Beam shaping using genetically optimized two-dimensional photonic crystals

We propose the use of two-dimensional photonic crystals with engineered defects for the generation of an arbitrary-profile beam from a focused input beam. The cylindrical harmonics expansion of complex-source beams is derived and used to compute the scattered wavefunction of a 2D photonic crystal via the multiple scattering method. The beam shaping problem is then solved using a genetic algorithm. We illustrate our procedure by generating different orders of Hermite-Gauss profiles, while maintaining reasonable losses and tolerance to variations in the input beam and the slab refractive index.