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1. Holographic fabrication of graded photonic super-crystals through pixel-by-pixel phase coding of laser beams in a spatial light modulator

   Sale, O; Hassan, S; Lowell, D; Hurley, N; Lin, Y (March 2019, Advanced Fabrication Technologies for Micro/Nano Optics and Photonics XII)

   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. 

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2. Effects of Photonic Band Structure and Unit Super-Cell Size in Graded Photonic Super-Crystal on Broadband Light Absorption in Silicon

   https://doi.org/10.3390/photonics6020050  

   Hassan, Safaa; Alnasser, Khadijah; Lowell, David; Lin, Yuankun (June 2019, Photonics)

   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. 

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3. Holographic Fabrication of 3D Moiré Photonic Crystals Using Circularly Polarized Laser Beams and a Spatial Light Modulator

   https://doi.org/10.3390/mi14061217  

   Hurley, Noah; Kamau, Steve; Cui, Jingbiao; Lin, Yuankun (June 2023, Micromachines)

   A moiré photonic crystal is an optical analog of twisted graphene. A 3D moiré photonic crystal is a new nano-/microstructure that is distinguished from bilayer twisted photonic crystals. Holographic fabrication of a 3D moiré photonic crystal is very difficult due to the coexistence of the bright and dark regions, where the exposure threshold is suitable for one region but not for the other. In this paper, we study the holographic fabrication of 3D moiré photonic crystals using an integrated system of a single reflective optical element (ROE) and a spatial light modulator (SLM) where nine beams (four inner beams + four outer beams + central beam) are overlapped. By modifying the phase and amplitude of the interfering beams, the interference patterns of 3D moiré photonic crystals are systemically simulated and compared with the holographic structures to gain a comprehensive understanding of SLM-based holographic fabrication. We report the holographic fabrication of phase and beam intensity ratio-dependent 3D moiré photonic crystals and their structural characterization. Superlattices modulated in the z-direction of 3D moiré photonic crystals have been discovered. This comprehensive study provides guidance for future pixel-by-pixel phase engineering in SLM for complex holographic structures. 

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4. Laser Diffraction Zones and Spots from Three-Dimensional Graded Photonic Super-Crystals and Moiré Photonic Crystals

   https://doi.org/10.3390/photonics9060395  

   Hurley, Noah; Kamau, Steve; Alnasser, Khadijah; Philipose, Usha; Cui, Jingbiao; Lin, Yuankun (June 2022, Photonics)

   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. 

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5. Generation of over 1000 Diffraction Spots from 2D Graded Photonic Super-Crystals

   https://doi.org/10.3390/photonics7020027  

   Hassan, Safaa; Jiang, Yan; Alnasser, Khadijah; Hurley, Noah; Zhang, Hualiang; Philipose, Usha; Lin, Yuankun (June 2020, Photonics)

   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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