arXiv subjects
Publications and source records attributed to Megan O'Brien.
The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with $Ω(n)$ edges. We conjecture that the extremal graph is a vertex joined to a path on $n-1$ vertices.
We investigated and demonstrated a 1.3 $μ$m-band laser grown by metalorganic vapour phase epitaxy (MOVPE) on a specially engineered metamorphic parabolic graded In$_x$Ga$_{1-x}$As buffer and epitaxial structure on a GaAs substrate. Bottom and upper cladding layers were built as a combination of AlInGaAs and InGaP alloys in a superlattice sequence. This was implemented to overcome (previously unreported) detrimental surface epitaxial dynamics and instabilities: when single alloys are utilised to achieve thick layers on metamorphic structures, surface instabilities induce defect generation. This has represented a historically limiting factor for metamorphic lasers by MOVPE. We describe a number of alternative strategies to achieve smooth surface morphology to obtain efficient compressively strained In$_{0.4}$Ga$_{0.6}$As quantum wells in the active layer. The resulting lasers exhibited low lasing threshold with total slope efficiency of 0.34 W/A for a 500 $μ$m long ridge waveguide device. The emission wavelength is extended as far as 1360 nm.