Homogenization of nanowire-based composites with anisotropic unit-cell and layered substructure
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lasmonics, Photonics, and Metamaterials Research Letter
Homogenization of nanowire-based composites with anisotropic unit-cell and layered substructure Brian M. Wells, Department of Physics, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117, USA; Department of Physics and Applied Physics, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA Wei Guo, and Viktor A. Podolskiy, Department of Physics and Applied Physics, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA Address all correspondence to Brian M. Wells at [email protected] (Received 29 December 2015; accepted 16 February 2016)
Abstract We analyze the optical properties of composite materials that combine nanowire and nanolayer platforms. We revisit effective-medium theory (EMT) description of wire materials with high filling fraction positioned in anisotropic unit cells and present a simple numerical technique to extend Maxwell–Garnett formalism in this limit. We also demonstrate that the resulting EMT can be combined with transfer-matrix technique to adequately describe photonic band gap behavior, previously observed in epitaxially grown semiconductor multilayer nanowires.
Modern material fabrication platforms enable production of a wide class of composites with ever more complex internal structures. Recently, plasmonic nanowire and nanolayer-based material assemblies have emerged as platforms of choice for modulating the diffraction limit and local density of photonic states,[1–3] opening potential applications in sensing, microscopy, and quantum optics.[4–9] In related but separate efforts, techniques for nanowire growth and nanolayer deposition have been perfected by the semiconductor research community. In this context, semiconductor nanowires have emerged as a promising platform for high-performance light-emitting devices, where InGaN nanowire light-emitting diodes (LEDs) have shown superior performance compared with their bulk counterparts.[10–15] There is still lack of development of highperformance nanowire lasers due to the inherent challenges to incorporate high-quality reflector mirrors to form low-loss laser cavities.[16–18] One possible candidate for such reflectors is AlN/GaN-distributed Bragg reflector (DBR) heterostructures, which can be directly implemented within the existing material fabrication framework. However, owing to the complexity of the nanowire heterostructures, the simple transfermatrix method (TMM)[19,20] cannot be applied directly as in the case of bulk DBR structure design, and full threedimensional (3D) solvers have to be used to design and characterize optical performance of nanowire-based DBRs.[21] Here we demonstrate that optical properties of nanowire/nanolayer arrays can be adequately described by effective-medium theories (EMTs), significantly reducing computational effort required for the analysis and optimization of epitaxial DBRs. EMT presented in this work is a convenient numerical extension to the well-known Maxwell–Garnett (MG)
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