Strong law of large numbers for functionals of products of random matrices

For the sequence A₁, A₂, ..., A_n, ... of m×m independent random matrices such that for each k there exists a joint density function P_k(X) of the elements _ij ^k, we prove the following theorem: if and for some positive constants ₁ and ₂, then with probability 1,

Frequency tuning and doubling in Yb-doped fiber lasers

A compact Yb-doped fiber laser (YDFL) based on a tunable fiber Bragg grating (FBG) with ～6 W output power and ～45 nm tuning around 1080 nm has been developed. The laser output power and its spectral width (～0.15 nm) do not change significantly at the tuning, while the FBG reflection coefficient increases with an increase in FBG compression. It has been shown that this increase is due to stress-induced changes in the FBG’s refractive-index modulation amplitude. Intracavity frequency doubling in the YDFL has also been performed. About 0.4 W of green radiation with tuning in the range 540–548 nm has been achieved with a KTP nonlinear crystal.