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At least 109 records · Page 6

Impacts of Land Carbon Flux Variability on Variations in Atmospheric CO2

To better understand the role of atmospheric CO2 in the global carbon cycle, it is important to understand the factors that control its variability in time and space. Here we investigate these factors using a coupled land-atmosphere modeling system (the NASA GEOS-5 model) fitted with land carbon physics and atmospheric CO2 transport. To separate the influences of land carbon flux variability and atmospheric transport variability on the variability of CO2 concentrations, we conducted two carbon-fitted GEOS-5 AGCM simulations run in replay mode (a technique that guides the model's weather to match that of the MERRA-2 reanalysis): (i) a control simulation of 15-year carbon cycle dynamics and climate, and (ii) a simulation in which the climatological seasonal cycles of net biosphere production (NBP), as determined from diagnostics produced in the control experiment, are applied at the surface to the atmosphere instead. The impact of land flux variability on atmospheric CO2 variability is then isolated by subtracting the variability inherent in the second simulation (as induced, e.g., by strong El Nino conditions) from that in the control. These results are also presented in the context of supplemental simulations that have examined the impact of imposed drought in a free running AGCM simulation on carbon fluxes and atmospheric CO2 variability.

Lee, Eunjee

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

Joanna N Schmidt

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

robust design

Spatio-Temporal Variability of Groundwater Storage in India

Groundwater level measurements from 3907 monitoring wells, distributed within 22 major river basins of India, are assessed to characterize their spatial and temporal variability. Ground water storage (GWS) anomalies (relative to the long-term mean) exhibit strong seasonality, with annual maxima observed during the monsoon season and minima during pre-monsoon season. Spatial variability of GWS anomalies increases with the extent of measurements, following the power law relationship, i.e., log-(spatial variability) is linearly dependent on log-(spatial extent).In addition, the impact of well spacing on spatial variability and the power law relationship is investigated. We found that the mean GWS anomaly sampled at a 0.25 degree grid scale closes to unweighted average over all wells. The absolute error corresponding to each basin grows with increasing scale, i.e., from 0.25 degree to 1 degree. It was observed that small changes in extent could create very large changes in spatial variability at large grid scales. Spatial variability of GWS anomaly has been found to vary with climatic conditions. To our knowledge, this is the first study of the effects of well spacing on groundwater spatial variability. The results may be useful for interpreting large scale groundwater variations from unevenly spaced or sparse groundwater well observations or for siting and prioritizing wells in a network for groundwater management. The output of this study could be used to maintain a cost effective groundwater monitoring network in the study region and the approach can also be used in other parts of the globe.

Groundwater monitoring

Understanding the Impact of Unobservable Variables on the Performance of Predictive Models: The Need for Feature Space Partitioning and Fusion

When developing predictive models over a dataset, the model is globally optimized across the entire feature space to learn a decision boundary. However, when unobservable variables—which cannot be measured or estimated—interact with the observable variables, this can negatively impact the optimization applied to the decision boundary since the data samples introduced by unobservable variables may have little to no association with the applied global optimization. This, consequently, penalizes the entire decision boundary and model performance. This paper examines some of the detrimental effects of unobservable variables, particularly their role in creating new modes in the distribution of observable variables and reducing the separability of class distributions. Such challenges result in skewed or warped decision boundaries and decreased accuracy of model predictions, particularly for interpretable models like logistic regression and decision trees. Through two illustrative case examples, we highlight the need to address the challenges imposed by unobservable variables. We propose a strategy to mitigate these challenges by creating local regions within the feature space through partitioning. This enables the optimization of local models within the regions to overcome the impact of unobservability in different feature space localities. Research into a more sophisticated partitioning strategy and where the partition should be relative to the sample of interest is left as future work. Through the analysis of the impact of unobservability and the development of a partitioning method, we demonstrate the clear need for a partitioning strategy that integrates knowledge from multiple local models to estimate risk factors using information fusion. Thus, we establish the foundation and motivation for using partitioning and information fusion to overcome the effects of unobservability in predictive models. Formal fusion methods, such as Dempster-Shafer theory, can better leverage the information from local regions to improve the performance of interpretable predictive models in the presence of unobservable variables.

