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We grow accustomed to the notion that optical susceptibilities can be treatedas a local property of a medium. In the context of nonlinear optics, both Kerrand Raman processes are considered local, meaning that optical fields at onelocation do not produce a nonlinear response at distinct locations in space.This is because the electronic and phononic disturbances produced within thematerial are confined to a region that is smaller than an optical wavelength.By comparison, Brillouin interactions can result in a highly nonlocal nonlinearresponse, as the elastic waves generated through the Brillouin process canoccupy a region in space much larger than an optical wavelength. Thenonlocality of these interactions can be exploited to engineer new types ofprocesses, where highly delocalized phonon modes serve as an engineerablechannel that mediates scattering processes between light waves propagating indistinct optical waveguides. These types of nonlocal optomechanical responseshave been recently demonstrated as the basis for information transduction,however the nontrivial dynamics of such systems has yet to be explored. In thiswork, we show that the third-order nonlinear process resulting from spatiallyextended Brillouin-active phonon modes involves mixing products from spatiallyseparated, optically decoupled waveguides, yielding a nonlocal'joint-susceptibility'. We further explore the coupling of multiple acousticmodes and show that multi-mode acoustic interference enables a tailorablenonlocal-nonlinear susceptibility, exhibiting a multi-pole frequency response.

Shaping nonlinear optical response using nonlocal forward Brillouin interactions