Band Gap Engineering and Light Localization in Si and InP Based Three-dimensional Photonic Crystals
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2025-08-29 |
| Journal | American Journal of Optics and Photonics |
| Authors | Fairuz Aniqa Salwa, Jahirul Khandaker, Mohammad Aminul Islam, Md. Abdur Rahman, Md Minhaz Chowdhury |
| Institutions | Jahangirnagar University |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research investigates the engineering of Photonic Band Gaps (PBGs) and light localization in three-dimensional (3D) Photonic Crystals (PCs) utilizing high-index contrast semiconductors, Silicon (Si) and Indium Phosphide (InP).
- Optimal PBG Achievement: The inverse diamond lattice structure (air spheres in a dielectric background) proved superior, yielding the largest complete PBG of 28.13% using a Si background.
- Material Performance: Complex lattices (Woodpile and Diamond) consistently generated significant PBGs, while simpler lattices (FCC and Inverse Opal) in Si failed to produce any complete PBGs.
- InP Performance: The InP-based inverse diamond lattice achieved a substantial PBG of 18.85%, confirming InPâs viability for 3D photon control, despite its lower refractive index compared to Si.
- Successful Localization: Light localization was successfully demonstrated in the InP Inverse Opal lattice (which possessed a small 1.39% PBG) by introducing a point defect.
- High-Q Resonator: The defect cavity in the InP lattice exhibited a high Quality Factor (Q) of 4.8959, enabling it to function effectively as a resonator and omnidirectional reflector at a resonant wavelength of 2.48 ”m.
- Conclusion for Design: The diamond structure is identified as the best 3D PC lattice for achieving large PBGs, attributed to its nearly spherical Brillouin zone and interconnected dielectric channels.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Silicon (Si) Refractive Index (n1) | 3.6 | N/A | At optical wavelength |
| Indium Phosphide (InP) Refractive Index (n1) | 3.156 | N/A | At optical wavelength |
| Lattice Period (a) | 1.0 | ”m | Standard parameter for all lattices |
| Maximum Complete PBG (Si) | 28.13 | % | Diamond Lattice (Air voids in Si) |
| Si Diamond Mid-Gap Frequency (Ïm) | 0.57 | Ïa/2Ïc | For 28.13% PBG |
| Maximum Complete PBG (InP) | 18.85 | % | Diamond Lattice (Air voids in InP) |
| InP Woodpile PBG | 15.34 | % | InP Rods in Air background |
| InP Inverse Opal PBG | 1.39 | % | Air voids in InP background |
| Defect Cavity Quality Factor (Q) | 4.8959 | N/A | InP Inverse Opal lattice resonator |
| Defect Resonant Wavelength (λ) | 2.48 | ”m | InP Inverse Opal defect mode |
| Woodpile Filling Fraction (f) | 37.62 | % | Si Rods in Air background |
| Woodpile Rod Width (w) | 0.266 | ”m | For 15.34% PBG structure |
Key Methodologies
Section titled âKey MethodologiesâThe study relied on rigorous electromagnetic simulations using established computational methods to analyze 3D PC structures.
- Band Structure Calculation (PWE): The Plane-wave Expansion (PWE) method, implemented via the RSoft BandSolve tool, was used to calculate the dispersion relation and identify the existence and width of hybrid Photonic Band Gaps (PBGs).
- Defect Mode and Localization Analysis (FDTD): The Finite-Difference Time-Domain (FDTD) method, implemented via RSoft FullWAVE, was used to simulate light propagation, measure the frequency response of defect structures, and calculate the Quality Factor (Q).
- Lattice Design: Twelve combinations were simulated, crossing four lattice types (FCC, Inverse Opal, Woodpile, Diamond) with two high-index materials (Si and InP).
- Inverse Structure Optimization: For diamond and inverse opal lattices, radius (r) scans were performed to determine the optimal sphere diameter that maximized the PBG size and gap-midgap ratio.
- Woodpile Geometry: The woodpile lattice utilized a four-layer ABCD stacking sequence of rectangular rods, with axes rotated 90° between adjacent layers, designed to maximize the gap width.
- Defect Creation: A point defect was introduced into the Inverse Opal lattice by removing a single central air void from the xz plane of the solid dielectric medium (InP or Si).
- FDTD Simulation Parameters: Simulations used a fine grid size (0.004 ”m) and employed Perfectly Matched Layer (PML) boundary conditions (0.5 ”m width) to accurately model energy loss and Q factor.
Commercial Applications
Section titled âCommercial ApplicationsâThe successful engineering of large PBGs in Si and InP, combined with high-Q light localization, positions this technology for advanced applications in integrated optics and quantum technology.
- Optical Telecommunication Devices: The high-Q InP defect cavity acts as an omnidirectional reflector and resonator, suitable for highly efficient filters, modulators, and multiplexers in fiber optic networks.
- High-Efficiency Light Sources (LEDs/Lasers): Large PBGs inhibit spontaneous emission, which is crucial for increasing the efficiency and directionality of Light Emitting Diodes (LEDs) and for developing ultra-low threshold photonic crystal lasers.
- Integrated Photonic Circuits: Utilizing Si and InP (materials compatible with semiconductor manufacturing) allows for the integration of complex 3D light guiding and confinement structures directly onto chips, enabling advanced on-chip optical processing.
- Quantum Optics and Sensing: High Q-factor cavities are essential for enhancing light-matter interaction, enabling applications in single-photon sources, quantum computing components, and high-sensitivity optical sensors.
- Solar Energy Harvesting: The ability of 3D PCs to control light absorption across a wide range of angles and frequencies can be leveraged to create enhanced absorption layers for high-efficiency solar cells.
- Frequency Selective Surfaces: The precise control over the band gap frequency allows these structures to be used as highly selective optical filters or reflectors in various industrial and scientific instruments.
View Original Abstract
We demonstrated photonic band diagrams of three-dimensional photonic crystals composed of InP and Si for four different lattice types:- face-centered cubic (FCC), inverse opal, woodpile, and diamond structures, making 12 combinations. The Si-based FCC and inverse opal lattices exhibited no photonic band gaps (PBGs). Then, the InP-based inverse opal demonstrated small, significant 1% PBGs. After that the woodpile lattices of dielectric rods in air and diamond lattices of air voids in dielectric for both InP and Si showed large complete PBGS, enabling better photon control. A point defect was introduced in the inverse opal lattice of air voids in Si and InP background. The Si lattice didnât have a cavity mode, as it had no PBGs. The InP inverse opal lattice localized light effectively within its defect cavity using its 1% PBG, enabling it to act as a resonator and reflector. Light emission was inhibited in the surrounding photonic crystal region, as it was trapped in the defect cavity. The results obtained here are an important step towards the complete control of photons in photonic crystals.