Time Series Data

X-ray spectra and time variability of active galactic nuclei

The X-ray spectra of broad line active galactic nuclei (AGN) of all types (Seyfert I's, NELG's, broadline radio galaxies) are well fit by a power law in the .5 to 100 keV band of man energy slope alpha = .68 + or - .15. There is, as yet, no strong evidence for time variability of this slope in a given object. The constraints that this places on simple models of the central energy source are discussed. BL Lac objects have quite different X-ray spectral properties and show pronounced X-ray spectral variability. On time scales longer than 12 hours most radio quiet AGN do not show strong, delta I/I .5, variability. The probability of variability of these AGN seems to be inversely related to their luminosity. However characteristics timescales for variability have not been measured for many objects. This general lack of variability may imply that most AGN are well below the Eddington limit. Radio bright AGN tend to be more variable than radio quiet AGN on long, tau approx 6 month, timescales.

Mushotzky, R. F.

Two Cepheid variables in the Fornax dwarf galaxy

Two fields surrounding globular clusters 2 and 3 in the Fornax dwarf spheroidal galaxy have been searched for short-period variable stars that are brighter than the horizontal branch. This survey confirmed as variable the two suspected suprahorizontal-branch variables discovered by Buonanno et al. (1985) in their photometry of the clusters. The observations show that the star in cluster 2 is a W Virginis variable of 14.4 day period. It is the first W Vir variable to be found in a dwarf spheroidal galaxy, and its proximity to the center of cluster 2 suggests that it is a cluster member. The other star appears to be an anomalous Cephpeid of 0.78 day period. It lies outside or very near the boundary of cluster 3, and is therefore probably a member of the field population of Fornax. Although no other suprahorizontal-branch variables were discovered in the survey, it did confirm as variable two of the RR Lyrae candidates of Buonanno et al., which appeared at the survey limit. The implications of these observations for the understanding of the stellar content at Fornax are discussed.

Light, R. M.

The GISS global climate-middle atmosphere model. II - Model variability due to interactions between planetary waves, the mean circulation and gravity wave drag

The variability which arises in the GISS Global Climate-Middle Atmosphere Model on two time scales is reviewed: interannual standard deviations, derived from the five-year control run, and intraseasonal variability as exemplified by statospheric warnings. The model's extratropical variability for both mean fields and eddy statistics appears reasonable when compared with observations, while the tropical wind variability near the stratopause may be excessive possibly, due to inertial oscillations. Both wave 1 and wave 2 warmings develop, with connections to tropospheric forcing. Variability on both time scales results from a complex set of interactions among planetary waves, the mean circulation, and gravity wave drag. Specific examples of these interactions are presented, which imply that variability in gravity wave forcing and drag may be an important component of the variability of the middle atmosphere.

Rind, D.

Distribution of Reynolds stress carried by mesoscale variability in the Antarctic Circumpolar Current

Satellite altimeter data collected by the Geosat Exact Repeat Mission were used to investigate turbulent stress resulting from the variability of surface geostrophic currents in the Antarctic Circumpolar Current. The altimeter measured sea level along the subsatellite track. The variability of the along-track slope of sea level is directly proportional to the variability of surface geostrophic currents in the cross-track direction. Because the grid of crossover points is dense at high latitudes, the satellite data could be used for mapping the temporal and spatial variability of the current. Two and a half years of data were used to compute the statistical structure of the variability. The statistics included the probability distribution functions for each component of the current, the time-lagged autocorrelation functions of the variability, and the Reynolds stress produced by the variability. The results demonstrate that stress is correlated with bathymetry. In some areas the distribution of negative stress indicate that eddies contribute to an acceleration of the mean flow, strengthening the hypothesis that baroclinic instability makes important contributions to strong oceanic currents.

Johnson, Thomas J.

Analysis and Design of Variable Stiffness Composite Cylinders

An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results lead to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that buckling behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response admirably. Thus, it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation.

Tatting, Brian F.

Predicting Ecologically Important Vegetation Variables from Remotely Sensed Optical/Radar Data Using Neural Networks

A number of satellite sensor systems will collect large data sets of the Earth's surface during NASA's Earth Observing System (EOS) era. Efforts are being made to develop efficient algorithms that can incorporate a wide variety of spectral data and ancillary data in order to extract vegetation variables required for global and regional studies of ecosystem processes, biosphere-atmosphere interactions, and carbon dynamics. These variables are, for the most part, continuous (e.g. biomass, leaf area index, fraction of vegetation cover, vegetation height, vegetation age, spectral albedo, absorbed photosynthetic active radiation, photosynthetic efficiency, etc.) and estimates may be made using remotely sensed data (e.g. nadir and directional optical wavelengths, multifrequency radar backscatter) and any other readily available ancillary data (e.g., topography, sun angle, ground data, etc.). Using these types of data, neural networks can: 1) provide accurate initial models for extracting vegetation variables when an adequate amount of data is available; 2) provide a performance standard for evaluating existing physically-based models; 3) invert multivariate, physically based models; 4) in a variable selection process, identify those independent variables which best infer the vegetation variable(s) of interest; and 5) incorporate new data sources that would be difficult or impossible to use with conventional techniques. In addition, neural networks employ a more powerful and adaptive nonlinear equation form as compared to traditional linear, index transformations, and simple nonlinear analyses. These neural networks attributes are discussed in the context of the authors' investigations of extracting vegetation variables of ecological interest.

Kimes, Daniel S.

Surface Salinity Variability in the North Atlantic During Recent Decades

The sea surface salinity (SSS) variability in the North Atlantic is investigated using numerical model simulations for the last 50 years based on atmospheric forcing variability from Comprehensive Atmosphere Ocean Data Set (COADS) and National Center for Environmental Prediction / National Center for Atmospheric Research (NCEP/NCAR) Reanalysis. The largest interannual and longer term variability occurs in two regions: the Labrador Sea and the North Equatorial Countercurrent (NECC) region. In both regions the seasonality of the surface salinity variability is prominent with the maximum standard deviation occurring in the summer/fall period. In the Labrador Sea the summer SSS anomalies far exceed those of wintertime in amplitude. The interannual SSS variability in the subpolar gyre can be attributed to two factors: excess ice melt and heat flux (i.e. deep mixing) variations. On the other hand, heat flux variability can also lead to meridional overturning changes on decadal time scales such that weak overturning is manifested in fresh surface conditions in the subpolar gyre. The overturning changes also influence the NECC region SSS variability. Moreover, the subpolar freshening events are expected to occur during the negative phase of North Atlantic Oscillation which is associated with a weak wintertime surface heat loss in the subpolar gyre. No excess sea ice melt or precipitation is necessary for the formation of the fresh anomalies, because with the lack of wide-spread deep mixing, the fresh water that would be expected based on climatology, would accumulate at the surface. Thus, the fresh water 'conveyor' in the Atlantic operates via the overturning circulation such that deep mixing inserts fresh water while removing heat from the water column.

Haekkinen, Sirpa

Interannual Variability, Global Teleconnection, and Potential Predictability Associated with the Asian Summer Monsoon

In this Chapter, aspects of global teleconnections associated with the interannual variability of the Asian summer monsoon (ASM) are discussed. The basic differences in the basic dynamics of the South Asian Monsoon and the East Asian monsoon, and their implications on global linkages are discussed. Two teleconnection modes linking ASM variability to summertime precipitation over the continental North America were identified. These modes link regional circulation and precipitation anomalies over East Asia and continental North America, via coupled atmosphere-ocean variations over the North Pacific. The first mode has a large zonally symmetrical component and appears to be associated with subtropical jetstream variability and the second mode with Rossby wave dispersion. Both modes possess strong sea surface temperature (SST) expressions in the North Pacific. Results show that the two teleconnection modes may have its origin in intrinsic modes of sea surface temperature variability in the extratropical oceans, which are forced in part by atmospheric variability and in part by air-sea interaction. The potential predictability of the ASM associated with SST variability in different ocean basins is explored using a new canonical ensemble correlation prediction scheme. It is found that SST anomalies in tropical Pacific, i.e., El Nino, is the most dominant forcing for the ASM, especially over the maritime continent and eastern Australia. SST anomalies in the India Ocean may trump the influence from El Nino in western Australia and western maritime continent. Both El Nino, and North Pacific SSTs contribute to monsoon precipitation anomalies over Japan, southern Korea, northern and central China. By optimizing SST variability signals from the world ocean basins using CEC, the overall predictability of ASM can be substantially improved.

