A versatile investigation has been accomplished on the performances of circular, square, triangular and hexagonal electromagnetic bandgap structures (EBGSs). The authors have observed that different EBGSs having an identical etching area perform identically. Therefore, a new definition of the filling factor (FF) has been proposed that yields an identical value of FF and identical performance for various electromagnetic bandgap shapes. After that, a rigorous investigation is carried out to find the optimum value of FF. Ring EBGS; furthermore, is presented as an effective means to improve overall performance. A detail characterisation of these designs is presented in this study, which is missing in the open literature. After meticulously analysing the behaviour of annular ring and square ring patterns, an equation of transforming a ring pattern to its equivalent solid shape (i.e. circular or square) has been established in terms of effective FF. It is observed that ring EBGS and corresponding solid shape fulfil the conviction of identical performance too.
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.
The newly discovered graded, superlattice photonic crystals with dual periodicity and dual basis present great opportunity for electromagnetic wave control in photonic devices. These graded superlattices can be holographically fabricated by eight beam interference lithography. We have computed, through electrodynamic simulation, the light extraction efficiency of planar, white organic light-emitting diodes where the Al cathode is patterned with the graded superlattice with dual basis. Two graded super-lattices with four-fold and two-fold symmetries are used to pattern the Al cathode. The decrease in power losses to surface plasmon and waveguide modes is explained by the varying plasmon path length and grating cycle, respectively, in the graded pattern. To the authors' best knowledge, the highest light extraction efficiency of 73.1% into the glass substrate in organic light-emitting diodes has been predicted through simulations.
Light-trapping enhancement in newly discovered graded photonic super-crystals (GPSCs) with dual periodicity and dual basis is herein explored for the first time. Broadband, wide-incident-angle, and polarization-independent light-trapping enhancement was achieved in silicon solar cells patterned with these GPSCs. These super-crystals were designed by multi-beam interference, rendering them flexible and efficient. The optical response of the patterned silicon solar cell retained Bloch-mode resonance; however, light absorption was greatly enhanced in broadband wavelengths due to the graded, complex unit super-cell nanostructures, leading to the overlap of Bloch-mode resonances. The broadband, wide-angle light coupling and trapping enhancement mechanism are understood to be due to the spatial variance of the index of refraction, and this spatial variance is due to the varying filling fraction, the dual basis, and the varying lattice constants in different directions.
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%.
Recently developed graded photonic super-crystals show an enhanced light absorption and light extraction efficiency if they are integrated with a solar cell and an organic light emitting device, respectively. In this paper, we present the holographic fabrication of a graded photonic super-crystal with a rectangular unit super-cell. The spatial light modulator-based pixel-by-pixel phase engineering of the incident laser beam provides a high resolution phase pattern for interference lithography. This also provides a flexible design for the graded photonic super-crystals with a different ratio of length over the width of the rectangular unit super-cell. The light extraction efficiency is simulated for the organic light emitting device, where the cathode is patterned with the graded photonic super-crystal. The high extraction efficiency is maintained for different exposure thresholds during the interference lithography. The desired polarization effects are observed for certain exposure thresholds. The extraction efficiency reaches as high as 75% in the glass substrate.
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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