Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Phase relationships between orbital forcing and the composition of air trapped in Antarctic ice cores

Orbital tuning is central for ice core chronologies beyond annual layer counting, available back to 60 ka (i.e. thousands of years before 1950) for Greenland ice cores. While several complementary orbital tuning tools have recently been developed using δ¹⁸Oatm, δO₂⁄N₂ and air content with different orbital targets, quantifying their uncertainties remains a challenge. Indeed, the exact processes linking variations of these parameters, measured in the air trapped in ice, to their orbital targets are not yet fully understood. Here, we provide new series of δO₂∕N₂ and δ¹⁸Oatm data encompassing Marine Isotopic Stage (MIS) 5 (between 100 and 160 ka) and the oldest part (340–800 ka) of the East Antarctic EPICA Dome C (EDC) ice core. For the first time, the measurements over MIS 5 allow an inter-comparison of δO₂∕N₂ and δ¹⁸Oatm records from three East Antarctic ice core sites (EDC, Vostok and Dome F). This comparison highlights some site-specific δO₂∕N₂ variations. Such an observation, the evidence of a 100 ka periodicity in the δO₂∕N₂ signal and the difficulty to identify extrema and mid-slopes in δO2∕N2 increase the uncertainty associated with the use of δO₂∕N₂ as an orbital tuning tool, now calculated to be 3–4 ka. When combining records of δ¹⁸Oatm and δO₂∕N₂ from Vostok and EDC, we find a loss of orbital signature for these two parameters during periods of minimum eccentricity (∼ 400 ka, ∼ 720–800 ka). Our data set reveals a time-varying offset between δO₂∕N₂ and δ¹⁸Oatm records over the last 800 ka that we interpret as variations in the lagged response of δ¹⁸Oatm to precession. The largest offsets are identified during Terminations II, MIS 8 and MIS 16, corresponding to periods of destabilization of the Northern polar ice sheets. We therefore suggest that the occurrence of Heinrich–like events influences the response of δ¹⁸Oatm to precession.

Abundance and biomass of protozooplankton from the iron-induced phytoplankton bloom during the EisenEx experiment in 2000 in the Southern Ocean

The responses of larger (>50 µm in diameter) protozooplankton groups to a phytoplankton bloom induced by in situ iron fertilization (EisenEx) in the Polar Frontal Zone (PFZ) of the Southern Ocean in austral spring are presented. During the 21 days of the experiment, samples were collected from seven discrete depths in the upper 150 m inside and outside the fertilized patch for the enumeration of acantharia, foraminifera, radiolaria, heliozoa, tintinnid ciliates and aplastidic thecate dinoflagellates. Inside the patch, acantharian numbers increased twofold, but only negligibly in surrounding waters. This finding is of major interest, since acantharia are suggested to be involved in the formation of barite (BaSO_4 ) found in sediments and which is a palaeoindicator of both ancient and modern high productivity regimes. Foraminifera increased significantly in abundance inside and outside the fertilized patch. However the marked increase of juveniles after a full moon event suggests a lunar periodicity in the reproduction cycle of some foraminiferan species rather than a reproductive response to enhanced food availability. In contrast, adult radiolaria showed no clear trend during the experiment, but juveniles increased threefold indicating elevated reproduction. Aplastidic thecate dinoflagellates almost doubled in numbers and biomass, but also increased outside the patch. Tintinnid numbers decreased twofold, although biomass remained constant due to a shift in the size spectrum. Empty tintinnid loricae, however, increased by a factor of two indicating that grazing pressure on this group mainly by copepods intensified during EisenEx. The results show that iron-fertilization experiments can shed light on the biology and the role of these larger protists in pelagic ecosystem which will improve their use as proxies in palaeoceanography.

Short-term spectral analysis of ODP Hole 114-704B

Short-term spectral analysis was carried out on geochemical logging data from ODP Site 704. The FFT was used to compute the amplitude spectra of short-term overlapping segments to produce depth-period-amplitude spectrograms of the logging data. The spectrograms provided a means of evaluating the significance of the observed periodic components. The periodic components that were consistently present and prominent across a given record interval were considered to be significant. Changes in the spectrogram characteristics seem to reflect changes in either lithology, sedimentation rates, or hiatuses and may therefore provide useful information to aid in stratigraphic and paleoenvironmental studies. The dominant periodicity during the late Pleistocene and Brunhes Chron (0.97 to 0.47 Ma) was determined to be > 100,000 yr whereas the upper Matuyama Chron was dominated by the 41,000-yr periodicity. These periodicities suggest that the sedimentation patterns within the upper Matuyama Chron (0.98-1.78 Ma) were influenced by the Milankovitch obliquity cycle and those within the latest Matuyama-Brunhes Chron (<0.98 Ma) by the eccentricity cycle. The Brunhes/Matuyama boundary therefore represents a major discontinuity. Periodicities observed within the lower Matuyama and the upper Gauss Chron did not correlate with any of the periodicities within the Milankovitch frequency bands.