Lau, K. M.

Structural Response of Compression-Loaded, Tow-Placed, Variable Stiffness Panels

Results of an analytical and experimental study to characterize the structural response of two compression-loaded variable stiffness composite panels are presented and discussed. These variable stiffness panels are advanced composite structures, in which tows are laid down along precise curvilinear paths within each ply and the fiber orientation angle varies continuously throughout each ply. The panels are manufactured from AS4/977-3 graphite-epoxy pre-preg material using an advanced tow placement system. Both variable stiffness panels have the same layup, but one panel has overlapping tow bands and the other panel has a constant-thickness laminate. A baseline cross-ply panel is also analyzed and tested for comparative purposes. Tests performed on the variable stiffness panels show a linear prebuckling load-deflection response, followed by a nonlinear response to failure at loads between 4 and 53 percent greater than the baseline panel failure load. The structural response of the variable stiffness panels is also evaluated using finite element analyses. Nonlinear analyses of the variable stiffness panels are performed which include mechanical and thermal prestresses. Results from analyses that include thermal prestress conditions correlate well with measured variable stiffness panel results. The predicted response of the baseline panel also correlates well with measured results.

Wu, K. Chauncey

Ionospheric Variability and Storms on Mars

The goal of this grant was to conduct the first-ever study of ionospheric variability on Mars. To do so, we used data from the Radio Science (RS) experiment onboard the Mars Global Surveyor (MGS) satellite. Dr. David Hinson of the RS team at Stanford University was a most helpful and valuable colleague throughout the studies we conducted. For the initial RS datasets available from the MGS mission, there were no severe storms caused by solar wind activity, so we concentrated on day-to-day effects. This turned out to be a wise approach since understanding "normal variability" had to be done before any claim could be made about "space weather" effects. Our approach was three-fold: (1) select a good dataset for characterization of ionosphere variability at Mars, one for which excellent terrestrial data were also available. This turned out to be the period 9-27 March 1999; (2) once the variability at Mars was described, develop and use a new photochemical model of the martian ionosphere to find the extent to which solar variability on those days caused or contributed to the observed patterns; (3) use the results from the above, together with additional datasets from the MGS/RS experiment, to describe some practical consequences that the martian ionosphere would have upon NASA s proposed navigation and communications systems for Mars. The results of these studies showed that: (a) solar variability is the dominant source of ionospheric variability at Mars (during periods of quiet solar wind), (b) that current models do a good job in portraying such effects at the height of the ionospheric peak electron density, and (c) that ionospheric structure on Mars can affect attempts at precise position-fixing at Mars should relatively high (GPS-like) frequencies not be used in a Mars communications and navigation system.

Mendillo, Michael

Conventional heart rate variability analysis of ambulatory electrocardiographic recordings fails to predict imminent ventricular fibrillation

OBJECTIVES. The purpose of this report was to study heart rate variability in Holter recordings of patients who experienced ventricular fibrillation during the recording. BACKGROUND. Decreased heart rate variability is recognized as a long-term predictor of overall and arrhythmic death after myocardial infarction. It was therefore postulated that heart rate variability would be lowest when measured immediately before ventricular fibrillation. METHODS. Conventional indexes of heart rate variability were calculated from Holter recordings of 24 patients with structural heart disease who had ventricular fibrillation during monitoring. The control group consisted of 19 patients with coronary artery disease, of comparable age and left ventricular ejection fraction, who had nonsustained ventricular tachycardia but no ventricular fibrillation. RESULTS. Heart rate variability did not differ between the two groups, and no consistent trends in heart rate variability were observed before ventricular fibrillation occurred. CONCLUSIONS. Although conventional heart rate variability is an independent long-term predictor of adverse outcome after myocardial infarction, its clinical utility as a short-term predictor of life-threatening arrhythmias remains to be elucidated.

