In a planar organic light-emitting diode (OLED), over 50% of emitted lights are trapped as a waveguide mode in the organic-indium tin oxide layer and as a surface plasmon polariton mode at the metal and organic layer interface. The light extraction efficiency into the glass substrate is greatly enhanced when the organic/Al interface of the OLED is patterned with a graded photonic super-crystal (GPSC), by destroying the plasmonic resonance condition through graded patterns and by scattering the surface plasmon polariton into the glass. The light extraction efficiency increases with the area fraction of graded regions in the GPSC. The efficiency can reach above 68.5%, 72.9%, and 78.9% for octagonal, square, and triangular GPSCs with area fractions of the graded regions of 53.9%, 78.5%, and 90.7%, respectively. The light extraction efficiency goes up to 83.0%, 81.2%, and 79.0% at the wavelengths of 447, 507, and 608 nm, respectively, in OLED patterned with triangular GPSC, compared with the targeted efficiency of 70%.
For the first time, we are able to generate over 1000 diffraction spots from a graded photonic super-crystal with a unit super-cell size of 12a × 12a where a is the lattice constant and hole radii are gradually changed in dual directions. The diffraction pattern from the graded photonic super-crystal reveals unique diffraction properties. The first order diffractions of (±1,0) or (0,±1) disappear. Fractional diffraction orders are observed in the diffraction pattern inside a square with vertices of (1,1), (1,−1), (−1,−1) and (−1,−1). The fractional diffraction can be understood from lattices with a period of a. However, a dual-lattice model is considered in order to explain higher-order diffractions. E-field intensity simulations show a coupling and re-distribution among fractional orders of Bloch waves. There are a total of 12 × 12 spots in E-field intensity in the unit supercell corresponding to 12 × 12 fractional diffraction orders in the diffraction pattern and 12 × 12 fractional orders of momentum in the first Brillouin zone in k-space.
The newly discovered graded photonic super-crystal (GPSC) with a large size of unit cell can have novel optical properties that have not been explored. The unit super-cell in the GPSC can be designed to be large or small and thus the GPSC can have no photonic band gap or several gaps. The photonic band structures in Si GPSC can help predict the light absorption in Si. Photonic resonance modes help enhance the absorption of light in silicon; however, photonic band gaps decrease the absorption for light with a large incident angle. The Si device patterned in GPSC with a unit super-cell of 6a × 6a (a is a lattice constant in traditional photonic crystal) has a broadband high absorption with strong incident-angular dependence. The device with the unit super-cell of 12a × 12a has relatively low light absorption with weak incident-angle dependence. The Si GPSC with a unit super-cell of 8a × 8a combines both advantages of broadband high absorption and weak dependence of absorption on the incident angle.
Twistronics has been studied for manipulating electronic properties through a twist angle in the formed moiré superlattices of two dimensional layer materials. In this paper, we study twistoptics for manipulating optical properties in twisted moiré photonic patterns without physical rotations. We describe a theoretic approach for the formation of single-layer twisted photonic pattern in square and triangular lattices through an interference of two sets of laser beams arranged in two cone geometries. The moiré period and the size of unit super-cell of moiré patterns are related to the twist angle that is calculated from the wavevector ratio of laser beams. The bright and dark regions in moiré photonic pattern in triangular lattices are reversible. We simulate E-field intensities and their cavity quality factors for resonance modes in moiré photonic pattern in square lattices. Due to the bandgap dislocation between the bright and dark regions, the resonance modes with very high quality-factors appears near bandgap edges for the moiré photonic pattern with a twist angle of 9.5 degrees. At the low frequency range, the resonance modes can be explained as Mie resonances. The cavity quality factor decreases for resonance modes when the twist angle is increased to 22.6 degrees.
The study of twisted bilayer 2D materials has revealed many interesting physics properties. A twisted moiré photonic crystal is an optical analog of twisted bilayer 2D materials. The optical properties in twisted photonic crystals have not yet been fully elucidated. In this paper, we generate 2D twisted moiré photonic crystals without physical rotation and simulate their photonic band gaps in photonic crystals formed at different twisted angles, different gradient levels, and different dielectric filling factors. At certain gradient levels, interface modes appear within the photonic band gap. The simulation reveals “tic tac toe”-like and “traffic circle”-like modes as well as ring resonance modes. These interesting discoveries in 2D twisted moiré photonic crystal may lead toward its application in integrated photonics.
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