Photonic crystals Joannopoulos, John D; Johnson, Steven G; Winn, Joshua N ...
2011., 2008-02-11
eBook
Since it was first published in 1995, "Photonic Crystals" has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the ...propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory.They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism.Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, "Photonic Crystals" is an indispensable resource for students and researchers. Extensively revised and expanded, this book: features improved graphics throughout; includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding; provides an introduction to coupled-mode theory as a powerful tool for device design; and, covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.
It is possible to learn about the orientation of a star's rotation axis by combining measurements of the star's rotation velocity (v) and its projection onto our line of sight (v sin i). This idea ...has found many applications, including the investigation of the obliquities of stars with transiting planets. Here, we present a method for the probabilistic inference of the inclination of the star's rotation axis based on independent data sets that constrain v and v sin i. We also correct several errors and misconceptions that appear in the literature.
Abstract
The third Gaia data release includes a catalog of exoplanets and exoplanet candidates identified via the star’s astrometric motion. This paper reports on tests for consistency between the ...Gaia two-body orbital solutions and precise Doppler velocities for stars currently amenable to such a comparison. For BD-17 0063, HD 81040, and HD 132406, the Gaia orbital solution and the Doppler data were found to be consistent and were fitted jointly to obtain the best possible constraints on the planets’ orbits and masses. Inconsistencies were found for four stars: HD 111232, probably due to additional planets that were not included in the astrometric model; HD 175167 and HR 810, possibly due to inaccurate treatment of non-Gaussian uncertainties in the Gaia orbital solutions; and HIP 66074, for unknown reasons. Consistency tests were also performed for HD 114762, which was reported in 1989 to have a brown dwarf or exoplanet but has since been shown to be a binary star. The joint Gaia–Doppler analysis shows the secondary mass to be 0.215 ± 0.013
M
⊙
and the orbital inclination to be 3.°63 ± 0.°06.
The Kepler mission revealed a population of compact multiple-planet systems with orbital periods shorter than a year, and occasionally even shorter than a day. By analyzing a sample of 102 Kepler and ...K2 multiple-planet systems, we measure the minimum difference ΔI between the orbital inclinations, as a function of the orbital distance of the innermost planet. This is accomplished by fitting all the planetary signals simultaneously, constrained by an external estimate of the stellar mean density. We find ΔI to be larger when the inner orbit is smaller, a trend that does not appear to be a selection effect. We find that planets with a/R < 5 have a dispersion in ΔI of 6 7 0 6, while planets with 5 < a/R < 12 have a dispersion of 2 0 0 1. The planetary pairs with higher mutual inclinations also tend to have larger period ratios. These trends suggest that the shortest-period planets have experienced both inclination excitation and orbital shrinkage.
The basic geometry of the Solar System-the shapes, spacings, and orientations of the planetary orbits-has long been a subject of fascination as well as inspiration for planet-formation theories. For ...exoplanetary systems, those same properties have only recently come into focus. Here we review our current knowledge of the occurrence of planets around other stars, their orbital distances and eccentricities, the orbital spacings and mutual inclinations in multiplanet systems, the orientation of the host star's rotation axis, and the properties of planets in binary-star systems.
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Terrestrial planets have been found orbiting Sun-like stars with extremely short periods-some as short as 4 hr. These "ultra-short-period planets" or "hot Earths" are so strongly irradiated that any ...initial H/He atmosphere has probably been lost to photoevaporation. As such, the sample of hot Earths may give us a glimpse at the rocky cores that are often enshrouded by thick H/He envelopes on wider-orbiting planets. However, the mass and radius measurements of hot Earths have been derived from a hodgepodge of different modeling approaches, and include several cases of contradictory results. Here, we perform a homogeneous analysis of the complete sample of 11 known hot Earths with an insolation exceeding 650 times that of the Earth. We combine all available data for each planet, incorporate parallax information from Gaia to improve the stellar and planetary parameters, and use Gaussian process regression to account for correlated noise in the radial-velocity data. The homogeneous analysis leads to a smaller dispersion in the apparent composition of hot Earths, although there does still appear to be some intrinsic dispersion. Most of the planets are consistent with an Earth-like composition (35% iron and 65% rock), but two planets (K2-141b and K2-229b) show evidence for a higher iron fraction, and one planet (55 Cnc e) has either a very low iron fraction or an envelope of low-density volatiles. All of the planets are less massive than 8 M⊕, despite the selection bias toward more massive planets, suggesting that 8 M⊕ is the critical mass for runaway accretion.
