Triply periodic bicontinuous structures through interference lithography: a level-set approach

Abstract

Interference lithography holds the promise of fabricating large-area, defect-free photonic structures on the sub-micrometer scale both rapidly and cheaply. There is a need for a procedure to establish a connection between the structures that are formed and the parameters of the interfering beams. There is also a need to produce self-supporting three-dimensional bicontinuous structures. A generic technique correlating parameters of the interfering beams with the symmetry elements present in the resultant structures by a level-set approach is developed. A particular space group is ensured by equating terms of the intensity equation to a representative level surface of the desired space group. Single- and multiple-exposure techniques are discussed. The beam parameters for certain cubic bicontinuous structures relevant to photonic crystals, viz.,the diamond(D), the simple cubic (P), and the chiral gyroid (G) are derived by utilizing either linear or elliptically polarized light.

Periodic nanostructures for photonics

“…[258,261]. The approach is to take advantage of the fact that functions (essentially sums consisting of trigonometric functions) of known crystal symmetry-which is generally different from the translational symmetry discussed above-are available from crystallography for all of the 230 space groups in three dimensions [258,262]. These functions are given in the crystal coordinate system (generally not a Cartesian system), whereas the above interference pattern (2.39) is quoted in the Cartesian laboratory frame.…”

Three-Dimensionally-Patterned Submicrometer-Scale Hydrogel/Air Networks That Offer a New Platform for Biomedical Applications

“…Interference lithography based calculations were used for the subsequent recombination of beams and to choose the appropriate structure corresponding to a given exposure dose. 39 This PMIL nanopatterning results in the formation of connected pores at the submicrometer scale. Since the swelling of the patterned hydrogel structure in developer solution (cyclopentanone in our case) is inevitable, the resultant structure shows slight pattern collapse.…”

Hypersonic phononic crystals

“…The combination of the motif and the translational periodicity determines the full set of symmetries associated with the resultant structure and hence its space group [49][50][51].…”