Anti-multipath digital signal detector

Detector operates in conjunction with radio frequency portion of receiver to detect digital signals transmitted in known modulation formats. Signal is constructed by assigning known and distinct modulation waveforms to sequence of message symbols. It reconstructs transmitted digital sequence with minimum probability that any reconstructed digit will be in error

Mathematical models for chemotaxis and their applications in self-organisation phenomena

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and mathematicians into biology. The Patlak-Keller-Segel (PKS) system forms part of the bedrock of mathematical biology, a go-to-choice for modellers and analysts alike. For the former it is simple yet recapitulates numerous phenomena; the latter are attracted to these rich dynamics. Here I review the adoption of PKS systems when explaining self-organisation processes. I consider their foundation, returning to the initial efforts of Patlak and Keller and Segel, and briefly describe their patterning properties. Applications of PKS systems are considered in their diverse areas, including microbiology, development, immunology, cancer, ecology and crime. In each case a historical perspective is provided on the evidence for chemotactic behaviour, followed by a review of modelling efforts; a compendium of the models is included as an Appendix. Finally, a half-serious/half-tongue-in-cheek model is developed to explain how cliques form in academia. Assumptions in which scholars alter their research line according to available problems leads to clustering of academics and the formation of "hot" research topics.Comment: 35 pages, 8 figures, Submitted to Journal of Theoretical Biolog

Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals

Building upon the results of recent work [1], we use momentum space design rules to investigate high quality factor (Q) optical cavities in standard and compressed hexagonal lattice photonic crystal (PC) slab waveguides. Beginning with the standard hexagonal lattice, the results of a symmetry analysis are used to determine a cavity geometry that produces a mode whose symmetry immediately leads to a reduction in vertical radiation loss from the PC slab. The Q is improved further by a tailoring of the defect geometry in Fourier space so as to limit coupling between the dominant Fourier components of the defect mode and those momentum components that radiate. Numerical investigations using the finite-difference time-domain (FDTD) method show significant improvement using these methods, with total Q values exceeding 10^5. We also consider defect cavities in a compressed hexagonal lattice, where the lattice compression is used to modify the in-plane bandstructure of the PC lattice, creating new (frequency) degeneracies and modifying the dominant Fourier components found in the defect modes. High Q cavities in this new lattice geometry are designed using the momentum space design techniques outlined above. FDTD simulations of these structures yield Q values in excess of 10^5 with mode volumes of approximately 0.35 cubic half-wavelengths in vacuum

Mode Coupling and Cavity-Quantum-Dot Interactions in a Fiber-Coupled Microdisk Cavity

A quantum master equation model for the interaction between a two-level system and whispering-gallery modes (WGMs) of a microdisk cavity is presented, with specific attention paid to current experiments involving a semiconductor quantum dot (QD) embedded in a fiber-coupled, AlGaAs microdisk cavity. In standard single mode cavity QED, three important rates characterize the system: the QD-cavity coupling rate g, the cavity decay rate kappa, and the QD dephasing rate gamma_perpendicular. A more accurate model of the microdisk cavity includes two additional features. The first is a second cavity mode that can couple to the QD, which for an ideal microdisk corresponds to a traveling wave WGM propagating counter to the first WGM. The second feature is a coupling between these two traveling wave WGMs, at a rate beta, due to backscattering caused by surface roughness that is present in fabricated devices. We consider the transmitted and reflected signals from the cavity for different parameter regimes of {g,beta,kappa,gamma_perpendicular}. A result of this analysis is that even in the presence of negligible roughness induced backscattering, a strongly coupled QD mediates coupling between the traveling wave WGMs, resulting in an enhanced effective coherent coupling rate g = sqrt(2)*g0 corresponding to that of a standing wave WGM with an electric field maximum at the position of the QD. In addition, analysis of the second-order correlation function of the reflected signal from the cavity indicates that regions of strong photon antibunching or bunching may be present depending upon the strength of coupling of the QD to each of the cavity modes. Such intensity correlation information will likely be valuable in interpreting experimental measurements of a strongly-coupled QD to a bi-modal WGM cavity.Comment: rev4: updated references and added additional correlation function calculations; to appear in Phys. Rev. A in Feb 200

Momentum space design of high-Q photonic crystal optical cavities

The design of high quality factor (Q) optical cavities in two dimensional photonic crystal (PC) slab waveguides based upon a momentum space picture is presented. The results of a symmetry analysis of defect modes in hexagonal and square host photonic lattices are used to determine cavity geometries that produce modes which by their very symmetry reduce the vertical radiation loss from the PC slab. Further improvements in the Q are achieved through tailoring of the defect geometry in Fourier space to limit coupling between the dominant momentum components of a given defect mode and those momentum components which are either not reflected by the PC mirror or which lie within the radiation cone of the cladding surrounding the PC slab. Numerical investigations using the finite-difference timedomain (FDTD) method predict that radiation losses can be significantly suppressed through these methods, culminating with a graded square lattice design whose total Q approaches 105 with a mode volume of approximately 0.25 cubic half-wavelengths in vacuum