We present the analysis of four months of Kepler photometry of the K4V star HAT-P-11, including 26 transits of its 'super-Neptune' planet. The transit data exhibit numerous anomalies which we ...interpret as passages of the planet over dark starspots. These spot-crossing anomalies preferentially occur at two specific phases of the transit. These phases can be understood as the intersection points between the transit chord and the active latitudes of the host star, where starspots are most abundant. Based on the measured characteristics of spot-crossing anomalies and previous observations of the Rossiter-McLaughlin effect, we find two solutions for the stellar obliquity Delta *v and active latitude l: either Delta *v = 106+15 --11 and l = 19.7+1.5 --2.2, or Delta *v = 97+8 --4 and l = 67+2 --4 (all in degrees). If the active latitude changes with time analogous to the 'butterfly diagram' of the Sun's activity cycle, future observations should reveal changes in the preferred phases of spot-crossing anomalies.
Observations of nine transits of WASP-107 during the K2 mission reveal three separate occasions when the planet crossed in front of a starspot. The data confirm the stellar rotation period to be 17 ...days-approximately three times the planet's orbital period-and suggest that large spots persist for at least one full rotation. If the star had a low obliquity, at least two additional spot crossings should have been observed. They were not observed, giving evidence for a high obliquity. We use a simple geometric model to show that the obliquity is likely in the range 40°-140°, i.e., both spin-orbit alignment and anti-alignment can be ruled out. WASP-107 thereby joins the small collection of relatively low-mass stars with a high obliquity. Most such stars have been observed to have low obliquities; all of the exceptions, including WASP-107, involve planets with relatively wide orbits ("warm Jupiters," with ). This demonstrates a connection between stellar obliquity and planet properties, in contradiction to some theories for obliquity excitation.
ABSTRACT The obliquities of planet-hosting stars are clues about the formation of planetary systems. Previous observations led to the hypothesis that for close-in giant planets, spin-orbit alignment ...is enforced by tidal interactions. Here, we examine two problems with this hypothesis. First, Mazeh and coworkers recently used a new technique-based on the amplitude of starspot-induced photometric variability-to conclude that spin-orbit alignment is common even for relatively long-period planets, which would not be expected if tides were responsible. We re-examine the data and find a statistically significant correlation between photometric variability and planetary orbital period that is qualitatively consistent with tidal interactions. However it is still difficult to explain quantitatively, as it would require tides to be effective for periods as long as tens of days. Second, Rogers and Lin argued against a particular theory for tidal re-alignment by showing that initially retrograde systems would fail to be re-aligned, in contradiction with the observed prevalence of prograde systems. We investigate a simple model that overcomes this problem by taking into account the dissipation of inertial waves and the equilibrium tide, as well as magnetic braking. We identify a region of parameter space where re-alignment can be achieved, but it only works for close-in giant planets, and requires some fine tuning. Thus, while we find both problems to be more nuanced than they first appeared, the tidal model still has serious shortcomings.
Probing the connection between a star's metallicity and the presence and properties of any associated planets offers an observational link between conditions during the epoch of planet formation and ...mature planetary systems. We explore this connection by analyzing the metallicities of Kepler target stars and the subset of stars found to host transiting planets. After correcting for survey incompleteness, we measure planet occurrence: the number of planets per 100 stars with a given metallicity M. Planet occurrence correlates with metallicity for some, but not all, planet sizes and orbital periods. For warm super-Earths having P = 10-100 days and = 1.0-1.7 , planet occurrence is nearly constant over metallicities spanning −0.4 to +0.4 dex. We find 20 warm super-Earths per 100 stars, regardless of metallicity. In contrast, the occurrence of warm sub-Neptunes ( = 1.7-4.0 ) doubles over that same metallicity interval, from 20 to 40 planets per 100 stars. We model the distribution of planets as , where β characterizes the strength of any metallicity correlation. This correlation steepens with decreasing orbital period and increasing planet size. For warm super-Earths β = , while for hot Jupiters β = . High metallicities in protoplanetary disks may increase the mass of the largest rocky cores or the speed at which they are assembled, enhancing the production of planets larger than 1.7 . The association between high metallicity and short-period planets may reflect disk density profiles that facilitate the inward migration of solids or higher rates of planet-planet scattering.
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