Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams

A newly reported method of making three-dimensional microstructures or photonic crystals by holographic lithography has some obvious advantages over other techniques with the same purpose. A systematic and comprehensive analysis of interference of four noncoplanar beams (IFNB) is provided. It shows that all 14 Bravais lattices can be formed by means of IFNB and gives explicit relationships between each lattice and the corresponding recording geometry. The concept of pattern contrast is extended to the case of IFNB, and it is indicated that a uniform contrast for each interference term can be obtained by properly choosing the beam ratio and polarization. A calculation algorithm is then developed to optimize the direction of polarization of each beam to ensure maximum uniform contrast. These results, verified by computer simulations, may lay a theoretical foundation for fabrication of photonic crystals with the approach of IFNB.