The present invention provides a multi-dimensional standing wave probe for microscale and nanoscale measurement, manipulation, and surface modification, including: a filament having a first free end and a second end that is attached to at least one actuator to apply oscillation cycles to the filament; wherein the oscillation of the filament during at least one complete cycle of oscillation of the actuator causes the free end to move in a multi-dimensional envelope, producing a defined virtual probe tip at the free end, wherein a shape of the virtual probe tip is defined by both a characteristic shape of the oscillation of the free end and a geometry of the filament. Optionally, the actuator includes a monolithic crystal actuator. Preferably, the monolithic crystal actuator includes a crystal having zero grain boundaries. The monolithic crystal actuator also includes a plurality of thin flexure structures. The monolithic crystal actuator further includes a plurality of metallic electrodes disposed on inside or outside surfaces, or a combination thereof, of the plurality of thin flexure structures.