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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. 

It is challenging to realize the complete broadband absorption of near-infrared in thin optical devices. In this paper, we studied high light absorption in two devices: a stack of Au-pattern/insulator/Au-film and a stack of Au-pattern/weakly-absorbing-material/Au-film where the Au-pattern was structured in graded photonic super-crystal. We observed multiple-band absorption, including one near 1500 nm, in a stack of Au-pattern/spacer/Au-film. The multiple-band absorption is due to the gap surface plasmon polariton when the spacer thickness is less than 30 nm. Broadband absorption appears in the near-infrared when the insulator spacer is replaced by a weakly absorbing material. E-field intensity was simulated and confirmed the formation of gap surface plasmon polaritons and their coupling with Fabry–Pérot resonance. 

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. 

This paper presents a holographic fabrication of a new type of photonic crystal, called graded photonic super-crystals with graded basis, dual period and dual symmetry. Pixel-by-pixel phase coding of laser beams in a spatial light modulator can produce the highest resolution in produced photonic super-lattice. Two-level designs in phase pattern are used to generate graded photonic super-crystals where graded square lattice clusters are orientated in four, five or six-fold symmetry. Further phase engineering in a super-cell of 12x8 pixels can produce small-period square lattice orientated in a large period rectangular pattern.