Highly efficient hybrid fiber taper coupled microsphere laser

A novel hybrid fiber taper is proposed and demonstrated as the coupler in a microsphere laser system. The pump wave and the laser emission, respectively, are more efficiently coupled to and from the sphere modes with this taper structure. A 980-nm pumped erbium–ytterbium codoped phosphate microsphere laser is demonstrated in the 1550-nm band. As much as 112 µW of single-frequency laser output power was measured, with a differential quantum efficiency of 12%

Highly efficient optical power transfer to whispering-gallery modes by use of a symmetrical dual-coupling configuration

We report that greater than 99.8% optical power transfer to whispering-gallery modes was achieved in fused-silica microspheres by use of a dual-tapered-fiber coupling method. The intrinsic cavity loss and the taper-to-sphere coupling coefficient are inferred from the experimental data. It is shown that the low intrinsic cavity loss and the symmetrical dual-coupling structure are crucial for obtaining the high coupling efficiency

Discussion: "A significance test for the lasso"

Discussion of "A significance test for the lasso" by Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani, Robert Tibshirani [arXiv:1301.7161].Comment: Published in at http://dx.doi.org/10.1214/13-AOS1175B the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive covariance matrix estimation through block thresholding

Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. A fully data-driven block thresholding estimator is proposed. The estimator is constructed by carefully dividing the sample covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding. The estimator is shown to be optimally rate adaptive over a wide range of bandable covariance matrices. A simulation study is carried out and shows that the block thresholding estimator performs well numerically. Some of the technical tools developed in this paper can also be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/12-AOS999 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal estimation of the mean function based on discretely sampled functional data: Phase transition

The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs. Minimax rates of convergence are established and easily implementable rate-optimal estimators are introduced. The analysis reveals interesting and different phase transition phenomena in the two cases. Under the common design, the sampling frequency solely determines the optimal rate of convergence when it is relatively small and the sampling frequency has no effect on the optimal rate when it is large. On the other hand, under the independent design, the optimal rate of convergence is determined jointly by the sampling frequency and the number of curves when the sampling frequency is relatively small. When it is large, the sampling frequency has no effect on the optimal rate. Another interesting contrast between the two settings is that smoothing is necessary under the independent design, while, somewhat surprisingly, it is not essential under the common design.Comment: Published in at http://dx.doi.org/10.1214/11-AOS898 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cognitive Beamforming for Multiple Secondary Data Streams With Individual SNR Constraints

In this paper, we consider cognitive beamforming for multiple secondary data streams subject to individual signal-to-noise ratio (SNR) requirements for each secondary data stream. In such a cognitive radio system, the secondary user is permitted to use the spectrum allocated to the primary user as long as the caused interference at the primary receiver is tolerable. With both secondary SNR constraint and primary interference power constraint, we aim to minimize the secondary transmit power consumption. By exploiting the individual SNR requirements, we formulate this cognitive beamforming problem as an optimization problem on the Stiefel manifold. Both zero forcing beamforming (ZFB) and nonzero forcing beamforming (NFB) are considered. For the ZFB case, we derive a closed form beamforming solution. For the NFB case, we prove that the strong duality holds for the nonconvex primal problem and thus the optimal solution can be easily obtained by solving the dual problem. Finally, numerical results are presented to illustrate the performance of the proposed cognitive beamforming solutions.Comment: This is the longer version of a paper to appear in the IEEE Transactions on Signal Processin