Trapping polarization of light in nonlinear optical fibers: An ideal Raman polarizer

The main subject of this contribution is the all-optical control over the state of polarization (SOP) of light, understood as the control over the SOP of a signal beam by the SOP of a pump beam. We will show how the possibility of such control arises naturally from a vectorial study of pump-probe Raman interactions in optical fibers. Most studies on the Raman effect in optical fibers assume a scalar model, which is only valid for high-PMD fibers (here, PMD stands for the polarization-mode dispersion). Modern technology enables manufacturing of low-PMD fibers, the description of which requires a full vectorial model. Within this model we gain full control over the SOP of the signal beam. In particular we show how the signal SOP is pulled towards and trapped by the pump SOP. The isotropic symmetry of the fiber is broken by the presence of the polarized pump. This trapping effect is used in experiments for the design of new nonlinear optical devices named Raman polarizers. Along with the property of improved signal amplification, these devices transform an arbitrary input SOP of the signal beam into one and the same SOP towards the output end. This output SOP is fully controlled by the SOP of the pump beam. We overview the sate-of-the-art of the subject and introduce the notion of an "ideal Raman polarizer"

Time dependent intrinsic correlation analysis of temperature and dissolved oxygen time series using empirical mode decomposition

In the marine environment, many fields have fluctuations over a large range of different spatial and temporal scales. These quantities can be nonlinear \red{and} non-stationary, and often interact with each other. A good method to study the multiple scale dynamics of such time series, and their correlations, is needed. In this paper an application of an empirical mode decomposition based time dependent intrinsic correlation, \red{of} two coastal oceanic time series, temperature and dissolved oxygen (saturation percentage) is presented. The two time series are recorded every 20 minutes \red{for} 7 years, from 2004 to 2011. The application of the Empirical Mode Decomposition on such time series is illustrated, and the power spectra of the time series are estimated using the Hilbert transform (Hilbert spectral analysis). Power-law regimes are found with slopes of 1.33 for dissolved oxygen and 1.68 for temperature at high frequencies (between 1.2 and 12 hours) \red{with} both close to 1.9 for lower frequencies (time scales from 2 to 100 days). Moreover, the time evolution and scale dependence of cross correlations between both series are considered. The trends are perfectly anti-correlated. The modes of mean year 3 and 1 year have also negative correlation, whereas higher frequency modes have a much smaller correlation. The estimation of time-dependent intrinsic correlations helps to show patterns of correlations at different scales, for different modes.Comment: 35 pages with 22 figure

Modeling competition between two pharmaceutical drugs using innovation diffusion models

The study of competition among brands in a common category is an interesting strategic issue for involved firms. Sales monitoring and prediction of competitors' performance represent relevant tools for management. In the pharmaceutical market, the diffusion of product knowledge plays a special role, different from the role it plays in other competing fields. This latent feature naturally affects the evolution of drugs' performances in terms of the number of packages sold. In this paper, we propose an innovation diffusion model that takes the spread of knowledge into account. We are motivated by the need of modeling competition of two antidiabetic drugs in the Italian market.Comment: Published at http://dx.doi.org/10.1214/15-AOAS868 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cross-Correlation in the Auditory Coincidence Detectors of Owls

Interaural time difference (ITD) plays a central role in many auditory functions, most importantly in sound localization. The classic model for how ITD is computed was put forth by Jeffress (1948). One of the predictions of the Jeffress model is that the neurons that compute ITD should behave as cross-correlators. Whereas cross-correlation-like properties of the ITD-computing neurons have been reported, attempts to show that the shape of the ITD response function is determined by the spectral tuning of the neuron, a core prediction of cross-correlation, have been unsuccessful. Using reverse correlation analysis, we demonstrate in the barn owl that the relationship between the spectral tuning and the ITD response of the ITD-computing neurons is that predicted by cross-correlation. Moreover, we show that a model of coincidence detector responses derived from responses to binaurally uncorrelated noise is consistent with binaural interaction based on cross-correlation. These results are thus consistent with one of the key tenets of the Jeffress model. Our work sets forth both the methodology to answer whether cross-correlation describes coincidence detector responses and a demonstration that in the barn owl, the result is that expected by theory

The physics of extreme sensitivity in whispering gallery mode optical biosensors

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and nonspecific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, λ_R, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored