Nonlinear propagation of an optical speckle field

We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010) ].. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates. © 2012 American Physical Society.

High resolution optical time-domain reflectometry based on correlation utilizing an all-fiber chaotic source

We propose a high-resolution optical time domain reflectometry (OTDR) based on an all-fiber supercontinuum source. The source simply consists of a laser with moderate power and a section of fiber which has a zero dispersion wavelength near the laser's central wavelength. Spectrum and time domain properties of the source are investigated, showing that the source has great capability in nonlinear optics, such as correlation OTDR. We analyze one of the key factors limiting the operational range of such an OTDR, i.e., sampling time. Finally, we experimentally demonstrate a correlation OTDR with 25km sensing range and 5.3cm spatial resolution, as a verification of theoretical analysis.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Long-range and high-precision correlation optical time-domain reflectometry utilizing an all-fiber chaotic source

We propose a long range, high precision optical time domain reflectometry (OTDR) based on an all-fiber supercontinuum source. The source simply consists of a CW pump laser with moderate power and a section of fiber, which has a zero dispersion wavelength near the laser's central wavelength. Spectrum and time domain properties of the source are investigated, showing that the source has great capability in nonlinear optics, such as correlation OTDR due to its ultra-wide-band chaotic behavior, and mm-scale spatial resolution is demonstrated. Then we analyze the key factors limiting the operational range of such an OTDR, e. g., integral Rayleigh backscattering and the fiber loss, which degrades the optical signal to noise ratio at the receiver side, and then the guideline for counter-act such signal fading is discussed. Finally, we experimentally demonstrate a correlation OTDR with 100km sensing range and 8.2cm spatial resolution (1.2 million resolved points), as a verification of theoretical analysis.

Seizure detection in subdural recordings using nonlinear decision functions

This dissertation proposed a new approach to seizure detection in intracranial EEG recordings using nonlinear decision functions. It implemented well-established features that were designed to deal with complex signals such as brain recordings, and proposed a 2-D domain of analysis. Since the features considered assume both the time and frequency domains, the analysis was carried out both temporally and as a function of different frequency ranges in order to ascertain those measures that were most suitable for seizure detection. In retrospect, this study established a generalized approach to seizure detection that works across several features and across patients. ^ Clinical experiments involved 8 patients with intractable seizures that were evaluated for potential surgical interventions. A total of 35 iEEG data files collected were used in a training phase to ascertain the reliability of the formulated features. The remaining 69 iEEG data files were then used in the testing phase. ^ The testing phase revealed that the correlation sum is the feature that performed best across all patients with a sensitivity of 92% and an accuracy of 99%. The second best feature was the gamma power with a sensitivity of 92% and an accuracy of 96%. In the frequency domain, all of the 5 other spectral bands considered, revealed mixed results in terms of low sensitivity in some frequency bands and low accuracy in other frequency bands, which is expected given that the dominant frequencies in iEEG are those of the gamma band. In the time domain, other features which included mobility, complexity, and activity, all performed very well with an average a sensitivity of 80.3% and an accuracy of 95%. ^ The computational requirement needed for these nonlinear decision functions to be generated in the training phase was extremely long. It was determined that when the duration dimension was rescaled, the results improved and the convergence rates of the nonlinear decision functions were reduced dramatically by more than a 100 fold. Through this rescaling, the sensitivity of the correlation sum improved to 100% and the sensitivity of the gamma power to 97%, which meant that there were even less false negatives and false positives detected. ^

Dynamical Heterogeneity and Nonlinear Susceptibility in Short-Ranged Attractive Supercooled Liquids

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here, we study in detail the behavior of non-linear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard non-linear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids.

Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.

