Holographic fabrication of graded photonic super-quasi-crystals with multiple-level gradients

Abstract

Photonic quasi-crystals and photonic crystals with certain degrees of disorder can have a broadband light-matter interaction. In this paper, we present the holographic fabrication of graded photonic super-quasi-crystals through pixel-by-pixel phase pattern engineering using a spatial light modulator. Using the same phase pattern arranged in a decagon, we have fabricated graded photonic super-quasi-crystals with five-fold symmetry and multiple levels of gradients and graded photonic super-crystals with rectangular unit super-cells, depending on the Fourier filter. Although a certain degree of disorder was incorporated in the quasi-crystals, we still observed the golden ratio in the diameters of the diffraction rings of the fabricated quasi-crystals, indicating five-fold symmetry. Using direct pixel-by-pixel phase engineering, the same laser projection system, consisting of an integrated spatial light modulator and a reflective optical element, can be used for the fabrication of graded photonic super-crystals with various symmetries. The multi-level gradient effects on the optical properties of an organic light-emitting diode were simulated. When the cathode of an organic light-emitting device is patterned in the graded photonic super-crystals, a light extraction efficiency up to 76% in the visible range can be achieved.

Holographic Fabrication and Optical Property of Graded Photonic Super-Crystals with a Rectangular Unit Super-Cell

“…The second-generation photonic crystals have shown enhanced light-matter interactions [5,6]. Very recently, we have studied a new type of photonic crystals titled graded photonic super-crystals (GPSC) [7][8][9][10][11]. Although the lattices are grouped by the blue and red dots, the size of the basis is different in GPSC.…”

“…"Period 1" is the period for the traditional photonic crystal, while "Period 2" is the second period in the x-direction for the GPSC, as shown in Figure 1. The lattice described by "Period 1" have a square symmetry, while the lattice described by "Period 2" can have square, hexagonal, or five-fold symmetry [7][8][9][10][11]. Thus, the GPSC can have dual-periods and dual-symmetries.…”

“…Thus, the GPSC can have dual-periods and dual-symmetries. The lattice with "Period 1" can have other symmetries, with a cost of reduced resolution in a phase pattern if a spatial light modulator (SLM) is used in the fabrication [7][8][9][10][11]. The filling fraction of the dielectric material in the GPSC is also the gradient for the regions where the dashed green rectangular region has a high filling fraction and the solid green rectangular region has a low filling fraction.…”

“…The computer-generated hologram method can be used for the fabrication of the desired structure using SLM. However, the pixel-by-pixel phase engineering in SLM can reach a high resolution in the holographic fabrication [7,10,11,26,27]. Another advantage of using pixel-by-pixel phase engineering is that a Fourier filter can be predicted, and the aforementioned reflective optical element can be integrated for large area holographic fabrication [10].…”

“…Another advantage of using pixel-by-pixel phase engineering is that a Fourier filter can be predicted, and the aforementioned reflective optical element can be integrated for large area holographic fabrication [10]. Using the pixel-by-pixel phase engineering method, graded photonic super-crystals with square [7], hexagonal [7], and five-fold symmetric [11] unit super-cells have been fabricated. These four-, five-, and six-fold structures were formed by four outer beams with large interfering angles, plus four, five, or six inner beams with small interfering angles, respectively [7,11].…”