Sea surface temperature reconstruction of a combined sediment record of the midlatitude North Pacific

Suborbital climate variability during the last glacial period is suggested to have involved a 1500-year pacing cycle, but the expression and spatial distribution of the ~1500-year oscillation during interglacials remains unclear. We generated a multidecade resolution record of alkenone sea surface temperature (SST) in the northwestern Pacific off central Japan during the Holocene. The SST record showed centennial and millennial variability with an amplitude of ~1 °C throughout the entire Holocene. Spectral analysis for SST variation revealed a statistically significant peak with 1470-year periodicity. The SST variation partly correlated with the variations of ice-rafted hematite-stained grain content in North Atlantic sediments. These findings indicate that the mean latitude of the Kuroshio Extension has varied on a 1500-year cycle, and suggest that a climatic link exists between the North Pacific gyre system and the high-latitude North Atlantic thermohaline circulation. The regular pacing at 1500-year intervals seen throughout both the Holocene and the last glacial period suggests that the oscillation was a response to external forcing.

Geochemistry of Globigerinoides ruber from ODP Hole 130-806B

A sea surface temperature (SST) record based on planktonic foraminiferal magnesium/calcium ratios from a site in the western equatorial Pacific warm pool reveals that glacial-interglacial oscillations in SST shifted from a period of 41,000 to 100,000 years at the mid-Pleistocene transition, 950,000 years before the present. SST changes at both periodicities were synchronous with eastern Pacific cold-tongue SSTs but preceded changes in continental ice volume. The timing and nature of tropical Pacific SST changes over the mid-Pleistocene transition implicate a shift in the periodicity of radiative forcing by atmospheric carbon dioxide as the cause of the switch in climate periodicities at this time.

Pliocene-Pleistocene biostratigraphic datums of ODP Site 184-1148

Based on the stable isotopic analysis of planktonic and benthic foraminifers from Ocean Drilling Program Core 1148 of the northern South China Sea (SCS), Pliocene-Pleistocene isotope stratigraphy and events have been reconstructed. The benthic foraminiferal delta18O record shows that the Pacific intermediate water had a greater influence upon the SCS or the Pacific deep water above ~2600 m was warmer before ~3.2Ma than at present. After that, the benthic delta18O conspicuously increased during the ~3.2-2.5 Ma period, in correspondence to the formation of the Northern Hemisphere ice sheet, whereas the planktonic delta18O signal suggests a stepwise overall decrease of sea surface temperature during the ~2.2-0.9 Ma period. Compared to the equatorial Pacific records, the decrease in planktonic (Globigerinoides ruber) delta13C during the ~3.2-2.2 Ma period is particularly striking, suggesting that fertility of surface water increased noticeably. According to the modern delta13C distribution of G. ruber in the northern SCS, it is inferred that the East Asian winter monsoon strengthened during this interval. Afterwards, there were several conspicuous decreases of G. ruber delta13C at ~1.7, 1.3, 0.9, 0.45 and 0.15 Ma BP, that is, about every 0.4 Ma, suggesting that the East Asian winter monsoon became episodically stronger. This is confirmed by changes in relative abundance of planktonic foraminifer species Neogloboquadrina dutertrei, a typical East Asian winter monsoon proxy. The deepwater delta13C of the SCS is close to that of the Pacific, but lighter than that of the Atlantic, implying that the pattern of deep water originating mainly from the Atlantic and through the Pacific entering the SCS existed at least since the early Pliocene. After 1.4 Ma, the benthic delta13C signal decreased conspicuously but with a periodicity of ~100 ka, suggesting that the deep-water ventilation of the SCS was reduced, probably corresponding to a decrease of the North Atlantic Deep Water and/or further isolation of the SCS deep basin from the Pacific during glaciations.

Ice rafted debris distribution in sediment core CRP-1

Lonestone abundances in CRP-1 were investigated using three methods: core examination at Cape Roberts Camp, analysis of digital core images and follow-up core examination. For all images of split-core, we determined size and depth of every detectable lonestone larger than 3 mm. Lonestone abundance decreases exponentially with clast size. Although no significant depth-dependent variations in lonestone size distribution were detected, a strong 0.5-0.7 m abundance periodicity, of unknown origin, is evident within diamicts. Lonestone volume percentage was estimated from size distribution: most size classes contribute approximately the same volume to the total. Sizes >16 mm have rare enough lonestones that their counts are nonrepresentative when based on short intervals of split core. This problem does not affect total counts significantly, but the volume analysis needs to be confined to <= 6 mm lonestones to avoid instability induced by rare and nonrepresentative larger lonestones. If lonestone abundance can be used as an indicator of glacial proximity, then our CRP-1 lonestone abundance logs confirm the overall character of previously inferred variations in relative distance to the ice margin. Large-scale changes in lonestone abundance also reflect the CRP-1 sequence stratigraphy, with individual sequences generally characterised by basal lonestone-rich diamict overlain by lonestone-poor sands and muds. The relationship between glacial proximity and lonestone abundance within diamicts and within sand-mud intervals is, however, less certain. For example, two or three gradual lonestone increases may indicate regressions during glacial advances, in contrast to the more common CRP-l pattern of dominantly transgressive sequences.

