Peculiarities of interaction of a quantum dot with non-classical light in the self-phase modulation regime

Influence of the self-phase modulation of quantum light on the induced resonant excitation of a semiconductor quantum dot is studied analytically in the case of the Kerr-nonlinearity of the medium. The phase nonlinearity is found to result actually in a resonance detuning specific for each field photon number state. This effect is shown to provide significant decrease of the excitation efficiency accompanied at the same time by more regular excitation dynamics obtained even for initial squeezed vacuum field state. The enhancement of entanglement between semiconductor and field subsystems with growing non-linearity is demonstrated. As a result, the formation of different types of non-Gaussian field states is found with features being analyzed in details.

A fast estimator for quantifying the shape dependence of the 3D bispectrum

The dependence of the bispectrum on the size and shape of the triangle contains a wealth of cosmological information. Here we consider a triangle parameterization which allows us to separate the size and shape dependence. We have implemented an FFT based fast estimator for the three dimensional (3D) bin averaged bispectrum, and we demonstrate that it allows us to study the variation of the bispectrum across triangles of all possible shapes (and also sizes). The computational requirement is shown to scale as ∼ N g 3 log N g 3 where N g is the number of grid points along each side of the volume. We have validated the estimator using a non-Gaussian field for which the bispectrum can be analytically calculated. The estimated bispectrum values are found to be in good agreement (< 10 % deviation) with the analytical predictions across much of the triangle-shape parameter space. We also introduce linear redshift space distortion, a situation where also the bispectrum can be analytically calculated. Here the estimated bispectrum is found to be in close agreement with the analytical prediction for the monopole of the redshift space bispectrum.

An Integrated Modeling Scheme For Characterizing 3D Hydrogeological Heterogeneity of The New Jersey Shelf

Continental shelves around the globe are hosts to vast reservoirs of offshore freshened groundwater. These systems show considerable complexity, often as a function of the geological heterogeneity. Data needed to characterise these systems are often sparse, and numerical models rely on generalized simplifications of the geological environment. In order to improve our understanding of these systems, it is necessary to implement modeling approaches that can produce large-scale geologically representative models using sparse data. We present an interdisciplinary stochastic modeling workflow incorporating borehole data, 2D depth-migrated seismic profiles, seismic attributes, and prior knowledge of the depositional setting. We generate a conditioned Gaussian field of porosity on the New Jersey shelf. We also perform a petrophysical conversion to a corresponding permeability distribution. The model dimensions are 134 km x 69 km x 1.7 km, with an adjustable resolution that can be adapted for process-based models of flow and solute transport. The integrated approach successfully translates small-scale porosity variations to a shelf-scale model that honors key characteristics of the New Jersey shelf wave-dominated depositional environment. The model was generated using open-source packages. All data and code to reproduce the complete workflow are provided along with this study so the model can be reproduced at any resolution for further studies of continental shelf processes offshore New Jersey.

Graph-based prior and forward models for inverse problems on manifolds with boundaries

This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matérn-type Gaussian field priors that enable flexible modeling near the boundaries, representing boundary values by superposition of harmonic functions with appropriate Dirichlet boundary conditions. We also investigate the graph-based approximation of forward models from PDE parameters to observed quantities. In the construction of graph-based prior and forward models, we leverage the ghost point diffusion map algorithm to approximate second-order elliptic operators with classical boundary conditions. Numerical results validate our graph-based approach and demonstrate the need to design prior covariance models that account for boundary conditions.

Effect of misalignment on coupling efficiency in laser diode to single-mode circular core graded-index fiber coupling via cylindrical microlens on the fiber tip

We report here the first theoretical prediction of coupling efficiency of the laser diode to single-mode graded-index fiber coupling via cylindrical microlens on the tip of the fiber in presence of possible transverse and angular mismatches. Moderately efficient cylindrical microlens on the fiber is easily fabricable and graded-index fiber has less sensitivity to macro as well as micro bending. Thus this coupling device emerges as a potential candidate in the field of coupling optics. The analysis takes into consideration the allowable aperture provided by cylindrical microlens. Further, we shall consider here the coupling in the vertical plane only since the coupling in the horizontal plane has poor performance. Using the relevant ABCD matrix of refraction for a cylindrical lens in the vertical plane, we prescribe analytical expressions of the coupling efficiencies in presence of said kinds of misalignments. In our analysis, we use Gaussian field distribution for both the laser and fiber fields. We carry on our investigation for two commonly used wavelengths namely 1.3 and 1.5 µm. As an example of graded-index fiber, we use some typical step, parabolic, and triangular index fibers in our study. The execution of the prescribed formulations involves little computation. Thus the evaluation of the concerned coupling efficiencies is very much user friendly. The present analysis surfaces the tolerance factors of the coupling devices. Accordingly, the results will prove beneficial to designers and packagers in respect of the design of such coupler involving cylindrical microlens in the field of optimum launch optics.

Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points $$\varvec{x}$$ x affects another set of points $$\varvec{y}$$ y but not vice versa. We use the model to investigate the effect of large trees on the locations of seedlings. In the model, every point in $$\varvec{x}$$ x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The parameters of the model are estimated in a Bayesian framework using Markov chain Monte Carlo where a Laplace approximation is used for the Gaussian field of the LGCP model. The proposed model is used to analyze the effect of large trees on the success of regeneration in uneven-aged forest stands in Finland.