Fig. 1.

Illustration of methods for mode control in the fiber mode basis. (a) Mode control via excitation and generation of pure fiber modes. (b) Fiber mode composition of the input and output fields in (a). Since individual pure modes are excited and detected, their corresponding mode compositions are identical delta functions. (c) Proposed method for mode control in the fiber mode basis via excitation of Hadamard functions and detection of focal spots. (d) Fiber mode composition of the input and output fields in (c). Since Hadamard functions and focal spots are complex combinations of the individual fiber modes, their mode compositions are distinct complex signals. By performing a change of basis we can select the fiber modes that we control at the output and minimize the other mode coefficients. Here, as an example we minimize the second half higher order mode coefficients in order to generate a target output pattern using only the first half lower order modes.