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Analogous to time signals that can be composed of multiple frequencyfunctions, we use uniquely structured orthogonal spatial modes to createdifferent beam shapes. We tailor the spatial structure by judiciously choosinga weighted combination of multiple modal states within an orthogonal basis set,and we can tunably create beam phase and intensity "shapes" that are nototherwise readily achievable. As an example shape, we use a series oforbital-angular-momentum (OAM) functions with adjustable complex weights tocreate a reconfigurable spatial region of higher localized power as compared totraditional beam combining. We simulate a structured beam created by coherentlycombining several orthogonal OAM beams with different complex weights, and weachieve a >10X localized power density enhancement with 19 beams. Additionally,we can create unique shapes by passing a single beam through a speciallydesigned phase and intensity mask that contains the combination of multiple OAMfunctions each with complex weights. Using this approach, we experimentallydemonstrate a ~2.5X localized power density increase when utilizing 9functions.

Spatial Phase and Amplitude Structuring of Beams Using a Combination of Multiple Orthogonal Spatial Functions with Complex Coefficients