Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.

Period Continuous Tuning of an Efficient Mid-Infrared Optical Parametric Oscillator Based on a Fan-out Periodically Poled MgO-Doped Lithium Niobate

We report a period continuously tunable, efficient, mid-infrared optical parametric oscillator (OPO) based on a fan-out periodically poled MgO-doped congruent lithium niobate (PPMgLN). The OPO is pumped by a Nd:YAG laser and a maximum idler output average power of 1.65 W at 3.93 mu m is obtained with a pump average power of 10.5 W, corresponding to the conversion efficiency of about 16% from the pump to the idler. The output spectral properties of the OPO with the fan-out crystal are analyzed. The OPO is continuously tuned over 3.78-4.58 mu m (idler) when fan-out periods are changed from 27.0 to 29.4 mu m. Compared with temperature tuning, fan-out period continuous tuning has faster tuning rate and wider tuning range.