  On-chip Brillouin optomechanics has great potential for applications in
communications, sensing, and quantum technologies. Tight confinement of
near-infrared photons and gigahertz phonons in integrated waveguides remains a
key challenge to achieving strong on-chip Brillouin gain. Here, we propose a
new strategy to harness Brillouin gain in silicon waveguides, based on the
combination of genetic algorithm optimization and periodic subwavelength
structuration to engineer photonic and phononic modes simultaneously. The
proposed geometry is composed of a waveguide core and a lattice of anchoring
arms with a subwavelength period requiring a single etch step. The waveguide
geometry is optimized to maximize the Brillouin gain using a multi-physics
genetic algorithm. Our simulation results predict a remarkable Brillouin gain
exceeding 3300 1/(W m), for a mechanical frequency near 15 GHz.
