The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adom.202201059.

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%.

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.

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.

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