The refractive index and wave vector in passive or active media

Materials that exhibit loss or gain have a complex valued refractive index $n$. Nevertheless, when considering the propagation of optical pulses, using a complex $n$ is generally inconvenient -- hence the standard choice of real-valued refractive index, i.e. n_s = \RealPart (\sqrt{n^2}). However, an analysis of pulse propagation based on the second order wave equation shows that use of $n_s$ results in a wave vector \emph{different} to that actually exhibited by the propagating pulse. In contrast, an alternative definition n_c = \sqrt{\RealPart (n^2)}, always correctly provides the wave vector of the pulse. Although for small loss the difference between the two is negligible, in other cases it is significant; it follows that phase and group velocities are also altered. This result has implications for the description of pulse propagation in near resonant situations, such as those typical of metamaterials with negative (or otherwise exotic) refractive indices.Comment: Phys. Rev. A, to appear (2009

Four Poynting Theorems

The Poynting vector is an invaluable tool for analysing electromagnetic problems. However, even a rigorous stress-energy tensor approach can still leave us with the question: is it best defined as \Vec{E} \cross \Vec{H} or as \Vec{D} \cross \Vec{B}? Typical electromagnetic treatments provide yet another perspective: they regard \Vec{E} \cross \Vec{B} as the appropriate definition, because \Vec{E} and \Vec{B} are taken to be the fundamental electromagnetic fields. The astute reader will even notice the fourth possible combination of fields: i.e. \Vec{D} \cross \Vec{H}. Faced with this diverse selection, we have decided to treat each possible flux vector on its merits, deriving its associated energy continuity equation but applying minimal restrictions to the allowed host media. We then discuss each form, and how it represents the response of the medium. Finally, we derive a propagation equation for each flux vector using a directional fields approach; a useful result which enables further interpretation of each flux and its interaction with the medium.Comment: 8 pages. Updated slightly from EJP versio

Large Area Crop Inventory Experiment (LACIE). Phase 3 direct wheat study of North Dakota

The author has identified the following significant results. The green number and brightness scatter plots, channel plots of radiance values, and visual study of the imagery indicate separability between barley and spring wheat/oats during the wheat mid-heading to mid-ripe stages. In the LACIE Phase 3 North Dakota data set, the separation time is more specifically the wheat soft dough stage. At this time, the barley is ripening, and is therefore, less green and brighter than the wheat. Only 4 of the 18 segments studied indicate separation of barley/other spring small grain, even though 11 of the segments have acquisitions covering the wheat soft dough stage. The remaining seven segments had less than 5 percent barley based on ground truth data

Composition and assembly of a spectral data base for corn and soybean multicrop segments

There are no author-identified significant results in this report

Causality-based criteria for a negative refractive index must be used with care

Using the principle of causality as expressed in the Kramers-Kronig relations, we derive a generalized criterion for a negative refractive index that admits imperfect transparency at an observation frequency $\omega$. It also allows us to relate the global properties of the loss (i.e. its frequency response) to its local behaviour at $\omega$. However, causality-based criteria rely the on the group velocity, not the Poynting vector. Since the two are not equivalent, we provide some simple examples to compare the two criteria.Comment: slightly longer version of published PR

Composition and assembly of a spectral data base for transition year spring wheat blind sites

There are no author-identified significant results in this report

The Secret to 85% First-Time Bar Passage Rates

Many law schools have implemented bar preparation courses either as free-standing courses or as an integral part of their academic support program. On April 1, 2016, the ABA Journal published an article on the subject of law school bar preparation courses. Three law schools were featured in that article: Belmont University College of Law ( Belmont ), Florida International University College of Law ( FIU ), and the University of Missouri-Kansas City School of Law ( UMKC ). According to the ABA Journal, these law schools are out-performing their peers on bar exams due in part to in-house bar preparation courses. The story in the ABA Journal, however, was published several months before the ABA released complete bar exam results for calendar-year 2015; those results were released on December 15, 2016. With complete 2015 bar exam results now available, the purpose of this article is to substantiate the thesis of the ABA Journal article and to provide more information about these three successful bar exam programs. The article will also show that these three schools did outperform their peers on the bar exam in 2015. Belmont, FIU, and UMKC each had a first-time bar passage rate of 85% or higher, a remarkable accomplishment in this era of plummeting bar passage rates. Section I of this article will examine whether the three law schools featured in the ABA Journal (Belmont, FR, and UMKC) truly excelled on bar exams in 2015. Using linear regression analyses, Section 11 will address a more important question: whether those law schools actually outperformed their peers on bar exams in 2015? Section III will disclose, based on available evidence, whether Belmont, FR, and UMKC continued to outperform other law schools on the bar exam in 2016 (and February 2017). Finally, Section IV will describe in detail a successful law school bar preparation course

Extending the spectrum of AKT1 mosaicism - not just the Proteus syndrome

A five-year-old girl was referred to our department for evaluation of a pigmented birthmark on her right cheek, present unchanged since birth. There was no other past medical history of note and no family history of relevant problems. Cutaneous examination revealed a pigmented keratinocytic epidermal naevus following fine Blaschko's lines on the right cheek and neck (Figure 1), and a solitary café-au-lait macule of 1cm on the lower leg