Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Continuous-wave watt-level Nd:YLF/KGW Raman laser operating at near-IR, yellow and lime-green wavelengths

A Nd:YLF/KGW Raman laser has been investigated in this work. We have demonstrated CW output powers at six different wavelengths, 1147 nm (0.70 W), 1163 nm (0.95 W), 549 nm (0.65 W), 552 nm (1.90 W), 573 nm (0.60 W) and 581 nm (1.10 W), with higher peak powers achieved under quasi-CW operation. Raman conversion of the 1053 nm fundamental emission is reported for the first time, enabling two new wavelengths in crystalline Raman lasers, 549 nm and 552 nm. The weak thermal lensing associated with Nd:YLF has enabled to achieve good beam quality, M-2 <= 2.0, and stable operation in relatively long cavities. (C) 2012 Optical Society of America