Matlab scripts for modeled obliquity amplitude modulations

The start of the Mesozoic Era is marked by roughly five million years (myr) of Earth system upheavals, including unstable biotic recovery, repeated global warming, ocean anoxia, and perturbations in the global carbon cycle. Intervals between crises were comparably hospitable to life. The causes of these upheavals are unknown, but are thought to be linked to recurrent Siberian volcanism. Here, two marine sedimentary successions at Chaohu and Daxiakou, South China are evaluated for paleoclimate change from astronomical forcing. In these sections, gamma-ray variations indicative of terrestrial weathering reveal enhanced obliquity cycling over prolonged intervals, characterized by a periodicity of 32.8 kiloyear and strong 1.2 myr modulations. This suggests a 22-hour length-of-day and 1.2 myr interaction between the orbital inclinations of Earth and Mars. The 1.2 myr obliquity modulation cycles in these sections are compared with Early Triassic records of global sea-level, temperature, redox and biotic evolution. The evidence collectively suggests that long-term astronomical forcing was involved in the repeated climatic and biotic upheavals that took place throughout the Early Triassic.

Magnetic susceptibility (MS) measurements on the Sancerre (France) drill-core

The Toarcian Oceanic Anoxic Event (T-OAE) of the early Jurassic period involves one of the largest perturbations of the carbon cycle in the past 250 Ma, recorded by a pronounced negative carbon-isotope excursion (CIE). Numerous studies have focused on potential causes of the T-OAE and CIE, but are hampered by an uncertain timescale. Here we present high-resolution (~2 kyr) magnetic susceptibility (MS) measurements from the marine marls of the Sancerre-Couy drill-core, southern Paris Basin, spanning the entire Toarcian Stage. The MS variations document a rich series of sub-Milankovitch to Milankovitch frequencies (precession, obliquity and eccentricity) with the periodic g2-g5 (405 kyr) and quasi-periodic g4-g3 (~2.4 Myr Cenozoic mean periodicity) eccentricity terms being the most prominent. The MS-related g4-g3 variation reflects third-order eustatic sequences, and constrains the sequence stratigraphic framework of the Toarcian Stage. In addition, MS variations reveal a modulation of g2-g5 by g4-g3 eccentricity related cycles, suggesting that sea-level change was the main control on the deposition of the Toarcian Sancerre marls, in tune with the astro-climatic frequencies. The stable 405 kyr cyclicity constrains a minimum duration of the Toarcian Stage to ~8.3 Myr, and the well documented CIE, associated with the T-OAE, to ~300 to 500 kyr. The 405 kyr MS timescale calibrates the periodicity of the prominent high-frequency d13C cycles that occur in the decreasing part of the CIE to 30 to 34 kyr, consistent with the Toarcian obliquity period predicted for an Earth experiencing sustained tidal dissipation.

Paleotemperature reconstructions of the Atlantic Sector of the Southern Ocean

Diatom assemblages from ODP Leg 177 sites 1093, 1094 and core PS2089-2, from the present Antarctic sea ice free zone and close to the Polar Front, were analyzed in order to reconstruct the climate development around the Mid-Brunhes Event 400 000 yr ago, as reflected by summer sea surface temperature (SSST) and sea ice distribution. Dense sample spacing allows a mean temporal resolution during Marine Isotope Stage (MIS) 11 (423-362 ka) of 300-400 yr. SSST values were estimated from diatom assemblages using a transfer function technique. The distribution pattern of sea ice diatoms indicates that the present-day ice free Antarctic Zone was seasonally covered by sea ice during the cold MIS 12 and MIS 10. These glacial periods are characterized by sea ice fluctuations with a periodicity of 3 and 1.85 kyr, suggesting the occurrence of Dansgaard-Oeschger-style millennial-scale oscillations in the Atlantic sector of the Southern Ocean during the glacial stages MIS 12 and MIS 10. Termination V (MIS 12/11) is characterized by a distinct temperature increase of 4-6°C, intersected especially at the southern site 1094 and core PS2089-2 by two distinct cooling events reminiscent of the Younger Dryas, which are associated with a northward shift of the winter sea ice edge in the Antarctic Zone. The SSST record is characterized by distinct temperature intervals bounded by stepwise, rapid changes. Maximum temperatures were reached during Termination V and the early MIS 11, exceeding modern values by 2°C over a period of 8 kyr. This pattern indicates a very early response of the Southern Ocean to global climate on Milankovitch-driven climate variability. The SSST optimum is marked by millennial-scale temperature oscillations with an amplitude of ca. 1°C and periodicities of ca. 1.85 and 1.47 kyr, probably reflecting changes in the ocean circulation system. The SSSTs during the MIS 11 temperature optimum do not exceed values obtained from other interglacial optima such as the early periods of MIS 5 or MIS 1 from the Antarctic Zone. However, the total duration of the warmest period was distinctly longer than observed from other interglacials. The comparison of the South Atlantic climate record with a high-resolution record from ODP Leg 162, site 980from the North Atlantic shows a strong conformity in the climate development during the studied time interval.

