Fabrication of arbitrary three-dimensional photonic crystals by four-plane-waves interference

Abstract

ABSTRACT This paper describes that arbitrary three-dimensional photonic crystals, so called fourteen Bravais lattices, and even a diamond structure can be fabricated by recording the four p lane-waves interference fringe. It is derived that the equation of maximum intensity point condition for interference fringe among four plane waves is the same as that between the lattice vectors and the reciprocal lattice vectors in the solid-state physics. This relation gives us the way to calculate the incident directions for four plane waves to fabricate any desired three-dimensional photonic crystal structures. The diamond structure consists of two same face centered cubic lattices, which are shifted by a quarter of their lattice constant to each other. This shift can be introduced by shifting the phases of four plane waves for interference. Therefore, the diamond structure can be fabricated by double exposures without and with phase shifts. Experimentally, a face centered cubic lattice structure was fabricated in the positive photoresist layer by using a He-Cd laser. The polarization directions of four beams were adjusted to obtain a maximum interference modulation depth. The SEM observation and the diffraction pattern observation of the fabricated sample show that the fabricated structure has a face centered cubic periodic structure. Keywords: photonic crystal, interference, holographic lithography