We theoretically investigate how phase-only spatial light modulation can enable controlling and focusing the second-harmonic light generated in transparent nonlinear random structures. The studied structures are composed of domains with random sizes and antiparallel polarization, which accurately model widely used ferroelectric crystals such as strontium barium niobate. Using a first-principles Green-function formalism, we account for the effect that spatial light modulation of the fundamental beam introduces into the second-order nonlinear frequency conversion occurring in the considered class of structures. This approach provides a complete description of the physical origin of the second-harmonic light generation in the system, as well as the optimization of the light intensity in any arbitrary direction. Our numerical results show how the second-harmonic light is influenced by both the disorder in the structure and the boundaries of the crystal. Particularly, we find that the net result from the interplay between disorder and boundary effects is strongly dependent on the dimensions of the crystal and the observation direction. Remarkably, our calculations also show that although in general the maximum possible enhancement of the second-order light is the same as the one corresponding to linear light scattering in turbid media, in the Cerenkov phase matching direction the enhancement can exceed the linear limit. The theoretical analysis presented in this work expands the current understanding of light control in complex media and could contribute to the development of a new class of imaging and focusing techniques based on nonlinear frequency mixing in random optical materials.

Peer Reviewed