Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Thermal effects are already important in currently operating interferometric gravitational wave detectors. Planned upgrades of these detectors involve increasing optical power to combat quantum shot noise. We consider the ramifications of this increased power for one particular class of laser beams—wide, flat-topped, mesa beams. In particular we model a single mesa beam Fabry–Perot cavity having thermoelastically deformed mirrors. We calculate the intensity profile of the fundamental cavity eigenmode in the presence of thermal perturbations, and the associated changes in thermal noise. We also outline an idealized method of correcting for such effects. At each stage we contrast our results with those of a comparable Gaussian beam cavity. Although we focus on mesa beams the techniques described are applicable to any azimuthally symmetric system

The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies $f \sim 40$ Hz to $\sim 200$ Hz is expected to be due to thermal fluctuations in the mirrors' substrates and coatings which induce random fluctuations in the shape of the mirror face. The laser-light beam averages over these fluctuations; the larger the beam and the flatter its light-power distribution, the better the averaging and the lower the resulting thermal noise. In semi-infinite mirrors, scaling laws for the influence of beam shape on the four dominant types of thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and substrate thermoelastic) have been suggested by various researchers and derived with varying degrees of rigour. Because these scaling laws are important tools for current research on optimizing the beam shape, it is important to firm up our understanding of them. This paper (1) gives a summary of the prior work and of gaps in the prior analyses, (2) gives a unified and rigorous derivation of all four scaling laws, and (3) explores, relying on work by J. Agresti, deviations from the scaling laws due to finite mirror size.Comment: 25 pages, 10 figures, submitted to Class. Quantum Gra

Managers Handbook for Software Development

Methods and aids for the management of software development projects are presented. The recommendations are based on analyses and experiences with flight dynamics software development. The management aspects of organizing the project, producing a development plan, estimation costs, scheduling, staffing, preparing deliverable documents, using management tools, monitoring the project, conducting reviews, auditing, testing, and certifying are described

A multi-color fast-switching microfluidic droplet dye laser

We describe a multi-color microfluidic dye laser operating in whispering gallery mode based on a train of alternating droplets containing solutions of different dyes; this laser is capable of switching the wavelength of its emission between 580 nm and 680 nm at frequencies up to 3.6 kHz -— the fastest among all dye lasers reported; it has potential applications in on-chip spectroscopy and flow cytometry

X-Ray Diffraction and Reflectance Spectroscopy of Murchison Powders (CM2) After Thermal Analysis Under Reducing Conditions to Final Temperatures Between 300 and 1300c

The asteroids Ryugu and Bennu have spectral characteristics in common with CI/CM type carbonaceous chondrites and are target bodies for JAXAs Hayabusa2 and NASAs OSIRIS-Rex missions, respectively. Analog studies, based primarily on the Murchison CM2 chondrite, provide a pathway to separate spectral properties resulting space weathering from those inherent to parent-body, mineralogy, chemistry, and processes. Ryugu shares spectral properties with thermally metamorphosed and partly dehydrated CI/CM chondrites. We have undertaken a multidisciplinary study of the thermal decomposition of Murchison powder samples as an analog to metamorphic process that may have occurred on Ryugu. Bulk analyses include thermal And evolved gas analysis, X-ray diffraction (XRD), and VIS-NIR and Mssbauer spectroscopy; micro- to nanoscale analyses included scanning and transmission electron microscopy and electron probe micro analysisWe report here XRD and VIS-NIR analyses of pre- and post-heated Murchison powders, and in a companion paper report results from multiple electron beam techniques

High reflectivity grating waveguide coatings for 1064nm

We propose thin single-layer grating waveguide structures to be used as high-reflectivity, but low thermal noise, alternative to conventional coatings for gravitational wave detector test mass mirrors. Grating waveguide (GWG) coatings can show a reflectivity of up to 100% with an overall thickness of less than a wavelength. We theoretically investigate GWG coatings for 1064nm based on tantala (Ta2O5) on a Silica substrate focussing on broad spectral response and low thickness

Markov bases and subbases for bounded contingency tables

In this paper we study the computation of Markov bases for contingency tables whose cell entries have an upper bound. In general a Markov basis for unbounded contingency table under a certain model differs from a Markov basis for bounded tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for contingency tables whose cell entries are bounded. However, in the process, one has to compute the universal Gr\"obner basis of the ideal associated with the design matrix for a model which is, in general, larger than any reduced Gr\"obner basis. Thus, this is also infeasible in small- and medium-sized problems. In this paper we focus on bounded two-way contingency tables under independence model and show that if these bounds on cells are positive, i.e., they are not structural zeros, the set of basic moves of all $2 \times 2$ minors connects all tables with given margins. We end this paper with an open problem that if we know the given margins are positive, we want to find the necessary and sufficient condition on the set of structural zeros so that the set of basic moves of all $2 \times 2$ minors connects all incomplete contingency tables with given margins.Comment: 22 pages. It will appear in the Annals of the Institution of Statistical Mathematic

Generation of a flat-top laser beam for gravitational wave detectors by means of a nonspherical Fabry-Perot resonator

We have tested a new kind of Fabry-Perot long-baseline optical resonator proposed to reduce the thermal noise sensitivity of gravitational wave interferometric detectors--the "mesa beam" cavity--whose flat top beam shape is achieved by means of an aspherical end mirror. We present the fundamental mode intensity pattern for this cavity and its distortion due to surface imperfections and tilt misalignments, and contrast the higher order mode patterns to the Gauss-Laguerre modes of a spherical mirror cavity. We discuss the effects of mirror tilts on cavity alignment and locking and present measurements of the mesa beam tilt sensitivity

Logistic regression for simulating damage occurrence on a fruit grading line

Many factors influence the incidence of mechanical damage in fruit handled on a grading line. This makes it difficult to address damage estimation from an analytical point of view. During fruit transfer from one element of a grading line to another, damage occurs as a combined effect of machinery roughness and the intrinsic susceptibility of fruit. This paper describes a method to estimate bruise probability by means of logistic regression, using data yielded by specific laboratory tests. Model accuracy was measured via the statistical significance of its parameters and its classification ability. The prediction model was then linked to a simulation model through which impacts and load levels, similar to those of real grading lines, could be generated. The simulation output sample size was determined to yield reliable estimations. The process makes it possible to derive a suitable line design and the type of fruit that should be handled to maintain bruise levels within European Union (EU) Standards. A real example with peaches was carried out with the aid of the software implementation SIMLIN®, developed by the authors and registered by Madrid Technical University. This kind of tool has been demanded by inter-professional associations and grading lines designers in recent year