Computation of the para-pseudoinverse for oversampled filter banks: Forward and backward Greville formulas

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience. In frame expansions, the least square signal reconstruction operator is called the dual frame, which can be obtained by choosing the synthesis filter bank as the para-pseudoinverse of the analysis bank. In this paper, we study the computation of the dual frame by exploiting the Greville formula, which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended. Here, we first develop the backward Greville formula to handle the case of row deletion. Based on the forward Greville formula, we then study the computation of para-pseudoinverse for extended filter banks and Laplacian pyramids. Through the backward Greville formula, we investigate the frame-based error resilient transmission over erasure channels. The necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived. A postfiltering structure is also presented to implement the para-pseudoinverse when the transform coefficients in one subband are completely lost

Mechanism of optical degradation in microstructured InGaN light-emitting diodes

While the enhancement of light extraction efficiency from microstructured InGaN light-emitting diodes (μLED) has been firmly established, there is concern over the effect of microstructuring on the device lifetimes. A study on the electrical characteristics and reliability of μLED arrays has been carried out. Despite improved optical performance, expanded device sidewalls served to accelerate the rate of optical degradation, adversely affect the lifetimes of devices. Through current-voltage plots and noise spectrum measurements, vertical current conduction along the plasma-damaged sidewalls was identified as the key degradation mechanism. © 2010 American Institute of Physics.published_or_final_versio

Flip-chip InGaN light-emitting diodes with an integrated microlens array

The fabrication of hexagonally close-packed lens array on flip-chip bonded InGaN LED by nanosphere lithography is reported. A self-assembled monolayer of silica spheres with diameters of 1-μm serves as an etch mask to be transferred onto the sapphire face of the LED to form hemispherical lenses. Without degrading electrical characteristic, the light output power of lensed LED is increased by more than one-quart, compared with an unpatterned LED. The optical behavior of individual lenses and converging effect of lensed LED are by ray-tracing and confocal imaging. © 2013 The Japan Society of Applied Physics.published_or_final_versio

Broadband emission from an ensemble of nano-pillars with multiple diameters

Conference 8641: Light-Emitting Diodes: Materials, Devices, and Applications for Solid State Lighting 17The Conference program's website is located at http://spie.org/x92791.xmlGenerating white light from monochromatic light sources is commonly achieved via one of two common methods: exciting fluorescence phosphors from a shorter wavelength LED, or mixing light from three or more LED chips, commonly known as RGB LEDs. Phosphor efficiency degrade over time, and have lifetimes shorter than the chip itself. RGB LEDs require turning on three or more p-n junctions and suffer from color mixing issues. We introduce a promising approach towards achieving phosphor-free white light emission, tapping on strain engineering and nanoscale processing. The proposed approach makes use of a long wavelength chip, which is …published_or_final_versio

Air-spaced GaN nanopillar photonic band gap structures patterned by nanosphere lithography

We report on the fabrication of ordered hexagonal arrays of air-spaced GaN nanopillars by nanosphere lithography. A self-assembled two-dimensional silica nanosphere mask was initially formed by spin-coating. Prior to pattern transfer to the GaN substrate, a silica-selective dry etch recipe was employed to reduce the dimensions of the nanospheres, without shifting their equilibrium positions. This process step was crucial to be formation of air-spaced hexagonal arrays of nanospheres, as opposed to closed-packed arrays normally achieved by nanosphere lithography. This pattern is then transferred to the wafer to form air-spaced nanopillars. By introducing air gaps between pillars, a photonic band gap (PBG) in the visible region can be opened up, which is usually nonexistent in closed-packed nanopillar arrays. The PBG structures were designed using the plane wave expansion algorithm for band structure computations. The existence and positions of band gaps have been verified through optical transmittance spectroscopy, which correlated well with predictions from simulations. From photoluminescence (PL) spectroscopy, a fourfold increase in PL intensity was observed and compared to an as-grown sample, demonstrating the effectiveness of well-designed self-assembled PBG structures for suppressing undesired optical guiding mode via PBG and for promoting light extraction. The effects of defects in the nanopillar array on the optical properties are also critically assessed. © 2011 American Institute of Physics.published_or_final_versio

InGaN light-emitting diodes with indium-tin-oxide photonic crystal current-spreading layer

Photonic crystal patterns on the indium tin oxide layer of an InGaN/GaN light-emitting diode are fabricated via nanosphere lithography in combination with dry etching. The silica spheres acting as an etch mask are self-assembled into a hexagonal closed-packed monolayer array. After etching, the photonic crystal (PhC) pattern is formed across the indium-tin-oxide (ITO) films so that the semiconductor layers are left intact and thus free of etch damages. Despite slight degradation to the electrical properties, the ITO-PhC light-emitting diodes (LEDs) exhibit enhancements of their optical emission power by as much as 64% over an as-grown LED. The optical performances and mechanisms of the photonic crystal LEDs are investigated with the aid of rigorous coupled wave analysis and finite-difference time-domain simulations. © 2011 American Institute of Physics.published_or_final_versio

Single-mode whispering gallery lasing from metal-clad GaN nanopillars

An ordered hexagonal closed-packed nanopillar array is fabricated on GaN. A metal coating is then applied to encapsulate the pillars for promoting optical confinement within the cylindrical cavity. Room-temperature lasing at 373 nm is observed under pulsed excitation, at a lasing threshold of 0.42 MW/cm 2. With pillar diameters of around 980 nm, the number of modes overlapping the emission spectrum is reduced, giving rise to single-mode whispering gallery stimulated emission. Finite-difference time-domain simulations are carried out for the prediction of resonant frequencies and electric field patterns corresponding to the resonant modes. © 2012 Optical Society of America.published_or_final_versio

Tunable clover-shaped GaN photonic bandgap structures patterned by dual-step nanosphere lithography

The fabrication of close-packed clover-shaped photonic crystal structure on GaN by dual-step nanosphere lithography is demonstrated. By shrinkage of spheres prior to pattern transfer, a non-closed-packed clover-shaped photonic bandgap (PBG) structure, as designed by modified 3D finite-difference time-domain simulation, is also realized. The PBG of the close-packed and non-close-packed clover-shaped structures is verified through optical transmission spectroscopy, found to agree well with simulated results. A threefold enhancement in photoluminescence (PL) intensity is observed from the optimized structure, when the PBG is tuned to overlap with the emission band of the InGaN/GaN multi-quantum wells. From time-resolved PL measurements, shortened decay lifetimes are observed. © 2012 American Institute of Physics.published_or_final_versio

InGaN light-emitting diodes with indium-tin-oxide sub-micron lenses patterned by nanosphere lithography

Close-packed micro-lenses with dimensions of the order of wavelength have been integrated onto the indium-tin-oxide (ITO) layer of GaN light-emitting diodes employing nanosphere lithography. The ITO lens arrays are transferred from a self-assembled silica nanosphere array by dry etching, leaving the semiconductor layer damage-free. An enhancement of up to 63.5% on optical output power from the lensed light-emitting diode (LED) has been observed. Lens-patterned LEDs are also found to exhibit reduced emission divergence. Three-dimensional finite-difference time-domain simulations performed for light extraction and emission characteristics are found to be consistent with the observed results. © 2012 American Institute of Physics.published_or_final_versio

Analysis of Micro-lens Integrated Flip-chip InGaN Light-emitting Diodes by Confocal Microscopy

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