Ultra-high speed reconfigurable microwave and radio frequency photonic intensity differentiators using Kerr frequency optical microcombs

We propose and experimentally demonstrate a microwave photonic intensity differentiator based on a Kerr optical comb generated by a compact integrated micro-ring resonator (MRR). The on-chip Kerr optical comb, containing a large number of comb lines, serves as a high-performance multi-wavelength source for the transversal filter, which will greatly reduce the cost, size, and complexity of the system. Moreover, owing to the compactness of the integrated MRR, up to 200-GHz frequency spacing of the Kerr optical comb can be achieved, enabling a potential operation bandwidth of over 100 GHz. By programming and shaping individual comb lines according to the calculated tap weights, a reconfigurable intensity differentiator with variable differentiation orders can be realized. The operation principle is theoretically analyzed, and experimental demonstrations of first-order, second-order, and third-order differentiation functions based on the principle are presented. The radio frequency (RF) amplitude and phase responses of multi-order intensity differentiations are characterized, and system demonstrations of real-time differentiations for Gaussian input signal are also performed. The experimental results show good agreement with theory, confirming the effectiveness of our approach.

On A Class of Time-Varying Gaussian ISI Channels

<p>This paper studies a class of stochastic and time-varying Gaussian intersymbol interference (ISI) channels. The $i^{th}$ channel tap during time slot $t$ is uniformly distributed over an interval of centre $c_i$ and radius $ r_{i}$. The array of channel taps is independent along both $t$ and $i$. The channel state information is unavailable at both the transmitter and the receiver. Lower and upper bounds are derived on the White-Gaussian-Input (WGI) capacity $C_{{WGI}$ for arbitrary values of the radii $ r_i$. It is shown that $C_{WGI}$ does not scale with the average input power. The proposed lower bound is achieved by a joint-typicality decoder that is tuned to a set of candidates for the channel matrix. This set forms a net that covers the range of the random channel matrix and its resolution is optimized in order to yield the largest achievable rate. Tools in matrix analysis such as Weyl's inequality on perturbation of eigenvalues of symmetric matrices are used in order to analyze the probability of error. </p>

On A Class of Time-Varying Gaussian ISI Channels

<p>This paper studies a class of stochastic and time-varying Gaussian intersymbol interference (ISI) channels. The $i^{th}$ channel tap during time slot $t$ is uniformly distributed over an interval of centre $c_i$ and radius $ r_{i}$. The array of channel taps is independent along both $t$ and $i$. The channel state information is unavailable at both the transmitter and the receiver. Lower and upper bounds are derived on the White-Gaussian-Input (WGI) capacity $C_{{WGI}$ for arbitrary values of the radii $ r_i$. It is shown that $C_{WGI}$ does not scale with the average input power. The proposed lower bound is achieved by a joint-typicality decoder that is tuned to a set of candidates for the channel matrix. This set forms a net that covers the range of the random channel matrix and its resolution is optimized in order to yield the largest achievable rate. Tools in matrix analysis such as Weyl's inequality on perturbation of eigenvalues of symmetric matrices are used in order to analyze the probability of error. </p>

Probability Forecast Combination via Entropy Regularized Wasserstein Distance

We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the assumption. More specifically, we show that the regularized Wasserstein barycenter between multivariate Gaussian input densities is multivariate Gaussian, and provide a simple way to compute mean and its variance–covariance matrix. Second, we show how this type of regularization can improve the predictive power of the resulting combined density. Third, we provide a method for choosing the tuning parameter that governs the strength of regularization. Lastly, we apply our proposed method to the U.S. inflation rate density forecasting, and illustrate how the entropy regularization can improve the quality of predictive density relative to its unregularized counterpart.

Bohmian-Based Approach to Gauss-Maxwell Beams

Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536–540) found a paraxial solution to Maxwell’s equation in vacuum, which includes polarization in a natural way, though still preserving the spatial Gaussianity of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams, are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics, a hydrodynamic-type extension of such a formulation is provided and discussed, complementing the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard, the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams.