Biomedical subjects

Steven G Johnson

Publications and source records attributed to Steven G Johnson.

17 recordsLinked to original sources

PubMed2006

Improving accuracy by subpixel smoothing in the finite-difference time domain.

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

Journal Article↗

PubMed2006

Doppler radiation emitted by an oscillating dipole moving inside a photonic band-gap crystal.

We study the radiation emitted by an oscillating dipole moving with a constant velocity in a photonic crystal, and analyze the effects that arise in the presence of a photonic band gap. It is demonstrated through numerical simulations that the radiation strength may be enhanced or inhibited according to the photonic band structure, and anomalous effects in the sign and magnitude of the Doppler shifts are possible, both outside and inside the gap. We suggest that this effect could be used to identify the physical origin of the backward waves in recent metamaterials.

Journal Article↗

PubMed2006

Geographic ranges, population structure, and ages of sexual and parthenogenetic snail lineages.

Asexual reproduction is thought to doom organisms to extinction due to mutation accumulation and parasite exploitation. Theoretical models suggest that parthenogens may escape the negative effects of conspecifics and biological enemies through escape in space. Through intensive sequencing of a mitochondrial DNA (mtDNA) and a nuclear intron locus in sexual and parthenogenetic freshwater snails (Campeloma), I examine three questions: (1) Are sexual mtDNA lineages more restricted geographically than parthenogenetic mtDNA lineages? (2) Are independent parthenogenetic lineages shorter lived than sexual lineages? and (3) Do parthenogens have higher intraindividual nuclear sequence diversity and form well-differentiated monophyletic groups as expected under the Meselson effect? Geographic ranges of parthenogenetic lineages are significantly larger than geographic ranges of sexual lineages. Based on coalescence times under different demographic assumptions, asexual lineages are short lived, but there is variation in clonal ages. Although alternative explanations exist, these results suggest that asexual lineages may persist in the short term through dispersal, and that various constraints may cause geographic restriction of sexual lineages. Both allotriploid and diploid Campeloma parthenogens have significantly higher allelic divergence within individuals, but show limited nuclear sequence divergence from sexual ancestors. In contrast to previous allozyme evidence for nonhybrid origins of diploid Campeloma parthenogens, cryptic hybridization may account for elevated heterozygosity.

Aging↗

PubMed2005

Disorder-immune confinement of light in photonic-crystal cavities.

We demonstrate by finite-difference time-domain simulations in 2D and 3D that optical cavities in realistic finite photonic crystals have lifetimes and modal volumes that are essentially insensitive to disorder (of various types, including surface disorder and randomized positions), even with unphysically large disorder. A lifetime Q = 10(8) is demonstrated in a 3D single-mode cavity with a half-wavelength mode diameter using only eight vertical periods of a disordered crystal.

Journal Article↗

PubMed2005

Evanescent-wave bonding between optical waveguides.

Forces arising from overlap between the guided waves of parallel, microphotonic waveguides are calculated. Both attractive and repulsive forces, determined by the choice of relative input phase, are found. Using realistic parameters for a silicon-on-insulator material system, we estimate that the forces are large enough to cause observable displacements. Our results illustrate the potential for a broader class of optically tunable microphotonic devices and microstructured artificial materials.

Journal Article↗

PubMed2005

Mode of origin differentially influences the fitness of parthenogenetic freshwater snails.

How parthenogenetic lineages arise from sexual ancestors may strongly influence their persistence over evolutionary time. Hybrid parthenogens often have elevated heterozygosity and ploidy, thus making it difficult to disentangle the influence of reproductive mode, hybridity and ploidy on their relative fitness. By comparing the relative fitness of both hybrid and non-hybrid parthenogens to their sexual ancestors, further insight may be gained into how these three factors influence the maintenance of sexual and parthenogenetic reproduction. In the present study, hybrid and non-hybrid parthenogenetic and sexual snails (Campeloma sp.) were compared for the following characteristics: female size-fecundity curves, offspring size, survivorship, and growth. Compared to nearby sexual populations, triploid hybrid parthenogens from the Florida Gulf coast have similar fecundity and offspring size, five-times higher survivorship, and 60% higher growth. Relative to nearby sexual populations, non-hybrid parthenogenetic C. limum from the Atlantic coast have significantly higher fecundity, smaller offspring size, similar survivorship and slightly lower growth. Given the considerable fitness advantages of parthenogens, especially hybrid parthenogens, it is enigmatic as to why these parthenogens occupy marginal natural habitats.

Analysis of Variance↗

PubMed2005

Microcavity confinement based on an anomalous zero group-velocity waveguide mode.

We propose and demonstrate a mechanism for small-modal-volume high-Q cavities based on an anomalous uniform waveguide mode that has zero group velocity at a nonzero wave vector. In a short piece of a uniform waveguide with a specially designed cross section, light is confined longitudinally by small group-velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are separated by approximately pi/k0, where k0 is the longitudinal wave vector for which the group velocity is zero.

Journal Article↗

PubMed2005

Age, phylogeography and population structure of the microendemic banded spring snail, Mexipyrgus churinceanus.

Recent theoretical and empirical studies of phylogeography and population structure indicate that many processes influence intraspecific evolutionary history. The present study represents the first examination of various forces influencing the spatial and temporal patterns of sequence variation in the freshwater Mexican banded spring snail, Mexipyrgus churinceanus. This snail occurs in one of the most critically endangered centres of freshwater endemism, the desert ecosystem of Cuatro Ciénegas. From cytochrome b mtDNA sequence variation, there is strong evidence of long-term isolation of three regions, suggesting that these regions represent evolutionarily distinct lineages. Molecular clock estimates of clade age indicate a time to most recent common ancestor of approximately 2.5 million years ago (Ma). The three regions differ considerably in the historical and demographic forces affecting population structure. The western populations have extremely low mtDNA diversity consistent with a severe bottleneck dating to 50,000 years before present (bp). The nearby Rio Mesquites drainage is characterized by fragmentation events, restricted gene flow with isolation by distance, and higher levels of mtDNA polymorphism. These patterns are consistent with the long-term stability of this drainage along with habitat heterogeneity and brooding contributing to population isolation and restricted gene flow. Southeastern populations show evidence of range expansion and a strong influence of genetic drift. Migration rates between drainages indicate very little gene flow between drainages except for asymmetric migration from the Rio Mesquites into both western and southeastern drainages.

Animals↗

PubMed2004

Discrete-mode cancellation mechanism for high-Q integrated optical cavities with small modal volume.

A mechanism to reduce radiation loss from integrated optical cavities without a complete photonic bandgap is introduced and demonstrated. It is applicable to any device with a patterned substrate (including both low and high index-contrast systems), when it supports discrete guided or leaky modes through which power escaping the cavity can be channeled into radiation. One then achieves the associated increase in Q by designing the cavity such that the near-field pattern becomes orthogonal to these discrete modes, therefore canceling the coupling of power into them and thus reducing the total radiation loss. The method is independent of any delocalization mechanism and can be used to create high-Q cavities with small modal volume.

Journal Article↗

PubMed2004

A three-dimensional optical photonic crystal with designed point defects.

Photonic crystals offer unprecedented opportunities for miniaturization and integration of optical devices. They also exhibit a variety of new physical phenomena, including suppression or enhancement of spontaneous emission, low-threshold lasing, and quantum information processing. Various techniques for the fabrication of three-dimensional (3D) photonic crystals--such as silicon micromachining, wafer fusion bonding, holographic lithography, self-assembly, angled-etching, micromanipulation, glancing-angle deposition and auto-cloning--have been proposed and demonstrated with different levels of success. However, a critical step towards the fabrication of functional 3D devices, that is, the incorporation of microcavities or waveguides in a controllable way, has not been achieved at optical wavelengths. Here we present the fabrication of 3D photonic crystals that are particularly suited for optical device integration using a lithographic layer-by-layer approach. Point-defect microcavities are introduced during the fabrication process and optical measurements show they have resonant signatures around telecommunications wavelengths (1.3-1.5 microm). Measurements of reflectance and transmittance at near-infrared are in good agreement with numerical simulations.

Journal Article↗

PubMed2003

Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions.

Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electromagnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fails when applied to the problem of shifted material boundaries. In this paper we developed coupled mode and perturbation theory formulations for treating generic perturbations of a waveguide cross section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate beyond the first order and rapidly converges to an exact result when used in a coupled mode theory framework even for the high-index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of such quantities as deterministic PMD and change in the GV and GVD of a mode due to generic profile distortion in a waveguide of arbitrary cross section. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary profile variations in high-index-contrast waveguides.

Journal Article↗

PubMed2003

Analysis of mode structure in hollow dielectric waveguide fibers.

In this paper, we analyze the electromagnetic mode structure of an OmniGuide fiber-a hollow dielectric waveguide in which light is confined by a large index-contrast omnidirectional dielectric mirror. In particular, we find that the modes in an OmniGuide fiber are similar to those in a hollow metallic waveguide in their symmetries, cutoff frequencies, and dispersion relations. We show that the differences can be predicted by a model based on a single parameter-the phase shift upon reflection from the dielectric mirror. The analogy to the metal waveguide extends to the transmission properties, resulting in the identification of the TE01 mode as the lowest-loss mode of the OmniGuide fiber.

Journal Article↗

PubMed2003

Optical bistability in axially modulated OmniGuide fibers.

We demonstrate the feasibility of optical bistability in an axially modulated nonlinear OmniGuide fiber through analytical theory and detailed numerical experiments. At 1.55-microm carrier wavelength, the in-fiber devices that we propose can operate with only a few tens of milliwatts of power, can have a nearly instantaneous response and recovery time, and can be shorter than 100 microm.

Journal Article↗

PubMed2003

Cerenkov radiation in photonic crystals.

In a conventional material, the coherent Cerenkov radiation due to a moving charged particle is associated with a velocity threshold, a forward-pointing radiation cone, and a forward direction of emission. We describe different behavior for the Cerenkov radiation in a photonic crystal. In particular, this radiation is intrinsically coupled with transition radiation and is observable without any threshold. Within one particle-velocity range, we found a radiation pattern with a backward-pointing radiation cone. In another velocity range, backward-propagating Cerenkov radiation can be expected. Potential applications include velocity-sensitive particle detection and radiation generation at selectable frequencies.

Journal Article↗

PubMed2002

Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals.

We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur, however, if the operating mode is propagating (nonevanescent) and guided at every point in the taper. Moreover, we demonstrate how straightforward taper designs in photonic crystals can violate these conditions, but that adiabaticity is restored by simple design principles involving only the independent band structures of the intermediate gratings. For these and other analyses, we develop a generalization of the standard coupled-mode theory to handle arbitrary nonuniform gratings via an instantaneous Bloch-mode basis, yielding a continuous set of differential equations for the basis coefficients. We show how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings. Unlike other numerical methods, our technique becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory. We also include numerical examples comparing to a well-established scattering-matrix method in two dimensions.

Journal Article↗

PubMed2002

Optimal bistable switching in nonlinear photonic crystals.

We present an analytical model and numerical experiments to describe optimal bistable switching in a nonlinear photonic crystal system. It is proved that only three parameters are needed to characterize a bistable switch: the resonant frequency omega(res), the quality factor Q, and parameter kappa that measures nonlinear "feedback strength." A photonic crystal enables the device to operate in single-mode fashion, as if it were effectively one dimensional. This provides optimal control over the input and output and facilitates further large-scale optical integration.

Journal Article↗

PubMed2002

Perturbation theory for Maxwell's equations with shifting material boundaries.

Perturbation theory permits the analytic study of small changes on known solutions, and is especially useful in electromagnetism for understanding weak interactions and imperfections. Standard perturbation-theory techniques, however, have difficulties when applied to Maxwell's equations for small shifts in dielectric interfaces (especially in high-index-contrast, three-dimensional systems) due to the discontinuous field boundary conditions--in fact, the usual methods fail even to predict the lowest-order behavior. By considering a sharp boundary as a limit of anisotropically smoothed systems, we are able to derive a correct first-order perturbation theory and mode-coupling constants, involving only surface integrals of the unperturbed fields over the perturbed interface. In addition, we discuss further considerations that arise for higher-order perturbative methods in electromagnetism.

Journal Article↗