Sliderule-like property of Wigner's little groups and cyclic S-matrices for multilayer optics

It is noted that two-by-two S-matrices in multilayer optics can be represented by the Sp(2) group whose algebraic property is the same as the group of Lorentz transformations applicable to two space-like and one time-like dimensions. It is noted also that Wigner's little groups have a sliderule-like property which allows us to perform multiplications by additions. It is shown that these two mathematical properties lead to a cyclic representation of the S-matrix for multilayer optics, as in the case of ABCD matrices for laser cavities. It is therefore possible to write the N-layer S-matrix as a multiplication of the N single-layer S-matrices resulting in the same mathematical expression with one of the parameters multiplied by N. In addition, it is noted, as in the case of lens optics, multilayer optics can serve as an analogue computer for the contraction of Wigner's little groups for internal space-time symmetries of relativistic particles.Comment: RevTex 13 pages, Secs. IV and V revised and expande

Robust IR Remote Sensing Technique of the Total Column of Trace Gases Including Carbon Dioxide and Methane

Progress on the development of a differential radiometer based upon the Fabry-Perot interferometer (FPI) for methane (CH4) and carbon dioxide (C02) detection in the atmosphere is presented. Methane measurements are becoming increasingly important as a component of NASA's programs to understand the global carbon cycle and quantifY the threat of global warming. Methane is the third most important greenhouse gas in the Earth's radiation budget (after water vapor and carbon dioxide) and the second most important anthropogenic contributor to global warming. The importance of global warming and air quality to society caused the National Research Council to recommend that NASA develop the following missions [1]: ASCENDS (Active Sensing of C02 Emissions over Nights, Days, and Seasons), GEOCAPE (Geostationary Coastal and Air Pollution Events), and GACM (Global Atmosphere Composition Mission). Though methane measurements are not specifically called out in these missions, ongoing environmental changes have raised the importance of understanding the methane budget. In the decadal survey is stated that "to close the carbon budget, we would also address methane, but the required technology is not obvious at this time. If appropriate and cost-effective methane technology becomes available, we strongly recommend adding a methane capability". In its 2007 report the International Panel on Climate Change identified methane as a key uncertainty in our understanding saying that the causes of recent changes in the growth rate of atmospheric CH4 are not well understood. What we do know is that methane arises from a number of natural sources including wet lands and the oceans plus man made sources from agriculture, as well as coal and petroleum production and distribution. It has recently been pointed out that large amount of methane are frozen in the permafrost of Canada and Siberia. There is a fear that melting of this permafrost driven by global warming may release large amounts of methane very suddenly further exacerbating climate change [2]. Last year our group began a joint effort with Johns Hopkins Applied Physics Laboratory to investigate the possibility of developing a small unmanned aerial vehicle (UAV) equipped to measure greenhouse gases-particularly methane. Although we are targeting our system for smaller UAV's the instrument will be directly applicable to missions involving larger NASA UAV's such as Global Hawk or even on missions utilizing manned aircraft. Because of its small size, inherent ruggedness and simplicity some version of our proposed instrument may find a role as a satellite instrument for NASA or NOAA

A New Remote Sensing Filter Radiometer Employing a Fabry-Perot Etalon and a CCD Camera for Column Measurements of Methane in the Earth Atmosphere

A portable remote sensing system for precision column measurements of methane has been developed, built and tested at NASA GSFC. The sensor covers the spectral range from 1.636 micrometers to 1.646 micrometers, employs an air-gapped Fabry-Perot filter and a CCD camera and has a potential to operate from a variety of platforms. The detector is an XS-1.7-320 camera unit from Xenics Infrared solutions which combines an uncooled InGaAs detector array working up to 1.7 micrometers. Custom software was developed in addition to the graphical user basic interface X-Control provided by the company to help save and process the data. The technique and setup can be used to measure other trace gases in the atmosphere with minimal changes of the etalon and the prefilter. In this paper we describe the calibration of the system using several different approaches

A Broad Bank Lidar for Precise Atmospheric CO2 Column Absorption Measurement from Space

Accurate global measurement of carbon dioxide column with the aim of discovering and quantifying unknown sources and sinks has been a high priority for the last decade. In order to uncover the "missing sink" that is responsible for the large discrepancies in the budget the critical precision for a measurement from space needs to be on the order of 1 ppm. To better understand the CO2 budget and to evaluate its impact on global warming the National Research Council (NRC) in its recent decadal survey report (NACP) to NASA recommended a laser based total CO2 mapping mission in the near future. That's the goal of Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) mission - to significantly enhance the understanding of the role of CO2 in the global carbon cycle. Our current goal is to develop an ultra precise, inexpensive new lidar system for column measurements of CO2 changes in the lower atmosphere that uses a Fabry-Perot interferometer based system as the detector portion of the instrument and replaces the narrow band laser commonly used in lidars with a high power broadband source. This approach reduces the number of individual lasers used in the system and considerably reduces the risk of failure. It also tremendously reduces the requirement for wavelength stability in the source putting this responsibility instead on the Fabry- Perot subsystem

