Time-harmonic solutions for Maxwell’s equations in anisotropic media and Bochner–Riesz estimates with negative index for non-elliptic surfaces

We solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of $L^p$ -spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces

Time-Harmonic Solutions for Maxwell’s Equations in Anisotropic Media and Bochner–Riesz Estimates with Negative Index for Non-elliptic Surfaces

We solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of $L^p$-spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces

Supersensitive measurement of angular displacements using entangled photons

We show that the use of entangled photons having non-zero orbital angular momentum (OAM) increases the resolution and sensitivity of angular-displacement measurements performed using an interferometer. By employing a 4$\times$4 matrix formulation to study the propagation of entangled OAM modes, we analyze measurement schemes for two and four entangled photons and obtain explicit expressions for the resolution and sensitivity in these schemes. We find that the resolution of angular-displacement measurements scales as $Nl$ while the angular sensitivity increases as $1/(2Nl)$, where $N$ is the number of entangled photons and $l$ the magnitude of the orbital-angular-momentum mode index. These results are an improvement over what could be obtained with $N$ non-entangled photons carrying an orbital angular momentum of $l\hbar$ per photonComment: 6 pages, 3 figure

Conditional preparation of states containing a definite number of photons

A technique for conditionally creating single- or multimode photon-number states is analyzed using Bayesian theory. We consider the heralded N-photon states created from the photons produced by an unseeded optical parametric amplifier when the heralding detector is the time-multiplexed photon-number-resolving detector recently demonstrated by Fitch, et al. [Phys. Rev. A 68, 043814 (2003).] and simultaneously by Achilles, et al. [Opt. Lett. 28, 2387 (2003).]. We find that even with significant loss in the heralding detector, fields with sub-Poissonian photon-number distributions can be created. We also show that heralded multimode fields created using this technique are more robust against detector loss than are single-mode fields.Comment: 6 pages, 6 figures, reference added, typos corrected, content update

Measurement of the Orbital Angular Momentum Spectrum of Partially Coherent Fields using Double Angular Slit Interference

We implement an interferometric method using two angular slits to measure the orbital angular momentum (OAM) mode spectrum of a partially coherent field. As the angular separation of the slits changes, an interference pattern for a particular OAM mode is obtained. The visibility of this interference pattern as a function of angular separation is equivalent to the angular correlation function of the field. By Fourier transforming the angular correlation function obtained from the double angular slit interference, we are able to calculate the OAM spectrum of the partially coherent field. This method has potential application for characterizing the OAM spectrum in high-dimensional quantum information protocols.Comment: 5 pages, 5 figure

Simulator-Based Driving with Hemianopia: Detection Performance and Compensatory Behaviors on Approach to Intersections

