  Analogous to time signals that can be composed of multiple frequency
functions, we use uniquely structured orthogonal spatial modes to create
different beam shapes. We tailor the spatial structure by judiciously choosing
a weighted combination of multiple modal states within an orthogonal basis set,
and we can tunably create beam phase and intensity "shapes" that are not
otherwise readily achievable. As an example shape, we use a series of
orbital-angular-momentum (OAM) functions with adjustable complex weights to
create a reconfigurable spatial region of higher localized power as compared to
traditional beam combining. We simulate a structured beam created by coherently
combining several orthogonal OAM beams with different complex weights, and we
achieve a >10X localized power density enhancement with 19 beams. Additionally,
we can create unique shapes by passing a single beam through a specially
designed phase and intensity mask that contains the combination of multiple OAM
functions each with complex weights. Using this approach, we experimentally
demonstrate a ~2.5X localized power density increase when utilizing 9
functions.