Differential Radiometers Using Fabry-Perot Interferometric Technique for Remote Sensing Determination of Various Atmospheric Trace Gases

New type of remote sensing instrument based upon the Fabry-Perot inte rferometric technique has been developed at NASA's Goddard Space Flight Center. Fabry-Perot interferometry (FPI) is a well known, powerful spectroscopic technique and one of its many applications is to be use d to measure greenhouse gases and also some harmful species in the at mosphere. With this technique, absorption of particular species is me asured and related to its concentration. A solid Fabry-Perot etalon is used as a frequency filter to restrict the measurement to particular absorption bands of the gas of interest. With adjusting the thicknes s of the etalon that separation (in frequency) of the transmitted fri nges can be made equal to the almost constant separation of the gas a bsorption lines. By adjusting the temperature of the etalon, which changes the index of refi-action of its material, the transmission fring es can be brought into nearly exact correspondence with absorption li nes of the particular species. With this alignment between absorption lines and fringes, changes in the amount of a species in the atmosph ere strongly affect the amount of light transmitted by the etalon and can be related to gas concentration. The instrument that we have dev eloped detects the absorption of various atmospheric trace gases in d irect or reflected sunlight. Our instrument employing Fabry-Perot interferometer makes use of two features to achieve high sensitivity. The first is high spectral resolution enabling one to match the width of an atmospheric absorption feature by the instrumental band pass. The second is high optical throughput enabled by using multiple spectral lines simultaneously. For any species that one wishes to measure, thi s first feature is available while the use of multiple spectral features can be employed only for species with suitable spectra and freedom from interfering species in the same wavelength region. We have deve loped an instrument for use as ground based, airborne and satellite s ensor for gases such as carbon dioxide (1570 nm), oxygen (762 nm and 768 nm lines sensitive to changes in oxygen pressure and oxygen temper ature) and water vapor (940 nm). Our current goal is to develop an ul tra precise, inexpensive, ground based device suitable for wide deplo yment as a validation instrument for the Orbiting Carbon Observatory (OCO) satellite. We show sensitivity measurements for CO2, 02, and H2 O, compare our measurements to those obtained using other types of sensors and discuss some of the peculiarities that must be addressed in order to provide the very high quality column detection required for solving problems about global distribution of greenhouse gases and cl imatological models. In another area of research we are interested in developing a small-size channel for CO2 capable of doing simultaneous measurements with the AERONET (Aerosol Robotic Network) at NASA, God dard to study the hypothesis that atmospheric aerosols affect the reg ional terrestrial carbon cycle. We present recent data from our groun d based measurements of O2, CO2, H2O and (13)CO2 and discuss extensio n of the technique to new species and applications

Staggering behavior of the low lying excited states of even-even nuclei in a Sp(4,R) classification scheme

We implement a high order discrete derivative analysis of the low lying collective energies of even-even nuclei with respect to the total number of valence nucleon pairs N in the framework of F- spin multiplets appearing in a symplectic sp(4,R) classification scheme. We find that for the nuclei of any given F- multiplet the respective experimental energies exhibit a Delta N=2 staggering behavior and for the nuclei of two united neighboring F- multiplets well pronounced Delta N=1 staggering patterns are observed. Those effects have been reproduced successfully through a generalized sp(4,R) model energy expression and explained in terms of the step-like changes in collective modes within the F- multiplets and the alternation of the F-spin projection in the united neighboring multiplets. On this basis we suggest that the observed Delta N=2 and Delta N=1 staggering effects carry detailed information about the respective systematic manifestation of both high order alpha - particle like quartetting of nucleons and proton (neutron) pairing interaction in nuclei.PACS number(s):21.10.Re, 21.60.FwComment: 22 pages and 6 figures changes in the figure caption

Electron effective mass in Al0.72_{0.72}Ga0.28_{0.28}N alloys determined by mid-infrared optical Hall effect

The effective electron mass parameter in Si-doped Al$_{0.72}$Ga$_{0.28}$N is determined to be $m^\ast=(0.336\pm0.020)\,m_0$ from mid-infrared optical Hall effect measurements. No significant anisotropy of the effective electron mass parameter is found supporting theoretical predictions. Assuming a linear change of the effective electron mass with the Al content in AlGaN alloys and $m^\ast=0.232\,m_0$ for GaN, an average effective electron mass of $m^\ast=0.376\,m_0$ can be extrapolated for AlN. The analysis of mid-infrared spectroscopic ellipsometry measurements further confirms the two phonon mode behavior of the E$_1$(TO) and one phonon mode behavior of the A$_1$(LO) phonon mode in high-Al-content AlGaN alloys as seen in previous Raman scattering studies

Communicative discourse of terminology used in gastronomical media culture

This article aims to analyze and describe the food discourse and terms of the French language, as well as to determine correlations with the French national and cultural worldview. The study also considers the current state of "gastronomical discourse" based on the French food semiotic and communicative mode