OBJECTIVES In 22 states people with homonymous hemianopia (complete loss of the visual field on the sameside in both eyes) are explicitly prohibited from driving, as they do not meet the minimum visualfield requirements for driver licensing. However, there is little scientific evidence derived eitherfrom on-road or driving simulator studies about the safety of driving with hemianopia. If the eyeand head were kept stationary, people with hemianopia would not detect anything on the side ofthe field loss. In the real world, however, they may be able to compensate for the loss byexploring the affected (blind) side using head- and eye-scanning. It has been reported that inHolland (where driving with hemianopia is permitted), driving examiners consider increasedhead-scanning (especially on approach to intersections) to be an effective compensation forperipheral visual field defects (Coeckelbergh et al., 2002). Whether increased head-scanningwhile driving results in better detection performance has never been quantitatively investigated.We conducted a simulator-based evaluation of driving with hemianopia to investigate detectionperformance and head movement behaviors on approach to intersections.METHODSTo date, eight people with complete homonymous hemianopia (5 left and 3 right), and withoutvisual neglect or significant cognitive decline have completed the study. All had current or recentdriving experience (within the last 6 years). They completed two simulator sessions, one weekapart, driving in a high-fidelity simulator. Each session consisted of a familiarization period of30-60 minutes followed by 6 test drives (each about 12 minutes in duration). The primarysimulator task was to detect and respond (by a horn press) to the appearance of pedestrian targetsin a variety of traffic situations while driving according to the normal rules of the road. Targetsappeared randomly in locations relevant to real-world driving. There were two types of targets:“roadway” targets, which appeared either on the left or right of the road at small (~ 4°) or large(~14°) eccentricities from the presumed line of sight, and “intersection” targets, which wereplaced near or at intersections to test whether drivers were scanning effectively whenapproaching an intersection. Primary outcome measures were the percentage of targets detectedand reaction times when detected. Head movements were recorded with an inexpensive, lightweight,head-mounted optical head tracking system. Preliminary analyses of head movementbehaviors were conducted for intersections with stop or yield signs. Based on visual inspectionof the head movement plots, the number and direction of head movements were recorded and head movement scanning was graded on a 4-point scale (from 1 inadequate to 4 excellent). Inaddition, we are developing methods to automatically quantify driving skills (e.g., steering, laneposition) from the simulator data output.RESULTSDetection rates for roadway pedestrian targets were lower and reaction times longer on the blindside than the seeing side (p ≤ 0.05). Blind side: median detection rate 47% (IQR 22 to 63%),median reaction time 1.65s (IQR 1.05 to 1.84s); seeing side: median detection rate 93% (IQR89% to 99%), median reaction time 0.93s, (IQR 0.88 to 1.25s). Detection rates on the blind sidewere lower at the larger eccentricity (median 23%) than the smaller eccentricity (median 66%; p= 0.01). Drivers with right hemianopia (RH) detected 83% of intersection pedestrian targets onthe extreme left of an intersection but none on the extreme right, whereas drivers with lefthemianopia (LH) detected 33% on the extreme left and 80% on the extreme right. Better headscanningscores were associated with better detection rates for intersection targets at extremepositions on the blind side (Spearman r = 0.79, p = 0.02). Two of the drivers with LH showedinadequate scanning (grade 1), failing to scan to the left at more than 60% of intersections. Therest of the drivers with LH and all three with RH demonstrated better head-scanning (grades 2-4)with some compensatory head movement behaviors. At T-intersections with no incoming roadon one side, they scanned more frequently in the direction of the “absent” road when it was onthe blind side (RH 40% and LH 80%) than when it was on the seeing side (RH and LH \u3c10%).When there were incoming roads on both sides, the first head scan was normally to the left forLH, but it was to the right about 30% of the time for drivers with RH.CONCLUSIONSThese results provide evidence of widely varying levels of compensation and detection abilitiesamongst drivers with hemianopia, suggesting that fitness to drive should be evaluated on anindividual basis. The preliminary finding of a relationship between head-scanning score andintersection detection performance will be further evaluated using automated methods toquantify head movement behaviors and a larger sample of drivers with hemianopia. Furthermore,we will compare head movement behaviors of drivers with hemianopia to matched controldrivers without visual field loss.REFERENCESCoeckelbergh, T.R., Brouwer, W.H., Cornelissen, F.W., van Wolffelaar, P., Kooijman, A.C.(2002). The effect of visual field defects on driving performance: a driving simulator study. ArchOphthalmol, 120, 1509-1516

Effects of Terms of Trade Gains and Tariff Changes on the Measurement of US Productivity Growth

The acceleration in US productivity growth since 1995 is often attributed to declining prices for information technology (IT ) goods, and therefore enhanced productivity growth in that sector. We investigate an alternative explanation for these IT price movements: gains in the US terms of trade and tariff reductions, especially for IT products, which led to greater gains than shown by official indexes. We do not, however, investigate the indexes used to deflate the domestic absorption components of GDP, and if upward biases are present in those indexes that could offset some of the effects of mismeasured export and import indexes. (JEL C43, E23, F13, F14, J24