Non-NASA Center

Mechanisms for Diurnal Variability of Global Tropical Rainfall Observed from TRMM

The behavior and various controls of diurnal variability in tropical-subtropical rainfall are investigated using Tropical Rainfall Measuring Mission (TRMM) precipitation measurements retrieved from the three level-2 TRMM standard profile algorithms for the 1998 annual cycle. Results show that diurnal variability characteristics of precipitation are consistent for all three algorithms, providing assurance that TRMM retrievals are producing consistent estimates of rainfall variability. As anticipated, most ocean areas exhibit more rainfall at night, while over most land areas, rainfall peaks during daytime; however, important exceptions are noted. The dominant feature of the oceanic diurnal cycle is a rainfall maximum in late-evening-early-morning (LE-EM) hours, while over land the dominant maximum occurs in the mid- to late afternoon (MLA). In conjunction with these maxima are pronounced seasonal variations of the diurnal amplitudes. Amplitude analysis shows that the diurnal pattern and its seasonal evolution are closely related to the rainfall accumulation pattern and its seasonal evolution. In addition, the horizontal distribution of diurnal variability indicates that for oceanic rainfall, there is a secondary MLA maximum coexisting with the LE-EM maximum at latitudes dominated by large-scale convergence and deep convection. Analogously, there is a preponderancy for an LE EM maximum over land coexisting with the stronger MLA maximum, although it is not evident that this secondary continental feature is closely associated with the large-scale circulation. Neither of the secondary maxima exhibit phase behavior that can be considered semidiurnal in nature. Diurnal rainfall variability over the ocean associated with large-scale convection is clearly an integral component of the general circulation. Phase analysis reveals differences in regional and seasonal features of the diurnal cycle, indicating that underlying forcing mechanisms differ from place to place. This is underscored by the appearance of secondary ocean maxima in the presence of large-scale convection, along with other important features. Among these, there are clear-cut differences between the diurnal variability of seasonal rainfall over the mid-Pacific and Indian Ocean Basins. The mid-Pacific exhibits double maxima in spring and winter but only LE-EM maxima in summer and autumn, while the Indian Ocean exhibits double maxima in spring and summer and only an LE-EM maximum in autumn and winter. There are also evident daytime maxima within the major large-scale marine stratocumulus regions off the west coasts of continents. The study concludes with a discussion concerning how the observational evidence either supports or repudiates possible forcing mechanisms that have been suggested to explain diurnal rainfall variability.

Yang, Song

Compact programmable photonic variable delay devices

Optical variable delay devices for providing variable true time delay to multiple optical beams simultaneously. A ladder-structured variable delay device comprises multiple basic building blocks stacked on top of each other resembling a ladder. Each basic building block has two polarization beamsplitters and a polarization rotator array arranged to form a trihedron; Controlling an array element of the polarization rotator array causes a beam passing through the array element either going up to a basic building block above it or reflect back towards a block below it. The beams going higher on the ladder experience longer optical path delay. An index-switched optical variable delay device comprises of many birefringent crystal segments connected with one another, with a polarization rotator array sandwiched between any two adjacent crystal segments. An array element in the polarization rotator array controls the polarization state of a beam passing through the element, causing the beam experience different refractive indices or path delays in the following crystal segment. By independently control each element in each polarization rotator array, variable optical path delays of each beam can be achieved. Finally, an index-switched variable delay device and a ladder-structured variable device are cascaded to form a new device which combines the advantages of the two individual devices. This programmable optic device has the properties of high packing density, low loss, easy fabrication, and virtually infinite bandwidth. The device is inherently two dimensional and has a packing density exceeding 25 lines/cm.sup.2. The delay resolution of the device is on the order of a femtosecond (one micron in space) and the total delay exceeds 10 nanosecond. In addition, the delay is reversible so that the same delay device can be used for both antenna transmitting and receiving.

Yao, X. Steve