Variation, correlation and heritability of interest characters for selection of African eggplant

The eggplant ( Solanum aethiopicum ) is the species of the Solanum genus, whose geographical distribution is broadest. It is grown throughout tropical Africa, and includes three groups of cultivars commonly called African or indigenous eggplant. Kumba group or “bitter eggplant” is an important Solanaceous vegetable crop in Burkina Faso. The objective of this study was to determine genetic variability, strength of association and level of heritability among agronomic interest traits. Phenotypic and genotypic variations and heritability of 14 traits were estimated in 61 accessions at Institut de Développement Rural (IDR), Gampela in Burkina Faso. High phenotypic and genotypic coefficients of variation were observed for fruit diameter, number of seeds per fruit, fruit weight, leaf blade length and width, and height at flowering. In addition, genetic and phenotypic variances were high for the number of seed, fruit weight, plant height at flowering and days to 50% flowering. High heritability estimates were recorded for all traits. Fruit weight showed a positive association with fruit diameter and thickness. The fifty percent flowering cycle registered positive correlations with plant height and fruit diameter. Fruit number showed a negative association with fruit weight and diameter, and 50% flowering cyle.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

High Diagnostic Accuracy And Reproducibility Of Fine-needle Aspiration Cytology For Diagnosing Salivary Gland Tumors: Cytohistologic Correlation In 182 Cases.

The purpose of this study was to assess the efficacy and reproducibility of the cytologic diagnosis of salivary gland tumors (SGTs) using fine-needle aspiration cytology (FNAC). The study aimed to determine diagnostic accuracy, sensitivity, and specificity and to evaluate the extent of interobserver agreement. We retrospectively evaluated SGTs from the files of the Division of Pathology at the Clinics Hospital of São Paulo and Piracicaba Dental School between 2000 and 2006. We performed cytohistologic correlation in 182 SGTs. The sensitivity, specificity, positive predictive value, negative predictive value, and diagnostic accuracy were 94%, 100%, 100%, 100%, and 99%, respectively. The interobserver cytologic reproducibility showed significant statistical concordance (P < .0001). FNAC is an effective tool for performing a reliable preoperative diagnosis in SGTs and shows high diagnostic accuracy and consistent interobserver reproducibility. Further FNAC studies analyzing large samples of malignant SGTs and reactive salivary lesions are needed to confirm their accuracy.

Core-valence Correlation Effects On Ir Calculations: The Bf3 And Bcl3 Cases.

The first theoretical results of core-valence correlation effects are presented for the infrared wavenumbers and intensities of the BF3 and BCl3 molecules, using (double- and triple-zeta) Dunning core-valence basis sets at the CCSD(T) level. The results are compared with those calculated in the frozen core approximation with standard Dunning basis sets at the same correlation level and with the experimental values. The general conclusion is that the effect of core-valence correlation is, for infrared wavenumbers and intensities, smaller than the effect of adding augmented diffuse functions to the basis set, e.g., cc-pVTZ to aug-cc-pVTZ. Moreover, the trends observed in the data are mainly related to the augmented functions rather than the core-valence functions added to the basis set. The results obtained here confirm previous studies pointing out the large descrepancy between the theoretical and experimental intensities of the stretching mode for BCl3.

Measuring The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy.

Fluorescence Correlation Spectroscopy (FCS) is an optical technique that allows the measurement of the diffusion coefficient of molecules in a diluted sample. From the diffusion coefficient it is possible to calculate the hydrodynamic radius of the molecules. For colloidal quantum dots (QDs) the hydrodynamic radius is valuable information to study interactions with other molecules or other QDs. In this chapter we describe the main aspects of the technique and how to use it to calculate the hydrodynamic radius of quantum dots (QDs).

Correlation Between Cephalometric Data And Severity Of Sleep Apnea.

Obstructive sleep apnea syndrome has a high prevalence among adults. Cephalometric variables can be a valuable method for evaluating patients with this syndrome. To correlate cephalometric data with the apnea-hypopnea sleep index. We performed a retrospective and cross-sectional study that analyzed the cephalometric data of patients followed in the Sleep Disorders Outpatient Clinic of the Discipline of Otorhinolaryngology of a university hospital, from June 2007 to May 2012. Ninety-six patients were included, 45 men, and 51 women, with a mean age of 50.3 years. A total of 11 patients had snoring, 20 had mild apnea, 26 had moderate apnea, and 39 had severe apnea. The distance from the hyoid bone to the mandibular plane was the only variable that showed a statistically significant correlation with the apnea-hypopnea index. Cephalometric variables are useful tools for the understanding of obstructive sleep apnea syndrome. The distance from the hyoid bone to the mandibular plane showed a statistically significant correlation with the apnea-hypopnea index.