Proceedings ...

Periodicity varies: 1915-1916, three times a year; 1916-1942, halfyearly.

[0 0 1] zone-axis bright-field diffraction contrast from coherent Ge(Si) islands on Si(0 0 1): Dedicated to Professor Fang-hua Li on the occasion of her 70th birthday

Coherent Ge(Si)/Si(001) quantum dot islands grown by solid source molecular beam epitaxy at a growth temperature of 700degreesC were investigated using transmission electron microscopy working at 300 kV. The [001] zone-axis bright-field diffraction contrast images of the islands show strong periodicity with the change of the TEM sample substrate thickness and the period is equal to the effective extinction distance of the transmitted beam. Simulated images based on finite element models of the displacement field and using multi-beam dynamical diffraction theory show a high degree of agreement. Studies for a range of electron energies show the power of the technique for investigating composition segregation in quantum dot islands. (C) 2003 Elsevier B.V. All rights reserved.

An investigation into effects of long-distance seed dispersal on organelle population genetic structure and colonization rate: a model analysis

A simulation-based modelling approach is used to examine the effects of stratified seed dispersal (representing the distribution of the majority of dispersal around the maternal parent and also rare long-distance dispersal) on the genetic structure of maternally inherited genomes and the colonization rate of expanding plant populations. The model is parameterized to approximate postglacial oak colonization in the UK, but is relevant to plant populations that exhibit stratified seed dispersal. The modelling approach considers the colonization of individual plants over a large area (three 500 km x 10 km rolled transects are used to approximate a 500 km x 300 km area). Our approach shows how the interaction of plant population dynamics with stratified dispersal can result in a spatially patchy haplotype structure. We show that while both colonization speeds and the resulting genetic structure are influenced by the characteristics of the dispersal kernel, they are robust to changes in the periodicity of long-distance events, provided the average number of long-distance dispersal events remains constant. We also consider the effects of additional physical and environmental mechanisms on plant colonization. Results show significant changes in genetic structure when the initial colonization of different haplotypes is staggered over time and when a barrier to colonization is introduced. Environmental influences on survivorship and fecundity affect both the genetic structure and the speed of colonization. The importance of these mechanisms in relation to the postglacial spread and genetic structure of oak in the UK is discussed.

Suitability of acoustic perturbation measures in analysing periodic and nearly periodic voice signals

In recent years, acoustic perturbation measurement has gained clinical and research popularity due to the ease of availability of commercial acoustic analysing software packages in the market. However, because the measurement itself depends critically on the accuracy of frequency tracking from the voice signal, researchers argue that perturbation measures are not suitable for analysing dysphonic voice samples, which are aperiodic in nature. This study compares the fundamental frequency, relative amplitude perturbation, shimmer percent and noise-to-harmonic ratio between a group of dysphonic and non-dysphonic subjects. One hundred and twelve dysphonic subjects ( 93 females and 19 males) and 41 non-dysphonic subjects ( 35 females and 6 males) participated in the study. All the 153 voice samples were categorized into type I ( periodic or nearly periodic), type II ( signals with subharmonic frequencies that approach the fundamental frequency) and type III ( aperiodic) signals. Only the type I ( periodic and nearly periodic) voice signals were acoustically analysed for perturbation measures. Results revealed that the dysphonic female group presented significantly lower fundamental frequency, significantly higher relative amplitude perturbation and shimmer percent values than the non-dysphonic female group. However, none of these three perturbation measures were able to differentiate between male dysphonic and male non-dysphonic subjects. The noise-to-harmonic ratio failed to differentiate between the dysphonic and non-dysphonic voices for both gender groups. These results question the sensitivity of acoustic perturbation measures in detecting dysphonia and suggest that contemporary acoustic perturbation measures are not suitable for analysing dysphonic voice signals, which are even nearly periodic. Copyright (C) 2005 S. Karger AG, Basel.