathan Wrubel), one postdoc (M. Sato) and one research associate (N. Agladze) contributed to this research.

Experimental studies of nanoscale energy localization in periodic condensed matter systems

A. J. Sievers, LASSP, Cornell University, DMR-0301035

Broader impact:The localization of energy observed for our nonlinear periodic cantilevers should also be relevant to some modern engineering problems, such as the vibration-induced fatigue failure of jet engine rotor blades. The large and localized vibrational blade amplitudes under forced response that are observed to appear at some rotational speeds are not predicted for a tuned linear system and have been described in terms of variations in blade geometry. From our work it is clear that even a bladed disk containing homogeneous blades of exactly the same geometry can give rise to large amplitude localized vibrations simply because each perfect nonlinear blade is coupled to its neighbors.

REU student learning how to use our ZEMAX EE ray tracing program