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The laser diffraction from periodic structures typically shows isolated and sharp point patterns at zeroth and ±nth orders. Diffraction from 2D graded photonic super-crystals (GPSCs) has demonstrated over 1000 spots due to the fractional diffractions. Here, we report the holographic fabrication of three types of 3D GPSCs through nine beam interferences and their characteristic diffraction patterns. The diffraction spots due to the fractional orders are merged into large-area diffraction zones for these three types of GPSCs. Three distinguishable diffraction patterns have been observed: (a) 3 × 3 Diffraction zones for GPSCs with a weak gradient in unit super-cell, (b) 5 × 5 non-uniform diffraction zones for GPSCs with a strong modulation in long period and a strong gradient in unit super-cell, (c) more than 5 × 5 uniform diffraction zones for GPSCs with a medium gradient in unit super-cell and a medium modulation in long period. The GPSCs with a strong modulation appear as moiré photonic crystals. The diffraction zone pattern not only demonstrates a characterization method for the fabricated 3D GPSCs, but also proves their unique optical properties of the coupling of light from zones with 360° azimuthal angles and broad zenith angles. 

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. 

Abstract Monolayer (ML) molybdenum disulfide (MoS₂) is a novel 2-dimensional (2D) semiconductor whose properties have many applications in devices. Despite its potential, ML MoS₂ is limited in its use due to its degradation under exposure to ambient air. Therefore, studies of possible degradation prevention methods are important. It is well established that air humidity plays a major role in the degradation. In this paper, we investigate the effects of substrate hydrophobicity on the degradation of chemical vapor deposition (CVD) grown ML MoS 2 . We use optical microscopy, atomic force microscopy (AFM), and Raman mapping to investigate the degradation of ML MoS 2 grown on SiO 2 and Si 3 N 4 that are hydrophilic and hydrophobic substrates, respectively. Our results show that the degradation of ML MoS₂ on Si 3 N 4 is significantly less than the degradation on SiO 2 . These results show that using hydrophobic substrates to grow 2D transition metal dichalcogenide ML materials may diminish ambient degradation and enable improved protocols for device manufacturing.